Passive components in indium phosphide generic integration

Passive components in indium phosphide genericintegration technologiesKleijn, E.

DOI:10.6100/IR775372

Published: 01/01/2014

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Passive components in indium phosphidegeneric integration technologies

Passive components in indium phosphidegeneric integration technologies

PROEFSCHRIFT

ter verkrijging van de graad van doctor aan de Technische UniversiteitEindhoven, op gezag van de rector magnificus prof.dr.ir. C.J. van Duijn,voor een commissie aangewezen door het College voor Promoties, in hetopenbaar te verdedigen op donderdag 11 september 2014 om 16:00 uur

door

Emil Kleijn

geboren te Nieuwegein

Dit proefschrift is goedgekeurd door de promotoren en de samenstelling van depromotiecommissie is als volgt:

voorzitter: prof.dr.ir A.H.M. van Roermundpromotor: prof.dr.ir. M.K. Smitcopromotor: dr. X.J.M. Leijtensleden: prof.dr.ir. W. Bogaerts (Ghent University - IMEC)

prof.dr. K.A. Williamsprof.dr. M.J. Waledr. A. Melloni (Politecnico di Milano)dr.ir. R. Stoffer (Phoenix B.V.)

This research was supported by the European Community’s Seventh FrameworkProgram FP7/2007-2013 under Grant ICT 257210 PARADIGM, and carried outin the Photonic Integration Group, at the Department of Electrical Engineering ofTU/e, the Netherlands.

Passive components in indium phosphide generic integration technologies, byEmil Kleijn

A catalogue record is available from the Eindhoven University of Technology(TU/e) Library.ISBN: 978-90-386-3654-2

Copyright © 2014 Emil Kleijn

Typeset using LATEX.Printed in the Netherlands.

aan mijn ouders

Contents

List of acronyms xi

1 Introduction 11.1 A vertically integrated industry . . . . . . . . . . . . . . . . . . . 11.2 Application opportunities . . . . . . . . . . . . . . . . . . . . . . 2

1.2.1 Structural health monitoring . . . . . . . . . . . . . . . . 21.2.2 Optical Coherence Tomography . . . . . . . . . . . . . . 31.2.3 Pulse shaping . . . . . . . . . . . . . . . . . . . . . . . . 31.2.4 Microwave photonics . . . . . . . . . . . . . . . . . . . . 41.2.5 Fiber-to-the-home . . . . . . . . . . . . . . . . . . . . . 4

1.3 Generic integration technology . . . . . . . . . . . . . . . . . . . 51.4 Component libraries . . . . . . . . . . . . . . . . . . . . . . . . . 61.5 Thesis outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Layer stack modeling 112.1 COBRA waveguide fabrication . . . . . . . . . . . . . . . . . . . 112.2 Propagation constant . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.1 Straight waveguide . . . . . . . . . . . . . . . . . . . . . 132.2.2 Curved waveguide . . . . . . . . . . . . . . . . . . . . . 172.2.3 Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3 Field profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.3.1 Straight waveguide . . . . . . . . . . . . . . . . . . . . . 202.3.2 Curved waveguide . . . . . . . . . . . . . . . . . . . . . 22

2.4 Overlap integrals . . . . . . . . . . . . . . . . . . . . . . . . . . 232.4.1 Straight waveguide . . . . . . . . . . . . . . . . . . . . . 232.4.2 Curved waveguide . . . . . . . . . . . . . . . . . . . . . 25

2.5 Offsets between straight and curved waveguides . . . . . . . . . . 252.5.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3 Multi-mode interference couplers 293.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

vii

Contents

3.2.1 Multimode section . . . . . . . . . . . . . . . . . . . . . 313.2.2 Junction . . . . . . . . . . . . . . . . . . . . . . . . . . . 323.2.3 S-matrix concatenation . . . . . . . . . . . . . . . . . . . 353.2.4 Verification . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Multimode interference couplers with reduced parasitic backscat-tering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 393.3.2 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.3.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 403.3.4 Measurement . . . . . . . . . . . . . . . . . . . . . . . . 423.3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.4 MMI based 90◦ optical hybrid . . . . . . . . . . . . . . . . . . . 443.4.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.4.2 Test structure . . . . . . . . . . . . . . . . . . . . . . . . 473.4.3 Fit method . . . . . . . . . . . . . . . . . . . . . . . . . 483.4.4 Measurements . . . . . . . . . . . . . . . . . . . . . . . 513.4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 52

4 Multi-mode interference reflectors 554.1 Multimode interference reflectors: a new class of components for

photonic integrated circuits . . . . . . . . . . . . . . . . . . . . . 554.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 554.1.2 Basic operation principle . . . . . . . . . . . . . . . . . . 574.1.3 Central image . . . . . . . . . . . . . . . . . . . . . . . . 584.1.4 Mirror losses . . . . . . . . . . . . . . . . . . . . . . . . 604.1.5 Practical MIR examples . . . . . . . . . . . . . . . . . . 614.1.6 Simulation methods . . . . . . . . . . . . . . . . . . . . 634.1.7 Measurements . . . . . . . . . . . . . . . . . . . . . . . 664.1.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 714.1.9 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5 Arrayed waveguide gratings 755.1 Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755.2 Layout specifics . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

5.2.1 Layout procedure . . . . . . . . . . . . . . . . . . . . . . 795.2.2 Suppressing reflections . . . . . . . . . . . . . . . . . . . 81

5.3 New analytical arrayed waveguide grating model . . . . . . . . . 815.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 825.3.2 Theoretical model . . . . . . . . . . . . . . . . . . . . . 835.3.3 Solving the diffraction integral . . . . . . . . . . . . . . . 875.3.4 Coupling to the array waveguides . . . . . . . . . . . . . 88

viii

Contents

5.3.5 Full AWG model . . . . . . . . . . . . . . . . . . . . . . 915.3.6 Comparison to existing models . . . . . . . . . . . . . . . 915.3.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 945.3.8 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . 95

5.4 Sidelobes in the response of arrayed waveguide gratings causedby polarization rotation . . . . . . . . . . . . . . . . . . . . . . . 965.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 965.4.2 Device design . . . . . . . . . . . . . . . . . . . . . . . . 975.4.3 Measurements . . . . . . . . . . . . . . . . . . . . . . . 975.4.4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 995.4.5 Eliminating the sidelobe . . . . . . . . . . . . . . . . . . 1025.4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 105

6 Component Libraries for MPW runs 1076.1 What is a library? . . . . . . . . . . . . . . . . . . . . . . . . . . 1076.2 Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

6.2.1 Layout view . . . . . . . . . . . . . . . . . . . . . . . . 1096.2.2 Symbol view . . . . . . . . . . . . . . . . . . . . . . . . 1106.2.3 S-matrix view . . . . . . . . . . . . . . . . . . . . . . . . 1106.2.4 Time domain view . . . . . . . . . . . . . . . . . . . . . 1126.2.5 PDAFlow . . . . . . . . . . . . . . . . . . . . . . . . . . 114

6.3 Design Rule Checking . . . . . . . . . . . . . . . . . . . . . . . 1146.4 Multi Project Wafer runs . . . . . . . . . . . . . . . . . . . . . . 117

6.4.1 Mask assembly . . . . . . . . . . . . . . . . . . . . . . . 1186.4.2 COBRA MPW library . . . . . . . . . . . . . . . . . . . 119

7 Conclusions and outlook 1237.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1237.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1247.3 Commercial MPW . . . . . . . . . . . . . . . . . . . . . . . . . 126

A PDAFlow 127A.1 Connecting to the PDAFlow . . . . . . . . . . . . . . . . . . . . 127A.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

B Effective Index Method validity 133B.1 Indium phosphide . . . . . . . . . . . . . . . . . . . . . . . . . . 133B.2 Silicon on insulator . . . . . . . . . . . . . . . . . . . . . . . . . 134

Bibliography 137

Summary 149

ix

Contents

Acknowledgments 151

Curriculum vitae 153

List of publications 155Journal publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155International conference publications . . . . . . . . . . . . . . . . . . . 156Local conference publications . . . . . . . . . . . . . . . . . . . . . . 157

x

List of acronyms

API Application Programming Interface

ASE Amplified Stimulated Emission

AWG Arrayed Waveguide Grating

BB Building Block

BEP Bidirectional Eigenmode Propagation

BPM Beam Propagation Method

CMOS Complementary Metal Oxide Semiconductor

CMRR Common Mode Rejection Ratio

COBRA COmmunication technologies Basic Research and Application

DBR Distributed Bragg Reflector

DUT Device Under Test

EDFA Erbium Doped Fiber Amplifier

EIM Effective Index Method

EM Electro Magnetic

EME Eigen Mode Expansion

EOPM Electro-Optic Phase Modulator

FBG Fiber Bragg Grating

FDTD Finite Difference Time Domain

FMM Film Mode Matching

FPR Free Propagation Region

xi

List of acronyms

FttH Fiber-to-the-Home

GDSII Graphic Database System version 2

HWP Half Wave Plate

I/O Input/Output

ICP Inductively Coupled Plasma

InGaAsP Indium Gallium Arsenide Phosphide

InGaAs Indium Gallium Arsenide

InP Indium Phosphide

IP Intellectual Property

LF Lensed Fiber

LO Local Oscillator

MIR Multimode Interference Reflector

MMI Multimode Interference coupler

MO Microscope Objective

MOSIS Metal Oxide Semiconductor Implementation Service

MPA Modal Propagation Analysis

MPW Multi-Project Wafer

MQW Multiple Quantum Well

MZI Mach-Zehnder Interferometer

OCT Optical Coherence Tomography

OLT Optical Line Terminal

ONU Optical Network Unit

OSA Optical Spectrum Analyzer

PBS Polarizing Beam Splitter

PC Polarization Controller / Personal Computer

xii

PDAFlow Photonic Design Automation Flow

PECVD Plasma Enhanced Chemical Vapor Deposition

PI Polyimide

PIC Photonic Integrated Circuit

PIN P-doped, Intrinsic, N-doped

PM Power Meter

PMF Polarization Maintaining Fiber

PR Polarization Rotation

RF Radio Frequency

RIE Reactive Ion Etching

RISC Reduced Instruction Set Computer

RMS Root Mean Square

S-matrix Scattering matrix

SMF Single Mode Fiber

SOA Semiconductor Optical Amplifier

S-parameters Scattering parameters

TDTW Time Domain Traveling Wave

TE Transverse Electric

TLS Tunable Laser Source

TM Transverse Magnetic

xiii

1Introduction

A paper by Miller in 1969 [1] describes what was then called ‘a miniature formof laser beam circuitry’. It describes an idea to combine lasers with modulatorsand dielectric waveguides to route light on a small chip. What we now call Pho-tonic Integrated Circuits (PICs) would be less sensitive to temperature gradientsdue to their small size. When using photolithographic techniques, PICs can alsobe produced at very low cost. Further more, power dissipation can be decreasedby turning to smaller components. During the past 40 years a lot of researcheffort has gone into realizing this. Indeed, using an indium phosphide based plat-form, tunable lasers integrated with modulators are now commercially available.These kind of circuits still have a relatively low component count of just a fewcomponents. Large scale integration of dozens of components onto a single chiphas been demonstrated repeatedly in research labs [2, 3]. These large scale PICshave only had very limited commercial success, despite investments in the orderof several billion dollars in integration technology [4]. The first real commerciallarge-scale photonic integrated circuit was marketed by Infinera in 2004 [5]. Oneof the reasons for the lack of commercial success is that the developed chips arenot cost effective when compared to alternative solutions.

A large part of the cost of a PIC consists of technology development costs.So far, project funding has been tied to a specific, challenging application [6].To meet the specifications the technology has to be fully optimized. By doingthis the developed technology is often application specific. As a result there ex-ist nowadays almost as many technologies as applications. The market size foreach application is usually not big enough to warrant further development of thetechnology to make it suitable for high volume manufacturing [7].

1.1 A vertically integrated industry

The photonics industry today is largely organized in a similar way as the elec-tronics industry was in the 1970s. The industry is dominated by a small numberof large players that employ a vertically integrated business model. In this busi-ness model a company controls the entire manufacturing chain from research andchip design down to fabrication and marketing. They have extensive and high

1

Chapter 1. Introduction

tech manufacturing capabilities using a well developed technology. This businessmodel requires immense investments to implement. A fabrication facility is anenormous drain on resources for a company. It therefore needs to be run at veryhigh utilization levels to be profitable. This business model is therefore unsuitablefor a start-up company with a single product targeting a small market. Tradi-tionally, only telecom applications warranted huge investments due to the largeamount of money available in that market. Light is very versatile and it would bea shame if its application in PICs would be limited to just that application area.Interesting other applications are in sensing, radar beam forming, and health care.In all these areas, photonic integration is seen as a major opportunity for cost andsize reduction, and performance improvement. Unfortunately, each market is ei-ther too small or it is too risky to warrant developing and optimizing a technologyplatform. A lot of markets thus remain difficult to access for photonic integrationtechnology.

1.2 Application opportunities

Photonic integration is a typical enabling technology [8, 9]. The ability to gener-ate, manipulate, and detect light on a single chip enables many applications. Herewe will present a brief overview of a number of fields where PICs could play amajor role. Even though the applications themselves are very different, the toolsneeded to create chips for those applications can be the same.

1.2.1 Structural health monitoring

Monitoring the structural integrity of large civil engineering structures such asbridges can offer early warnings on damage and can help guarantee safety [10].These objects are normally monitored by measuring displacements or strains dueto loads on the structure at a number of discrete points [11]. Traditionally this wasdone with electrical strain gauges, but the last decade saw a strong trend of movingto fiber optic based sensors [12]. These optical sensors have a number of advan-tages over electrical sensors. They are immune to electromagnetic interference,which enables monitoring of metallic structures [12]. High sensitivity, accuracyand resolution has also been reported [13]. When using a Brillouin scatteringbased measurement technique, a distributed strain and temperature measurementcan be performed with resolutions down to 20 cm [14]. In this measurementmethod, an optical pulse scatters inelastically off phonons. This effect shifts thefrequency of the back scattered photons by an amount that depends on the phononenergy. As the phonon energy is determined by the local strain and temperaturegradient, measuring the frequency of the back scattered light allows for measur-ing these quantities. Another common technique measures the peak reflection

2

Application opportunities

wavelength (Bragg wavelength) of Fiber Bragg Gratings (FBG), which dependson the temperature and strain in the grating [13]. This latter method provides datafrom discrete points along the fiber, where a grating has been written. Unfortu-nately the read-out equipment for these sensors is usually quite heavy, bulky, andcostly [15]. Photonic integration could enable a small, power efficient system thatcan be produced at low cost in large quantities [15, 16].

1.2.2 Optical Coherence Tomography

Optical Coherence Tomography (OCT) can generate cross-sectional images of bi-ological tissue with a resolution of a few micrometers up to a few mm in depth[17]. OCT is very suitable for analyzing skin and retina tissue for medical diag-nostics. In one variant of this technique, so called Spectral Domain OCT, lightfrom a broadband source is projected onto the tissue and the spectrum of thebackscattered light is analyzed. A Fourier transform reveals the intensity of scat-tering points along the longitudinal axis. Every measurement provides a depthprofile of the tissue. By repeatedly measuring different points on a surface, a full3D image of the tissue can be obtained. An optical spectrum analyzer is requiredfor recording the spectrum of the backscattered light. This is usually a bulky, ex-pensive bench-top instrument. In [18] an integrated spectrum analyzer for OCTis presented and used to create a cross-sectional image of a test sample. Such anintegrated approach can offer significant cost and size reduction in OCT systems.Another way of performing a similar measurement is by sweeping a laser sourceand recording the backscattered power, which is done in Swept-Source OCT. Thisoffers even more opportunities for photonic integration, as the tunable laser sourceand photo-detector could be integrated on the same chip. However, with currenttechnologies this is still challenging because long wavelengths around 1.7 µm arepreferred for OCT for skin imaging [19, 20].

1.2.3 Pulse shaping

Optics can be used to generate trains of ultrafast pulses with lengths in the or-der of femto- and picoseconds [21]. A way to generate these pulses is by usingsemiconductor mode-locked lasers. These lasers are subject to a large amount offrequency chirp [22]. This distorts the shape of the generated pulses. A pulseshaper can manipulate the pulse train so that the individual pulses have the de-sired shape. The spectrum of a pulse train consists of discrete lines. The relativephase and amplitude of these lines determine the shape of the pulse. Therefore,by manipulating the phase and amplitude of each spectral line, the shape of thepulse can be configured. Compression of the pulses is a typical application ofpulse shaping.

3


A straight forward way of making an optical pulse shaper is by first split-ting the input spectrum into individual lines by using a dispersive element. Eachindividual spectral line can then be worked on separately. The lines are then com-bined again to obtain the output signal. In integrated optics the dispersive elementis usually an Arrayed Waveguide Grating (AWG). Amplitude can be controlledby a Semiconductor Optical Amplifier (SOA), while the phase can be set usingan Electro-Optic Phase Modulator (EOPM) [23]. Arbitrary pulse shaping is onlypossible when each passband of the AWG contains a single spectral line. Thisis challenging as both the channel spacing and passband position of the AWGhas to match that of the pulse source and normally requires a tunable AWG [24].However, functioning integrated optical pulse shaping devices have already beenpresented [23–26].

1.2.4 Microwave photonics

Electromagnetic waves in the frequency range 30 GHz to 300 GHz are interestingfor many applications from telecommunication to inspection of structures [27,28]. Direct electrical generation of these signals has proved challenging [29].Such signals can also be generated optically, by beating two laser signals witha wavelength spacing equal to the desired radio frequency (RF). Coupling thetwo optical signals to a photodetector of sufficient bandwidth will generate theRF signal [30]. Optical integration allows for combining the two lasers onto thesame chip, and even the photodetector could be monolithically integrated withthem. Because the two lasers are on the same chip, any variation in wavelengthof a single laser due to temperature or other effects is likely to affect the secondlaser in a similar way. In this way, the generated RF signal is robust againstnoise shared between the lasers, because correlated phase noise is removed whilebeating the lasers. If the lasers are not only on the same chip, but also share thesame gain medium, even more phase noise sources will be correlated and theirnegative effects diminished [31].

1.2.5 Fiber-to-the-home

A typical fiber-to-the-home (FTTH) transceiver at the subscriber side consists of ameans for detecting data sent from the central office (down-link), and of a meansfor sending information back (up-link). Typically a single fiber is employed andcoarse wavelength division multiplexing is used to separate the up- and down-links [32]. A single Optical Line Terminal (OLT) serves N subscribers, who eachhave an Optical Network Unit (ONU).

Though fiber-to-the-home is a telecom application, the requirements are verydifferent from the regular long-haul telecommunication applications of integrated

4

Generic integration technology

optics. For the ONUs there is a strong drive to keep costs to a minimum, as theyrepresent about 85% of the total system cost [32]. The performance specifica-tions are usually much more relaxed when compared to long-haul communica-tions. There is also a strong need for solutions to be easy to produce in hugenumbers [33]. This provides an excellent opportunity for PICs. By combininggeneration, detection and modulation of light in a single chip, a large reduction inpackaging cost can be achieved. Integration can also improve reliability as opticalcomponents no longer can become misaligned over time [32].

1.3 Generic integration technology

As described above, many interesting application areas exist that could benefitfrom photonic integration, but are by itself too small to warrant large scale invest-ments in infrastructure necessary to produce photonic integrated chips. A similarproblem was faced by the electronics industry in the past. In the 70s the elec-tronics industry was organized much like todays integrated photonics industry. Acompany would both design and produce semiconductor devices. As manufactur-ing processes improved it became possible to develop standardized technologies.This allowed for the separation of manufacturing and design. As a result, the firstmerchant foundries emerged in the 1980s as an effort of fab owning companiesto utilize the overcapacity of their fab by also producing for others. The foundrymodel was born. The Metal Oxide Semiconductor Implementation Service (MO-SIS) run by the University of Southern California [34] served as a broker betweendesigners and manufacturers. This service was, and still is, aimed at small busi-nesses, government agencies and universities. It provides low cost access to smallvolume production of electronic integrated circuits. It does this by merging manyprojects onto a Multi-Project Wafer run (MPW run). In this way overhead costscan be shared between users, which in turn enables cheap prototyping capabili-ties [35]. MOSIS does not only allow access to fabrication facilities, but also tostandard components contained in Design Kits. These standardized componentsenable designers to make advanced circuits without needing detailed knowledgeon device physics. This is only possible if the underlying technology is standard-ized and can provide a large variety of functionality and reproducibility. This isthe case in a so called Generic Integration Technology. A Generic IntegrationTechnology is not optimized for a single application, but instead functions as aplatform that can be used for many different applications [4]. Many technolo-gies that are widely used nowadays were first run through MOSIS, such as theReduced Instruction Set Computer (RISC) [36]. RISC based processors form thecomputational heart of most of todays portable devices [37]. MOSIS also enabledinnovative chips that initially received only skepticism from the scientific com-

5


munity, such as asynchronous microprocessors [38]. Another indication of thesuccess of the MOSIS approach is that the service still exists today.

Looking at the history of the electronics industry, the way to access smallmarkets with photonic integration technology therefore is to introduce genericintegration technologies that can serve a wide variety of applications [4, 7, 39].Generic integration technologies revolve around the idea that a broad range offunctionalities can be realized from a rather small set of basic building blocks.If a technology supports these basic building blocks it automatically supports allfunctionality that can be created by combining these blocks in clever ways. Inelectronics these are the familiar transistor, capacitor, resistor, etc. In photonics,similar building blocks exist. A wide range of photonic circuits can be decom-posed into lasers, optical amplifiers, modulators, detectors and passive compo-nents such as couplers, filters and (de)multiplexers [40]. By optimizing these ba-sic building blocks for high performance, competitive circuits can be developed.Generic integration technologies justify investments in developing the technol-ogy for high performance on the building block level because they can serve alarge market [4]. By keeping the number of basic building blocks low, progressin process technology can be quickly propagated to achieve better circuit levelperformance.

There will not be a single generic integration technology suitable for all appli-cations. Just like in CMOS there is room for a few technologies targeting differentbroad application areas, like high-power, low-power, high-speed etc. In photon-ics one could also think of different technologies targeting different wavelengthranges, i.e. 1550nm vs 2000nm.

1.4 Component libraries

By making use of proper design tools the total development time for PICs can bemuch shorter when using a generic integration technology [5]. Hierarchical de-sign methods are essential for this. The first major step to be taken in this processis to go from device level design to circuit level design. At the device level designmany physical effects are taken into account in time consuming simulations inorder to obtain accurate estimates of the device behavior. This becomes too timeconsuming for circuit level design. Simplified models of the devices are thereforenecessary to enable simulation at circuit level. A common approach is to restrictthe interaction between the circuit and the device to input/output ports. The devicebehavior can then be described by the relations between these ports. Already atthis point the abstraction levels become apparent. The circuit designer only hasto know about the ports and not about the intricate inner workings of the device.On the circuit level the component can now be represented as a symbol with a

6

Component libraries

number of ports. Circuit design is further sped up by having an efficient way ofsharing and reusing components. This is done by using component libraries. Byusing component libraries, designers can design very complex PICs in a relativelyshort time. The description of a component in the library essentially consists ofthree types of information [41]. The first kind is the layout information: the geo-metrical information needed to fabricate the component. The second is behavioralinformation: how many ports does a device have and what is the response betweenthem. Finally there is also some meta-data: the symbol for the component.

In the foundry approach, every fab would provide a library with a descriptionof their basic building blocks. Together with the design manual, this library is suf-ficient for designers to make a design that conforms to the requirements, knownas design rules, set by the fab. By providing building blocks as ‘black boxes’,the foundry does not have to disclose any sensitive information on the buildingblocks themselves. Apart from the BBs provided by the foundry, more advancedbuilding blocks and design routines could be provided by separate companies un-der license. This is similar to the Intellectual Property (IP) Blocks being marketedby design houses in the electronics community. This design methodology ensuresthat designers are not overwhelmed with insignificant details at the time of circuitdesign.

To explore and develop the presented generic integration strategy, the CO-BRA Research Institute at TU/e has offered MPW services on InP for severalyears [42]. To increase the speed and efficiency of the design process leadingup to an MPW, we have developed two libraries together with PhoeniX Soft-ware [43]. The foundry library contains basic building blocks like straight andcurved waveguides, SOAs, EOPMs, Multimode Interference Couplers (MMIs),Multimode Interference Reflectors (MIRs), photo-detectors (PINs) etc. The sec-ond library provides design routines for creating and simulating AWGs for threefoundry platforms: COBRA, Oclaro, and HHI. This AWG library is similar toIntellectual Property block libraries in electronics.

The efforts of COBRA are focused on generic integration on InP. The prob-lems associated with photonic design are not limited to InP, though. Especiallysilicon photonics has received a lot of attention from research groups around theworld. The collaboration between Ghent University and imec has led to a frame-work that interconnects different design tools [44]. This framework allows todefine BBs and connect those together to form circuits. Individual BBs can beexported to physical simulators [45], while circuits can be exported to a circuitsimulator [44, 46]. For simulation the framework depends heavily on physicallevel simulation. This is understandable since the high index contrast of siliconphotonics prevents the use of many common approximations. As a result, detailedsimulation of circuits can be prohibitive in terms of computation times.

7


1.5 Thesis outline

The goal of the work described in this thesis is to reduce the effort involved withthe design of Photonic Integrated Circuits that can be fabricated in the COBRAgeneric integration technology and several similar technologies. The work aimsto develop component libraries that are suitable for hierarchical design methods.A strong focus is laid on models that are sufficiently fast to enable the simulationof large photonic circuits, while retaining sufficient detail to provide meaningfulresults. The simulation time per component should be on the order of millisec-onds to enable simulation of a large collection of components. This will allowdesigners to use circuit simulation during the design process, rather than run alengthy simulation for verification when the design is done. The thesis also in-troduces new components and improvements of existing components. The scopeof the thesis is limited to passive components based on indium phosphide ridgewaveguides. Because most derivations use the Effective Index Method (EIM), theapplicability to other technology platforms is tied to the applicability of the EIM.This is discussed in appendix B. The most important results of the thesis are:

• A novel approach to model the optical properties of layer stacks. Chapter 2describes fitting methods that take the results of extensive 2D mode solvercalculations as an input and reduce this to a number of fit parameters. Byfitting a model to the mode solver results an enormous increase in speed isobtained, and reliable interpolation is easily achieved. The content of thischapter is an extension of the work published in: Kleijn, E., Smit, M.K.and Leijtens, X.J.M. (2011). “Photonic component design libraries and fastcircuit simulation”, in Proceedings of the 16th Annual symposium of theIEEE Photonics Benelux Chapter, 01-02 December 2011, Ghent, Belgium,(pp. 261-264). Ghent, Belgium: Unversiteit Gent.

• An approximate simulation method to model reflections at MMI junctions.Due to the high computational cost of existing methods that model reflec-tions, reflection effects were often excluded in circuit level simulations.For many circuits small reflections can lead to a strong reduction in per-formance. Including them in circuit level simulation provides valuable in-sights in circuit operation. An approximate method is still able to providethis insight, but keeps the computational load sufficiently low to be appliedon a full circuit. Such a method, along with a general method for simulatingMMIs, is presented in chapter 3.

• A new geometry for MMIs that strongly suppresses parasitic reflections inMMIs. It offers a 7.3 dB reduction in reflection levels compared to the state-of-the-art. It was published before in: E. Kleijn, D. Melati, A. Melloni, T. de

8

Thesis outline

Vries, M. Smit, and X. Leijtens, “Multimode interference couplers withreduced parasitic reflections,” IEEE Photonics Technology Letters, vol. 26,no. 4, pp. 408-410, 2014. This is also described in chapter 3.

• A new kind of reflective component, so called Multimode Interference Re-flectors (MIR). These are new components that can provide a reflectionand they can be placed anywhere on-chip. Compared to existing on-chipreflectors, the fabrication of MIRs is less complicated and more tolerant.Generalized design methods are presented that can be applied to MIRs withany number of ports. The work is described in chapter 4, and was publishedin: E. Kleijn, M. Smit, and X. Leijtens, “Multimode interference reflec-tors: a new class of components for photonic integrated circuits,” Journalof Lightwave Technology, vol. 31, no. 18, pp. 3055–3063, 2013.

• A new analytical model for AWGs. This models predicts the wavelengthresponse with very low computational effort. It was published as E. Kleijn,M. Smit, and X. Leijtens, “New analytical arrayed waveguide grating model,”Journal of Lightwave Technology, vol. 31, no. 20, pp. 3309–3314, 2013.The model is described in chapter 5, along with the effect of polarizationrotation on AWG performance, and general layout strategies.

• Chapter 6 discusses some fundamental properties of component libraries. Italso explores the requirements for a framework that facilitates interoperabil-ity between component libraries and photonic design software. The chap-ter continues with describing how Design Rule Checking can be achievedwithin the design software packages. Finally, the contents of the COBRAlibrary is discussed and compared to similar libraries for InP based MPWruns.

9

2Layer stack modeling

Photonic Integrated Circuits are typically formed by growing several layers on asubstrate, after which patterning is used to create waveguides. The stack of layersthus forms the basis for the passive waveguide devices. As a result, the propertiesof many devices can be derived from the properties of the layer stack. To enablecircuit level simulation of these devices, fast yet accurate models of the layer stackproperties need to be employed. Typically numerical solvers are used to calculatethe layer stack properties. These solvers can be applied to a wide range of differentlayer stack types, but usually require a considerable computational effort to obtainaccurate results. In generic integration technology the layer stack is fixed. Thisallows to pre-calculate many properties and fitting the results to a model. Thisis a novel approach and has not been used in integrated optics to the best of myknowledge. The layer stack properties that are modeled are:

• the propagation constants of straight and curved waveguide modes. Thisallows to predict the phase response of a mode for any waveguide length.

• the field profile of straight waveguide modes. This enables the calcula-tion of forward coupling coefficients at junctions between waveguides usingoverlap integrals.

• analytical expressions for these overlap integrals.

• the offset between straight and curved waveguides for minimum fundamen-tal mode loss.

This chapter describes the employed models and the achieved accuracy. It starts,however, with a brief description of the fabrication process used at COBRA toform waveguides.

2.1 COBRA waveguide fabrication

A dielectric waveguide consists of at least two regions with a different index ofrefraction. In its most basic form, a waveguide is defined by a high refractiveindex region cladded by a low refractive index region. At COBRA we use a

11

Chapter 2. Layer stack modeling

more complex multi-layer ridge structure, a simplified representation of which isshown in Fig. 2.1. A deep (high-contrast) and a shallow (low contrast) waveguidecross-section are available. The COBRA platform offers active-passive integra-tion through butt-coupling. The guiding layers for active and passive waveguidesare formed out of quaternary indium gallium arsenide phosphide material withvarying band gaps. These materials are referred to as “Qw”, where w is the bandgap wavelength expressed in µm. To calculate the refractive index of such mate-rials, we use the Fiedler and Schlachetzki model [47]. The active layer consistsof a 120 nm thick Q1.55 layer sandwiched between two Q1.25 layers. The ac-tive layer is first grown epitaxially on a n-doped indium phosphide (n-InP) sourcewafer [48]. The areas where active devices are desired are masked by a siliconnitride (SiNx) layer that protects the underlying area from being etched. At ex-posed areas, all active material is removed, after which a Q1.25 layer is regrownuntil it matches the height of the active layer. Both active and passive areas arethen overgrown by a series of layers of p-doped indium phosphide (p-InP), witha total thickness of 1600 nm. The doping concentration in each layer graduallyincreases towards the top. As the last growth step, a highly doped p-InGaAs con-tact layer is deposited. Processing then continues by etching the waveguides. A600 nm SiNx layer, which will serve as a hard mask, is deposited using PlasmaEnhanced Chemical Vapor Deposition (PECVD). Contact lithography is used totransfer the waveguide pattern. The hard mask is opened using Reactive Ion Etch-ing (RIE), after which Inductively Coupled Plasma (ICP) etching is used to etchthe waveguides. By using a double-etch process, both the shallow and deep wave-guide types can be realized [49]. After etching, polyimide is spun to passivate theactive areas and to planarize the sample. This completes the passive waveguides,as shown in figure 2.1. The full process contains more steps after this, but this isbeyond the scope of this thesis.

The InGaAsP layer in figure 2.1 has a higher index than the p-InP superstrate,n-InP substrate and PI cladding. Optical confinement is thus achieved and opti-cal modes can therefore propagate in the z-direction. Finding which modes areguided, and what their propagation constants are, is essential to design passiveintegrated components. Specialized computer routines (mode solvers) are usedto calculate this. However, depending on the accuracy, they can take up to afew minutes on modern computers to find a single mode. When designing largeand complicated PICs this is usually too slow. The process can be sped up sig-nificantly by pre-calculating the propagation constants as a function of severalparameters, and then fitting them to a model. This can reduce calculations timesto microseconds per mode. By using a model, stable interpolation is achievedeasily. This essentially trades some flexibility for speed. This trade-off is not re-ally present when designing for a generic integration technology, because many

12

Propagation constant

Figure 2.1: Schematic cross-section of passive deep and shallow waveguides in the CO-BRA layer stack. The dimension of every layer is indicated, as well as the constitutingmaterials. The typical width of a waveguide in the COBRA technology is 1.5 µm for deep-etched waveguides and 2.0 µm for shallow waveguides. Designers can choose differentvalues though. p-InP: p-doped indium phosphide, n-InP: n-doped indium phosphide, In-GaAsP: indium gallium arsenide phosphide, PI: polyimide.

process parameters have been fixed by the foundry already. Additionally, correctconvergence of a mode solver algorithm is not always guaranteed. Sometimes thepropagation constant of the first order mode is reported as being the propagationconstant for the fundamental mode and vice versa. Such incorrect mode solverresults can be filtered out prior to fitting the results to a model. In the followingsections the developed models for describing the propagation constants will bediscussed. Only straight and curved waveguides will be treated, as these are themost frequently used waveguide geometries.

2.2 Propagation constant

2.2.1 Straight waveguide

In the COBRA generic integration technology, the layer thicknesses and etchdepths are fixed. There are still a number of parameters that can vary. In termsof the geometry, the waveguide width d can be chosen by a designer. For therest there are the wavelength λ, polarization p and mode number m. A model forthe propagation constant should have at least those parameters. It would be verydifficult to find a model that is valid over all possible values of these parameters.Luckily, we can assign reasonable ranges for each parameter that are typical forthe technology used. The COBRA process was designed to support the telecomwavelength window spanning 1500 nm to 1600 nm. The properties of the layerstack change relatively slowly with wavelength so a large step of 10 nm is justi-fied. For these wavelengths, the minimum waveguide width supporting a modeis around 1 µm. There is no clearly defined maximum waveguide width, save the

13


Figure 2.2: Mode solver result set for the fundamental mode in COBRA deep waveguideswith the wavelength as a parameter.

width of the chip which is typically on the order of 4 mm. Analysis of designsmade in the COBRA technology showed that the largest waveguide width usedwas 13 um, and occurred inside MMIs. A maximum waveguide width of 20 µmwas chosen to allow some design headroom for even larger MMIs. The waveguidewidth step size was set to 0.1 µm, which is one fifth of the wavelength inside thematerial, to allow for sufficient resolution to model the fast changing behaviorclose to mode cut-off. Once the wavelength and width ranges are known, a singlemode solver run at the shortest wavelength and widest width will show the maxi-mum order of the guided modes. This is then used as the upper boundary for theconsidered modes. We thus obtain the following ranges and step sizes.

1500 nm ≤ λ≤ 1600 nm step 10 nm1.0 µm ≤ d ≤ 20.0 µm step 0.1 µm

0 ≤ m < 20 step 1p ∈ {TE,TM}

Throughout this thesis, the TE polarization is defined to have Ex as dominantelectric field component in the axis system of figure 2.1. For TM-polarization thedominant electrical field component is Ey. By also including wide waveguidesand high order modes, it is possible to use the layer stack model for MMIs aswell. This is discussed in chapter 3. A fully vectorial 2D FMM based modesolver [43] is used to find the propagation constant for all possible combinationsof these parameters. This results in a multidimensional map that will be fitted toa model. Figure 2.2 shows a typical mode solver result set for the fundamentalmode in a deep COBRA waveguide. In this plot, the wavelength is a parameter,with the highest values for β belonging to λ = 1500 nm.

14


Model

Instead of applying a polynomial fit, we start from a physical description of thepropagation constant. This has the advantage that it captures some of the under-lying physics and is thus well suited for interpolation between data points. Also,the number of required parameters that are needed to reach a certain accuracy canbe kept low with respect to multivariate polynomials. The model that we will useis based on the concept of effective waveguide width. In this approach, a dielec-tric waveguide of width d is modeled as a metallic waveguide of width deff [50].The solution for the propagation constant β for a 1D dielectric waveguide has theform [51]

βp,m =√

k2− k2x (2.1)

k =2πns

λ

kx =(m+1)π

deff

deff ≈ d +λ

π√

n2s −n2

c

(nc

ns

)2σ

(2.2)

with ns the slab index, nc the cladding index and σ = 1 for p = TE and σ = 0 forp = TM. The first step in applying this model is to use a slab mode solver to findthe slab index ns as a function of λ and p. An excellent fit was obtained using asecond order polynomial in λ. This led to the use of three fit coefficients for ns.Equation (2.2) shows that the effective width is approximated as a linear functionof λ. A fourth fit coefficient was introduced to capture this behavior. Finally, afifth and last fit coefficient was used in the expression for kx. This last coefficientcaptures the influence of the mode number m. Because m is discrete, a differentvalue for this fit coefficient can be adopted for each m. Combining (2.1) and (2.2)and introducing the five fit coefficients Ci, we derive

βp,m =

√k2− k2

x (2.3)

k =2π

λ

(C0,p,mλ

2 +C1,p,mλ+C2,p,m)

kx =C3,p,m

d +C4,p,mλ

In deriving this model we made the assumption that an expression for a 1D slabwaveguide could be applied to a full 2D waveguiding structure. This limits theaccuracy of the presented model. It is, therefore, important to determine required

15


level of accuracy and evaluate whether the model meets this target. The model alsoignores several effects that are present in fabricated layer stacks, such as variationsin layer thickness and composition. If these effects are small and independent, themodel could be extended by including a linear term for each effect.

Accuracy

The propagation constant estimator in (2.3) is applied to each polarization p andmode m separately, hence the subscript indices. A fit error ε can now be definedas

εp,m = max|βp,m−βp,m|

βp,m(2.4)

Generally, the presented model works well for high index contrast and mediumindex contrast cross-sections. However, additional fit terms are in some situationsrequired to reduce the fit error ε to acceptable levels. It is acceptable when ε islower than the random errors due to fabrication imperfections. One such fabri-cation imperfection is sidewall rougness. Sidewall roughness will give rise to arandom error in the local propagation constant in a fabricated waveguide. Thevalue for ε should be lower than the error introduced by sidewall roughness, inorder for the method to introduce a negligible error to the design. The error dueto sidewall roughness can be calculated as follows.

Suppose waveguides are fabricated with a RMS roughness value of σ meter.This is equivalent to a statistical spread of waveguide width along the length of thewaveguide. Multiplying this value with the first order derivative of βp,m in d givesan estimate of the uncertainty in βp,m due to inherent uncertainties in the process.It is important to differentiate between true random errors, for example due toroughness, and between systematic errors like an overall increase in waveguidewidth, i.e. critical dimension loss. Equation (2.5) expresses the desire for the fiterror to be much smaller than uncertainty introduced by roughness. The two sidesof the waveguide are assumed to have independent roughness, hence the factor√

2.

εp,m�1

βp,m

∂βp,m

∂d

√2σ (2.5)

Mode solver results on the COBRA stack show that for 1.5 µm wide deep etchedwaveguides at 1550 nm, β

−1TE,0

∂βTE,0∂d ≈ 1.5 ·10−5. Typical ICP etched waveguides

in InP show RMS roughness of around 3.5 nm to 5 nm [52–54]. Alternatively,the Payne and Lacey [55] waveguide roughness model can be used to derive σ

from observed waveguide scattering loss. In COBRA’s deep waveguides, the totalwaveguide loss can be as low as 2.0 dB/cm. Around 1.0 dB/cm can be attributedto absorption loss in the p-doped cladding. This leaves 1.0 dB/cm that can be

16


contributed to scattering induced by roughness. Using equation (18) from thePayne and Lacey model in [55], the scattering loss α in dB/m can be estimated.Please note that Payne and Lacey use 2d as the waveguide width, while here weuse d to denote the waveguide width. This causes the factor 16 to appear here.Because we use units of dB/m, a conversion factor of 10loge is included.

α ≤ 10loge16σ2

2k0nsd4 g [dB/m] (2.6)

g =d4k4

0(n2s −n2

eff)(n2s −n2

c)

16+8dk0

√n2

eff−n2c

with neff the mode index. The parameter g is set fully by the waveguide geometry.For COBRA deep-etched waveguides, g≈ 20. Entering this in (2.6) we obtain thefollowing estimate for σ

σ≥[2k0nsd4 α

4.34 ·16 ·20

]1/2= 3.1nm (2.7)

This corresponds well to the values reported in literature. Such roughness valuesput the desired value of εTE,0 to around 10−5.

Unfortunately, using the expression of (2.3) it turned out to be impossible toobtain this accuracy for the COBRA deep-etched waveguides. To solve this, therange of the fit was reduced and the model was expanded with more fit terms.The form of the extra terms was chosen based on the observed behavior of the fiterror as a function of λ and d. Introducing higher order terms will improve thefit error, but may degrade the interpolation performance. A polynomial of degreen− 1 will perfectly fit a data set of size n, but may oscillate wildly in betweenthe data points. It is therefore desirable to keep the number of fit parameters toa minimum. Clearly though, the fitting process is quite empirical. In the end, avalue of 0.7 ·10−6 was obtained for εTE,0 for the COBRA layer stack, by using thefollowing fit model.

βp,m =

√k2− k2

x (2.8)

k =2π

λ

(C7,p,mλ

3 +C0,p,mλ2 +C1,p,mλ+C2,p,m

)kx =

C3,p,m

d +C6,p,md2 +(λC4,p,m +C5,p,mλ2)/(C8,p,md4)+

C9,p,mλC10,p,m

d2

2.2.2 Curved waveguide

Similar to the straight waveguides, we begin by defining for which parameters andassociated ranges we wish to model the angular propagation constants βφ. With

17


respect to the straight waveguides, we add the radius parameter R. We restrictthe model to the propagation constant for the fundamental mode, because higherorder modes are not frequently used for curved waveguides. The following rangesand step sizes were chosen for the deep waveguides in the COBRA process.

1.0 µm ≤ d ≤ 2.0 µm step 0.1 µm1500 nm ≤ λ≤ 1600 nm step 10 nm

p ∈ {TE,TM}m = 0

50 µm ≤ R≤ 500 µm step 5 µm

A fully vectorial 2D Finite Difference solver [43] was employed to rigorouslycalculate the angular propagation constant at every grid point. The total numberof points is around 22000. At about one minute per point this took approximately2 weeks to calculate on a 2.67 GHz Intel Core i7 920 processor.

Model

In a model proposed by Melloni in [56], the curved mode is described as a com-bination of the fundamental and first order modes in a straight waveguide. Thismodel predicts the real part of the propagation constant very well, but fails to de-scribe the curved mode attenuation. However, for designing many passive struc-tures, such as delay lines and AWGs, only the phase properties of the mode areimportant, as long as radiation losses remain low (< 0.01 dB/90◦). This is the casefor large bending radii as compared to the waveguide width and the wavelength.The standard curved waveguides in generic integration technologies are chosen tomeet this criterion. Following [56], the equation describing the expansion of thecurved mode in terms of first two straight modes is

Ma =

([R 00 R

]+

[c00 c01c10 c11

])[β0 00 β1

]a = βφa (2.9)

with β0 the propagation constant of the fundamental mode in a straight waveguide,and β1 the propagation constant of the first order mode. Equation (2.9) is theeigenvalue equation of M, with eigenvalues βφ that equal the angular propagationconstants of the curved modes. Solving this equation analytically results in thefollowing solutions for βφ.

βφ = β0c00 +R

2+β1

c11 +R2± 1

2

[(β0(c00 +R)+β1(c11 +R))2

−4β0β1 ((c00 +R)(c11 +R)− c01c10)]1/2

(2.10)

18

Field profiles

Expanding all brackets in (2.10), rewriting it as a polynomial in R and collectingterms we get

βφ =c00β0 + c11β1

2+R

β0 +β1

2± 1

2

[R2(β0−β1)

2 +2R ·

(c00β0− c11β1)(β0−β1)+4c01c10β0β1 +(c00β0− c11β1)2]1/2

(2.11)

In the limit of R→ ∞, (2.11) tends towards Rβ0, which means the model ex-hibits the desirable behavior that a curved mode with infinite radius behaves likea straight mode. By replacing the coefficients in (2.11) with fit coefficients andadding weighing factors to each term, the final model is obtained.

βφ = c4c0β0 + c2β1

2+ c3R

β0 +β1

2+ c5

12

[c6R2(β0−β1)

2 +

2c7R(c0β0− c2β1)(β0−β1)+4c1β0β1 +(c0β0− c2β1)2]1/2

(2.12)

In (2.12) there is no explicit dependence on wavelength, polarization or waveguidewidth. These dependencies are all included through β0 and β1.

2.2.3 Accuracy

Curved waveguides are more complex than straight waveguides because they re-quire an extra parameter, R, to describe their geometry. As such, it is more dif-ficult to obtain fits with equal accuracy as those presented earlier in the straightwaveguide section. However, the same argument on waveguide roughness holds.Again for the COBRA deep stack, for 1.5 µm wide waveguides with radius 100 µmat 1550 nm, the coefficient β

−1φ,TE,0

∂βφ,TE,0∂d ≈ 1.7 · 10−5. Using once more an esti-

mated roughness σ of 3.1 nm, we set εφ,TE,0 to 10−5. For the COBRA layer stack,the best accomplished overall fit has a relative error of around 10−4. We thereforemade a separate fit for d = 1.5 µm, which is the standard waveguide width. Thislast fit has a relative error of 10−5, meeting the target.

2.3 Field profiles

The field profile of a set of modes on either side of a waveguide junction canbe used to calculate the transmission through such a junction [57]. For a fully-vectorial 2D field profiles this is generally a very complex electro-magnetic prob-lem. Due to this complexity, finding exact solutions can be a lengthy process. Thecomplexity can be strongly reduced when the effective index method (EIM) canbe used. The EIM approximates the waveguide structure as a combination of two

19


slab waveguides. This approximation works well for low-contrast waveguides,but also the high-contrast deep waveguides used at COBRA can be modeled withreasonable accuracy [58]. The validity of the EIM when applied to COBRA wave-guides is discussed in more detail in appendix B. In the effective index method,the dominant field component U(x,y) is described as the multiplication of twoseparate slab-waveguide profiles:

U(x,y) =Ux(x)Uy(y) ={

Hy(x)Hy(y) for TEEy(x)Ey(y) for TM

(2.13)

In the COBRA waveguides, the core is much thinner than the typical waveguidewidth. Perturbation analysis [58] shows that in that case errors are minimizedwhen the EIM is used to eliminate the y axis. Further more, when consideringplanar integrated optics, the index profile in the y direction is the same on bothsides of the junction. This means there is no discontinuity in the y direction andtherefore there is no contribution to the transmission loss from Uy. The generaljunction is thus reduced to a junction of two slab waveguides. Marcuse [59] de-rived relatively simple integral expressions describing the transmission througha junction of two slab waveguides. Marcuse’s approach is known as the overlapintegral method. It describes the transmission between an incident mode i and atransmitted mode t as the overlap integral between the dominant, non-vanishingfield components of both modes on either side of the junction. Only the x depen-dent component needs to be considered. We label it U(x) here. The overlap inte-gral describing the amplitude transmission coefficient through the slab-waveguidejunction is then [59, 60]:

Si j =

∫∞

−∞Ui(x)U∗t (x)dx∫

∞

−∞Ui(x)U∗i (x)dx

∫∞

−∞Ut(x)U∗t (x)dx

(2.14)

with a∗ the complex conjugate of a. To calculate this integral, the field profileof both modes needs to be known. If we assume normalized field profiles, then(2.14) can be rewritten to

Si j =∫

∞

−∞

Ui(x)U∗t (x)dx (2.15)

To evaluate (2.15) only Ui(x) and Ut(x) need to be known. The next subsectionsshow how these profiles can be obtained for straight and curved waveguides.


The 1D field profile along x for the guided fundamental mode of a straight threelayer waveguide is shown in figure 2.3. The waveguide edges are indicated by

20

Field profiles

vertical lines at −1/2 and 1/2. This creates three regions: I, II and III. The fieldhas a cosine shape in region II, and exponential tails in regions I and III. Higherorder guided modes have similar properties, but have more extrema in region II.The profiles can be expressed analytically in the following way [59–61]:

U(x) =C

cos(u/2−φ)exp( v

2+vxd ) for x <−d

2

cos(ux/d+φ) for |x| ≤ d2

cos(u/2+φ)exp(w2−

wxd ) for x > d

2

(2.16)

with

v = k0d[n2eff−n2

0]1/2

u = k0d[n21−n2

eff]1/2

w = k0d[n2eff−n2

2]1/2

φ =12

{arctan(w/u)− arctan(v/u)+mπ for TE

arctan(n22w

n20u )− arctan( n2

1vn2

0u)+mπ for TM

Where k0 = 2π/λ0, m the mode number, defined as b uπc, and neff the mode index.

The arctangent terms in φ take care of shifting the maximum of the cosine term inthe case of waveguides with an asymmetric index profile. The mode is normalizedthrough the coefficient C. Its value can be calculated by satisfying the followingequation

1 =∫

∞

−∞

U(x)U∗(x)dx

From this it follows that C equals

C =

√2d

[1+

cos(u/2−φ)2

Re(v)+

sin(u)cos(2φ)

u+

cos(u/2+φ)2

Re(w)

]−1/2

The equations presented above are for a 1D field. The fit routines that were in-troduced in section 2.2 for β, and by extension neff, are for 2D modes. Simplyplugging a 2D propagation constant into an expression for a 1D field leads toerrors. For example, different mode orders in the same waveguides are then nolonger orthogonal. To solve this, we also fitted 1D propagation constants withsimilar routines as for the 2D ones. By using the 1D values, the correct mode pro-files are obtained. This is the approach that has been implemented in the COBRAlibrary. This approach works well in the regime where the effective index methodalso works well. This is the case for waveguides operated at a large normalizedfrequency V and having a thin core compared to the waveguide width [58]. Thisis the case for COBRA waveguides.

21


Figure 2.3: 1D mode field profile along x for the fundamental mode of a three layerwaveguide.


According to the approach taken in [56], the field profile of a curved mode canbe expressed in terms of the mode profiles of a straight waveguide with the samecross-section.

Uφ =N−1

∑n=0

anUn (2.17)

Strictly speaking the sum in (2.17) should run up to infinity and include a set oforthonormalised radiation modes. It was mentioned in section 2.2.2 that we as-sume low radiation loss because large radii are used compared to the wavelengthand waveguide width. This means contributions of radiation modes can be ne-glected. It also means that the curved mode still resembles a straight waveguidemode quite well. In this case it is sufficient to consider only the fundamental andfirst order modes. Consequently we choose N = 2. In section 2.2.2 the matrixM was introduced as part of the model for the angular propagation constant. Itcan be shown that the weighing factors an are the components of the eigenvectorof M [56]. The field profile of the fundamental curved mode can therefore beexpressed in terms of the straight mode profiles as follows.

Uφ =[c2

10β20 +(βφ−β1(c11 +R))2]−1/2

(βφ−β1(c11 +R)

c10β0

)(U0 U1

)(2.18)

Because for curved waveguides usually only the fundamental mode is of interest,there is no large issue if the modes in the curved waveguide are not perfectlyorthogonal. This means that the 2D angular propagation constant might be usedfor βφ in (2.18). This was not tested though, and further research is required toinclude the curved waveguide mode profiles in the COBRA library.

22

Overlap integrals

2.4 Overlap integrals

As mentioned in section 2.3, the coupling between two modes at a junction isgiven by the overlap integral of their field profiles. In that section an expressionfor the straight and curved waveguide modes was derived as well. The study ofoverlap integrals in this section will be limited to those field profiles. Without lossof generality we define the value of Ui(0) to occur at the geometrical center of awaveguide. An additional parameter o is introduced to denote the lateral offsetbetween two mode profiles. The overlap integral we wish to evaluate can thus bewritten as

Si j =∫

∞

−∞

Ui(x)U j(x−o)dx (2.19)


From figure 2.3 and from equation (2.16) it can be seen that straight mode profilesconsist of three regions. This means that the product U1(x)U2(x−o) can also besplit into a number of different regions. The boundaries of those different regionscan be found easily by sorting the boundaries of the individual mode profile re-gions. Let B be the ascending sorted list of boundary positions. The list is thengiven by

B = {b0,b1, . . . ,bm, . . . ,bN−1} with bm ≤ bm+1 and 0≤ m≤ N−2

Thus for the two straight waveguides, the following list of region boundaries isobtained

B = Sort({−∞,−d1

2,d1

2,−d2

2+o,

d2

2+o,∞

})(2.20)

Two consecutive values in B, bm and bm+1, define a domain. To be able toevaluate the overlap integral, the function type of both mode fields in this domainhas to be known. To this end we define a domain centre position xm = 0.5bm +0.5bm+1. A simple function can then be written that calculates the function typeof the mode field at position xm. We label the three regions as EXPV (also knownas region I), COSU (also known as region II), and EXPW (also known as regionIII). Each region label is given a value equal to a power of two. We thus get values1, 2 and 4 respectively. The following pseudo code determines the region type ata certain position xm.

enum RegionType {EXPV=1, COSU=2, EXPW=4};RegionType Type(xm,d,o) {if(xm<-d/2+o) return EXPV;if(xm>d/2+o) return EXPW;return COSU;

}

23


Figure 2.4: An example of how different combinations of regions are formed. The firstprofile is shown in blue, the second in red. The bottom line shows the region combinationresulting from this particular configuration as a combination of two numerals.

There are nine different combinations of regions. They are listed in table 2.1.Each combination is assigned a unique number in the following way.

TypeCombine(Type1,Type2) {return Type1<<3 | Type2;

}

The above code concatenates the binary value of both types. For example, takeType1=2 and Type2=4. Their binary values are 010 and 100. A call to TypeCom-bine would return 010100. Each combination has a function associated with it thathas to be integrated over. Because the functions are multiplications of exponen-tial and cosine functions, the primitives can be found analytically. This enablesfast and easy calculation of overlap values. The derivation of these primitives islengthy and cumbersome, but easily done with programs like Mathematica [62].We therefore only show the final result here in table 2.1. To evaluate the total over-lap integral, the value of the primitives are calculated and summed. Even thoughthe expressions in table 2.1 are quite complicated, evaluating them is still muchfaster than numerically estimating the value of the overlap integral. Also, no sam-pling error is made by using these expressions. As a quick comparison, supposewe have two field profiles, each with 100 points. This means that evaluating theoverlap integral takes 100 multiplications and 100 additions. To obtain the fieldsto begin with requires performing 200 exponential or cosine routine calls, but theresults could be cached. The analytical method only uses around 50 multiplica-tions and additions, and maximally 5 exponential or cosine routine calls. Whenhigh order modes are considered, more field points are necessary for an accurateresults, and the differences will be even bigger.

24

Offsets between straight and curved waveguides

Type1 Type2 Primitive functionEXPV EXPV Av1Av2d1d2 exp(v1x/d1 + v2(x−o)/d2)/(d2v1 +d1v2)EXPV COSU Av1d1d2 exp(v1x/d1)(d2v1 cos(φ2 +u2(x−o)/d2)+

d1u2 sin(φ2 +u2(x−o)/d2))/(d21u2

2 +d22v2

1)EXPV EXPW −Av1Aw2d1d2 exp(v1x/d1−w2(x−o)/d2)/(−d2v1 +d1w2)COSU EXPV Av2d1d2 exp(v2(x−o)/d2)(d1v2 cos(φ1 +u1x/d1)+

d2u1 sin(φ1 +u1x/d1))/(d22u2

1 +d21v2

2)COSU COSU 0.5d1d2(sin(φ1−φ2 +u1x/d1−u2(x−o)/d2)/(d2u1−d1u2)+

sin(φ1 +φ2 +u1x/d1 +u2(x−o)/d2)/(d2u1 +d1u2))COSU EXPW Aw2d1d2 exp(−w2(x−o)/d2)(−d1w2 cos(φ1 +u1x/d1)+

d2u1 sin(φ1 +u1x/d1))/(d22u2

1 +d21w2

2)EXPW EXPV Av2Aw1d1d2 exp(−w1x/d1 + v2(x−o)/d2)/(d1v2−d2w1)EXPW COSU Aw1d1d2 exp(−w1x/d1)(−d2w1 cos(φ2 +u2(x−o)/d2)+

d1u2 sin(φ2 +u2(x−o)/d2))/(d21u2

2 +d22w2

1)EXPW EXPW −Aw1Aw2d1d2 exp(−w1x/d1−w2(x−o)/d2)/(d2w1 +d1w2)with Avi = cos(ui/2−φ)exp(vi/2)

Awi = cos(ui/2+φ)exp(wi/2)

Table 2.1: Function primitives for the various regions of the overlap integral.


Section 2.3.2 showed that the profile of a curved waveguide can be written as asum of straight waveguide modes. If we combine equations (2.17) and (2.19),we obtain the following expression for the coupling between straight and curvedmodes.

Si j =∫

∞

−∞

N−1

∑n=0

anUn(x)U j(x−o)dx =N−1

∑n=0

an

∫∞

−∞

Un(x)U j(x−o)dx (2.21)

Because the overlap integral is linear, it can be split into an integral of each con-stituent mode to another. Each of those integrals is then of the straight-straighttype, and can be evaluated in the manner described in the previous section. Theoverlap integral between two curved waveguides can be evaluated in the samemanner, but it involves two sums.

2.5 Offsets between straight and curved waveguides

A standard way of maximizing the coupling between the fundamental mode ina straight waveguide and the fundamental mode in a curved waveguide is by ap-plying a small offset to the junction between the waveguides [63]. This approach

25


50 100 150 200 250 300 350 400 450 5000

10

20

30

40

50

60

70

R [µm]

Opt

imum

offs

et [n

m]

Input dataModel

Figure 2.5: Optimum offset between 1.5 µm wide curved and straight deep waveguides inthe COBRA process at a wavelength of 1550 nm. The data from the overlap calculation isshown as open symbols. This input data is quantized to a grid of 1 nm. This grid is equalto the grid used in mask layout. The fitted model result is shown as a line, and matchesvery well to the data.

works because the maximum of the curved waveguide mode is shifted outwardsomewhat. To find the optimum offset, the overlap integral between a straight andcurved mode profile is maximized as a function of the lateral offset. This can inprinciple be done using the expressions derived in section 2.4. However, thoseexpressions use 1D field profiles. It is more accurate to use the full 2D field pro-files. Instead of storing the full 2D profiles, we calculate the optimum offset andstore that value. Subsequently, a model is fitted to this data. The model serves tointerpolate the discrete results and to reduce the calculation times. A slice of theoptimum offset data is shown in figure 2.5.

2.5.1 Model

In [63] the following formula is given for the optimum offset between the twowaveguide types:

o =π2n2

s d4

λ2R(2.22)

Equation (2.22) forms the basis of a model that returns the optimum offset tomatch a straight and a curved waveguide of the same width. The same ranges aswere used for the curved waveguide propagation constants are also applied. Fullyvectorial 2D mode solvers were used to find the field profiles in the straight andcurved sections. The optimum overlap was determined with a resolution of 1 nm.

26

Offsets between straight and curved waveguides

By adding fit coefficients to (2.22), we obtain the following model.

o = π2n2

sc0d4 + c1

(c2λ2 + c3)(c4R+ c5)(2.23)

With this model an accuracy of 1 nm was obtained, which was the resolution ofthe input data. This accuracy was achieved over the full considered parameterrange, which is the same as the parameter range for the curved waveguide modedescribed in section 2.2.2.

27

3Multi-mode interferencecouplers

A multi-mode interference device in its most basic form is a waveguide that cansupport multiple modes [51]. As the device name suggest the multiple modeswill interfere with each other. Because of this, self-imaging will occur. Self-imaging is a property of multi-mode waveguides by which an input field profile isreproduced in single or multiple images at periodic intervals along the propagationdirection of the waveguide [51]. This property can be used to create splittersand combiners, making MMIs one of the most frequently used building blocks inphotonic integration. The first part of this chapter describes the approach takento model MMIs. This approach is rooted in Modal Propagation Analysis, andsimilar to the method used by Soldano [51]. His method did not include reflectionsat the MMI junctions. This chapter describes an adaptation of this method toinclude approximate junction reflections. The second part introduces a new MMIgeometry that can significantly reduce these back-scattering effects. This part waspublished in a peer reviewed journal. Finally, we discuss 4×4 MMIs that can beused as 90◦ optical hybrids.

3.1 Geometry

An MMI in its most elementary form is a rectangular waveguide section support-ing multiple modes, with input and output waveguides connected to it. Figure 3.1shows the geometry of a 2× 2 MMI as an example. The geometry is fully de-scribed by a number of parameters. These are the width of the MMI (WMMI), thelength of the MMI (LMMI), and the widths and position of the access waveguides(wa and o). The access waveguide positions are referenced from the MMI centerline. The arrow in the figure indicates a positive value of the waveguide position.Generally speaking, MMIs can have any number of input and output waveguides,which each can have different widths. In practice the number is usually limited toaround four waveguides of equal width. To support high port counts, high ordermodes are necessary. These high order modes are subject to larger phase errorsthan the low order modes. Such phase errors result in blurred images and a sub-sequent reduction in performance.

29

Chapter 3. Multi-mode interference couplers

Figure 3.1: The geometry of a standard 2×2 MMI. In the junction components, overlapintegrals are used to calculated the scatter parameters. In the multimode section, purepropagation occurs and modes are not coupled. All ports are bidirectional.

Many variations to the presented geometry can be made to add extra function-ality to the MMI. The multimode section can, for example, be tapered to allow awide range of splitting ratios [64,65]. Another possibility is to angle the back-wallof the MMI to reduce reflections [66]. In the following derivation of a model de-scribing the response of an MMI we limit ourselves to the rectangular geometry.

3.2 Model

For the typical InP layer stacks and optical power densities we consider, non-lineareffects in passive components can usually be ignored. This allows us to modelMMIs as linear components. In RF engineering, linear components are modeledvery successfully through the scattering matrix method [67]. In this method, anumber of bidirectional ports are identified through which the component can in-teract with other components. A scattering matrix then describes the couplingbetween fields entering and leaving these ports. This principle can also be appliedto optical components [68]. In that case, a port is assigned to each consideredmode. The set of modes can be limited to guided modes, provided that the totalradiated power is low. This is a reasonable assumption for MMIs, and in fact formost components in PICs. We further assume that there is no coupling betweenTE and TM polarized modes. Please note that in this discussion we use the stan-dard definitions for polarization for 2D cross-sections. That is, TE polarized lighthas its major electric field component parallel to the guiding film, which is thex-axis in figure 2.1. The operating wavelength can be varied, but is the same forall considered modes.

We wish to find a model that calculates the coupling between the input andoutput modes as a function of wavelength and MMI geometry. Modal Propaga-tion Analysis (MPA) has been used early on to achieve this [51]. Unfortunately

30

Model

Figure 3.2: The three sections of a 2× 2 MMI, plus the input and output waveguides.Each dot is a bidirectional port, which represents a mode.

MPA is not able to model reflections occurring at the junctions in the MMI. In var-ious applications it is very important to have a low level of back scattered light.Examples are lasers or applications involving optical amplifiers, where even backscattering in the order of −50 dB can adversely affect operation. Understandingparasitic reflections and modeling them is therefore of high significance for theseapplications. We have created an adapted method based on MPA that approxi-mately models such reflections. It is the first method we believe to be sufficientlyfast yet accurate for circuit level simulation. The approximate model was devel-oped to describe back scattering in a junction between a wide multi mode wave-guide and several narrow waveguides which can be single mode but may supportany number of modes. The purpose of this model is to be used as a design tool togain insight in the level of back scattered light, not as a highly accurate physicalmodeling tool. For the latter kind of application FDTD and EME1 methods arebetter suited.

Our method splits the MMI into three sections: an input junction, a multi-mode section, and an output junction. We calculate the S-matrices of each sectionseparately and then concatenate those to form a single S-matrix. This is shownschematically in figure 3.2. We will now model the multimode section and junc-tions in the MMI, after which we will concatenate their S-matrices to find theresponse of the full MMI.

3.2.1 Multimode section

The multimode section is invariant along its length. This means that the localeigen modes are constant along the section. No coupling between modes thereforeoccurs. While propagating through the section, a mode experiences a phase shiftand may be attenuated. Without loss of generality, we define the number of guidedmodes in the section to be M. The ports on the left side are numbered 1 . . .M, inincreasing fashion according to the mode order. Similarly, the ports on the right

1Eigen Mode Expansion, also known as Bidirectional Eigenmode Propagation

31


(a) (b)

Figure 3.3: (a): Index profile of a junction between a wide waveguide and two narrowerwaveguides. (b): Schematic representation of the same junction.

are numbered M+1 . . .2M. The S-parameters Smn from port n to port m are thengiven by

Smn =

{exp(−(α+ jβ)L) for |m−n|= M0 elsewhere

(3.1)

with α the attenuation constant, β the propagation constant, and L the length ofthe section.

3.2.2 Junction

In MMIs, a junction between a wide multimode waveguide and a number of nar-row other waveguides, identified as wgi, occurs. This is shown in figure 3.3a. Asdiscussed in the section above, M is defined to be the number of guided modes inthe wide waveguide. On one side of the junction there are therefore M ports. Onthe other side of the junction, the total number of modes is

N = ∑i

Ni (3.2)

where Ni is the number of modes supported by waveguide i, which is typicallyless than three. A schematic representation of the junction is shown in figure3.3b. Each narrow waveguide in this figure has an associated width wi and offsetoi. We consider the collection of modes of all the narrow waveguides form a setof size N, with N defined in (3.2). A mode from this set is labeled mode v. Themodes in the wide waveguide form a set of size M. Modes from this set are labeledm or n, because we need to use multiple modes from this set simultaneously in theS-parameter calculation. Both mode sets are required to be orthonormal.

32

Model

The first step in calculating the response of the junction is to obtain modeprofiles for the guided modes m in the wide and modes v in the narrow waveguides.The approach outlined in chapter 2 can be used for this. The field profiles φm(x)and φv(x) for all m and v are now known. The forward S-parameters from inputmode m to output mode v are calculated by evaluating the overlap integral:

Svm = O(v,m) =∫

φv(x−oi)φ∗m(x)dx (3.3)

The S-matrix has now been filled with the transmission coefficients. Calcu-lating the reflection coefficients is a little bit more difficult. Before we start thederivation of these coefficients it is important to realize that the power reflectedback into mode m does not just depend on the input presented in mode m, but alsoon the input presented at all other modes n of the wide waveguide. To clarify this,suppose the mode excitation in the wide waveguide is such that a single spot is im-aged onto the output side of the junction. The position of this spot is determinedby the relative phases and amplitudes of the mode’s excitations. This means thereis coupling between mode m and all other modes n.

Conventional, rigorous electromagnetic modeling calculates the back reflec-tion coefficients by performing field matching on both side of the junction. This isa complex procedure because also radiation modes need to be taken into account.In our approach the radiation modes are not considered. Instead, we estimatewhich parts of the field at the junction are not transmitted to the narrow wave-guides. We assume that those “left over” field components are reflected off theinterface with a coefficient equal to that of a Fresnel plane wave reflection. Con-sidering a mode m, we wish to calculate the coupling coefficient to mode n dueto a reflection at the interface. Previously the transmission from mode m to thenarrow waveguide mode v, Svm, was already calculated. Using these parameterswe can construct a “left over” field profile φ′m(x) that is the original profile φm(x)minus the sum over all the output mode profiles weighted by their transmissionparameters Svm:

φ′m(x) = φm(x)−∑

vφv(x)Svm (3.4)

The novel idea in this model is that the back reflection coefficient Snm is approxi-mated by reflecting this “left over” field with a Fresnel reflection coefficient:

Snm =∫

φn(x)rmφ′m(x)dx (3.5)

The Fresnel reflection coefficient rm is calculated for each mode separately, de-

33


Figure 3.4: The equivalent index is the index profile (red) weighted by the mode profile(blue). Multiplying the two and integrating over x results in the shaded green area.

pending on the considered polarization [69]:

rm[TE] =neq cos(θi)−neff cos(θt)

neff cos(θt)+neq cos(θi)

rm[TM] =neff cos(θi)−neq cos(θt)

neff cos(θi)+neq cos(θt)

Here θi and θt are the familiar incidence and transmission angles:

θi = arctan√

n2s/n2

eff−1.0

θt = arcsin(neff/neq sin(θi))

with neff the mode index of mode m, and neq an equivalent cladding index. Theequivalent cladding index is found by weighing the index profile on the opposingside of the junction by the mode profile of mode m. This is illustrated in figure3.4 and expressed in the formula below.

neq =∫

∞

−∞

|φm(x)|2n(x)dx (3.6)

Because the mode profiles are normalized, the equivalent index will always lie be-tween the cladding index and the slab index: nc ≤ neq ≤ ns. Combining equations(3.4) and (3.5) results in:

Snm = rm

∫φn(x)

(φm(x)−∑

vφv(x)Svm

)dx

= rm

[∫φn(x)φm(x)dx−∑

vSvm

∫φn(x)φv(x)dx

]

34

Model

Because modes m and n are both part of the same orthonormal set, their overlapintegral reduces to the Kronecker delta:

Snm = rm

[δnm−∑

vSvmSvn

](3.7)

With δ the Kronecker delta function:

δmn =

{1 m = n0 m 6= n

(3.8)

Inspection of (3.7) shows that the back-reflections can be estimated solely fromthe forward scattering coefficients and an effective reflection coefficient. This iscomputationally much more efficient than calculating the coupling to radiationmodes and performing field matching. As a result, the presented model can beevaluated on a computer four orders of magnitude faster than rigorous methods.In section 3.2.4 we will compare the accuracy of this novel method to rigorousEM simulation. For now the found S-matrices still need to be concatenated inorder to obtain the full MMI model.

3.2.3 S-matrix concatenation

After calculating the S-matrix of the input junction Jin, the output junction Jout andthe multimode section W, the total S-matrix of the MMI can be calculated. Thestandard way of concatenating S-matrices works as follows [70–72]. Consider twocomponents, A and B that together form a system C. This is shown schematicallyin figure 3.5. All components are required to have 2N ports. The last N ports ofA are connected to the first N ports of B. Both components have an associatedS-matrix of size 2N× 2N, which are denoted A and B. Only few systems willmeet the 2N port count requirement. Any system, however, can put in the formof figure 3.5 by adding dummy ports and feed-through ports. After cascading, thedummy and feed-through ports are removed again. This is merely a mathematicalconstruct to satisfy the requirements.

The S-matrices A, B and C have to be partitioned into four N×N sub-matrices.These sub-matrices are defined as follows, with the indices of the sub-matrices in-dicating their position.

A =

S1,1 · · · SN,1 SN+1,1 · · · S2N,1...

. . ....

.... . .

...S1,N · · · SN,N SN+1,N · · · S2N,N

S1,N+1 · · · SN,N+1 SN+1,N+1 · · · S2N,N+1...

. . ....

.... . .

...S1,2N · · · SN,2N SN+1,2N · · · S2N,2N

=

[A11 A12

A21 A22

]

35


Figure 3.5: Two concatenated components, A and B, together form a system C. The portnumbering convention is shown for all components.

Using this partitioning, the sub-matrices of the full system matrix C then equal[70–72]:

C11 = A12B11(I−A22B11)−1A21 +A11 (3.9)

C12 = A12B11(I−A22B11)−1A22B12 +A12B12 (3.10)

C21 = B21(I−A22B11)−1A21 (3.11)

C22 = B21(I−A22B11)−1A22B12 +B22 (3.12)

Denoting this concatenation operation as C=Conc(A,B), the total MMI S-matrixthus equals

S = Conc(Conc(Jin,W),Jout) (3.13)

3.2.4 Verification

As mentioned, the described reflection model is approximate. It is important to getan estimate of the accuracy of the model to be able to evaluate its usefulness. Tothis end we use the simplest junction possible, between two straight waveguides ofthe same width, in the COBRA layer stack. Bidirectional Eigenmode Propagation(BEP) simulations will be used to determine reference reflection values. BEPis very efficient for simulating rectangular structures, and it includes reflectionsaccurately.

The waveguide junction was implemented using deep-etched waveguides. Thewidths were the standard 1.5 µm for this cross-section. The back-reflection as afunction of lateral offset between the two waveguides was simulated for TE polar-ized light. The results of both the BEP and our model are shown in figure 3.6. Thetwo simulation methods agree well. The presented model predicts lower reflectioncoefficients for small offsets. The final value for completely offset waveguides isthe same for both methods. Our method is significantly faster though, as only

36

Multimode interference couplers with reduced parasitic backscattering

0 0.5 1 1.5 2 2.5 3 3.5 4−30

−25

−20

−15

−10

−5

0

Lateral offset [µm]

Ref

lect

ion

coef

ficie

nt [d

B]

Model TEModel TMBEP TEBEP TM

Figure 3.6: Simulation reflection of a junction between two deep 1.5 µm wide waveguidesas a function of the lateral offset.

the guided modes have to be calculated. On a regular PC (processor Intel Corei5 M540 2.53GHz) the BEP simulation took 3 s per point. Our method simulatedthe same structure in 0.1 ms per point, thus showing four orders of magnitudeimprovement in speed.

As the described model is aimed at predicting reflections off junctions inMMIs, we also verified its accuracy for such a structure. A standard 2× 1 MMIwas analyzed when used as a combiner. Because of reasons explained in detailin section 3.3, there will be a significant reflection when using a standard MMIin this way. The MMI used has straight back-walls, is 5.0 µm wide, and 26.4 µmlong. The access waveguides are 1.5 µm wide and are 1.2 µm offset from the MMIcenter. The whole structure is deeply etched. Figures 3.7 and 3.8 show the trans-mission and reflection coefficients calculated by our model and a BEP simulation,respectively. The transmission shows a very good match, though the predictedripple is stronger in the BEP results. The stronger ripple in the BEP results canbe explained by looking at the reflection results. Our model matches the BEP rea-sonable, but under estimates the reflection. With larger reflections, interferencebecomes stronger hence a larger ripple in the BEP results.

3.3 Multimode interference couplers with reducedparasitic backscattering

This following section was published in a peer reviewed journal. Reprinted, withpermission: E. Kleijn, D. Melati, A. Melloni, T. de Vries, M. Smit, and X. Leij-tens, “Multimode interference couplers with reduced parasitic reflections,” IEEEPhotonics Technology Letters, vol. 26, no. 4, pp. 408-410, © 2014 IEEE. It is

37


1520 1530 1540 1550 1560 1570 1580−4

−3.8

−3.6

−3.4

−3.2

−3

Wavelength [nm]

Tra

nsm

issi

on c

oeffi

cien

t [dB

]


Figure 3.7: Simulated transmission through a 2× 1 MMI, when operated in combinermode.

1520 1530 1540 1550 1560 1570 1580−14.5

−14

−13.5

−13

−12.5

−12

−11.5

−11

Wavelength [nm]

Ref

lect

ion

coef

ficie

nt [d

B]


Figure 3.8: Simulated reflection of a 2×1 MMI, when operated in combiner mode, backto the input waveguide.

included here verbatim.

Abstract

Parasitic reflections can deteriorate the performance of a photonic integrated cir-cuit. This is especially true in circuits containing amplifiers, but even in passivecircuits, small reflections can already have a strong influence on circuit perfor-mance. It is known that strong reflections can be present when using a 2×1 MMIas a combiner. We investigate methods for reducing these spurious reflections ina generic integration technology. We present a novel MMI shape which measure-ments show reduces reflections by 17.5 dB.

38


3.3.1 Introduction

Multimode interference couplers (MMIs) are frequently used as splitters and com-biners in photonic integrated circuits (PICs). However, because they containabrupt junctions, these components are liable to generate parasitic reflections [73].These reflections can disturb the desired behavior of the circuit. In circuits con-taining amplifiers, parasitic reflections may cause gain ripples or even unwantedlasing. In this paper we discus a new geometry to suppress parasitic reflections inMMI couplers. We will focus on 1×2 MMIs, as they are known to be especiallyliable to generate reflections when used as combiners [74].

When used as a splitter, 1×2 MMIs divide light efficiently over the two outputwaveguides. Due to limited imaging resolution, some light will be imaged on theback edge of the MMI. The index step present there causes some light to scatterback to the input. In splitter operation the amount of back-scattered light is verylow because almost all the light ends up in the output waveguides. This is not thecase when using the same MMI as a combiner. Only when light in the two inputsis coherent, in phase, and of equal magnitude, will it be efficiently coupled to theoutput waveguide. When only the fundamental mode in one input is present, nomore than half of the light will be coupled to the fundamental mode of the outputwaveguide for reciprocity reasons. The other half of the light will be scattered andsome of it reflected backwards. This reflection process can be highly efficient dueto the imaging properties of the MMI [51, 74, 75].

Previous attempts to reduce the reflection level of 2×1 MMI combiners usedlossy waveguides [74], or reduced contrast access waveguides [76]. However, insome technologies these approaches may not work. There may not be room fordummy waveguides, or reduced contrast may not be offered by the technologyplatform. In [66], the corners of the MMI were cut to reduce reflections. Here wetake the MMI structure of [66] as a starting point, and add additional structures toreduce reflections. The approach we present can be used in any technology thatoffers designers to freely determine the waveguide shape in the plane.

3.3.2 Design

We consider deep-etched ridge waveguides in an indium phosphide based genericintegration technology, with the layer stack shown in figure 3.9. The describedapproach can be applied equally well to other technologies such as silicon oninsulator. The waveguides are defined by surrounding them with deep-etchedtrenches of width wt. As a result, most of the chip surface remains unetched. Thisstabilizes dry-etch rates, improves mechanical robustness, and eases planarization.

Figure 3.10 shows the proposed layout of the etched areas that together define

39


p-InP

n-InP

InGaAsP500 nm

1.6 μm2.2 μm

Air

1.5 μm

Figure 3.9: The COBRA layer stack. The layer thicknesses and composition are indicated.

the MMI combiner. The parameters LMMI, WMMI, wa and o, are the regular MMIparameters for the length, width, access waveguide width, and offset, respectively.The offset is defined with respect to the MMI center line. In addition, the anglesα1 through α4, together with width w1 and trench width wt, define the shape ofthe etched regions. All surfaces where reflection could occur are angled in thislayout. Additionally, the openings on the top and bottom of the MMI allow lightto continue propagating to a slab region, instead of scattering backward. Careshould be taken that this light does not couple into other structures further alongthe slab. This could be avoided by placing absorbing material some distance awayfrom the MMI.

We will compare the performance of the new proposed layout to two previ-ously reported MMI layouts. These are the the regular rectangular layout, and theshape described in [66]. We refer to the first shape as ‘Regular’, and to the secondas ‘Cut’. A number of devices of these two types were also included in our studyto serve as reference devices. A total of seven devices were designed for the layerstack of figure 3.9, which has an effective slab index of 3.27 at a wavelength of1550 nm. Their parameters are shown in table 3.1, and an image of each fabricateddevice is in figure 3.11. The basic parameters like LMMI, WMMI, wa and o are thesame for all devices. We varied the values for the angles α1 and α2. The angle α3was kept fixed at 60◦ and α4 was fixed at 15◦. The width w1 is determined by theminimum lithographical feature size. This width was fixed at 0.4 µm. The trenchwidth wt was set to 10 µm.

3.3.3 Simulation

The amount of reflection in each of the designs was numerically evaluated usinga commercially available 2D Finite Difference Time Domain method [43]. Aneffective slab index of 3.27 was used for the non-etched areas, and index 1.0 forthe etched areas where semi-conductor material was replaced by air. An 80 fs longmodal pulse centered at a wavelength of 1550 nm was used as the starting field forthe simulation. The pulse was launched into port 1. The total simulated time wasaround 1 ns in order to obtain 110 unique samples in the wavelength range from

40


(a) (b)

Figure 3.10: Low reflection MMI combiner layout. (a) 3d view of the device layout. (b)2d top view. The lighter areas are deeply-etched. The port numbers are indicated by thebold numbers.

Table 3.1: Fabricated MMI properties

Design Type L W wa o α1 α2 α3 α4ID µm µm µm µm [◦] [◦] [◦] [◦]

A Regular 26.4 5.0 1.5 ±1.2 - - - -B Cut 26.4 5.0 1.5 ±1.2 60 - - -C Cut 26.4 5.0 1.5 ±1.2 30 - - -D LR 26.4 5.0 1.5 ±1.2 60 20 60 15E LR 26.4 5.0 1.5 ±1.2 60 10 60 15F LR 26.4 5.0 1.5 ±1.2 30 20 60 15G LR 26.4 5.0 1.5 ±1.2 30 10 60 15

1500 nm to 1600 nm. In order to easily compare the performance of the differentdevices, we took the average value over the recorded spectra.

Figure 3.12 shows the simulation results for the various devices. The parasiticreflections from port 1 to port 1 and from port 1 to port 2 are suppressed, as in-dicated by the triangular and circular shapes in figure 3.12. The ‘Regular’ MMI,labeled A, has reflection levels of around −13 dB. The ‘Cut’ MMI proposed ear-lier can reduce this to−26 dB. The simulation indicates that our device design canreach reflection levels of −35 dB. Figure 3.12 also shows the transmission fromport 1 to 3 and that it is not affected by the change in shape of the MMI.

41


A B C D E F G

Figure 3.11: Optical microscope image of the fabricated devices. Device D through Guse the new layout.

A B C D E F G−40

−35

−30

−25

−20

−15

−10

−5

0

Ref

lect

ed [d

B]

Design

−7.0

−6.5

−6.0

−5.5

−5.0

−4.5

−4.0

−3.5

−3.0

Tra

nsm

itted

[dB

]

Port 1 to 1Port 1 to 2Port 1 to 3

Figure 3.12: FDTD simulation result. Reflection level from port 1 to port 1 and fromport 1 to port 2 is shown on the left y-axis. The transmitted light from port 1 to port 3 isshown on the right y-axis. A low reflection of around −35 dB can be obtained by settingα1 = 30◦ and α2 = 10◦.

3.3.4 Measurement

The devices were fabricated at NanoLab@TU/e, in an all-deep indium phos-phide generic integration technology. The devices were characterized by mak-ing a wavelength sweep. The measurement setup used is shown in Figure 3.13.An Ando AQ4320A tunable laser is controlled by an optical spectrum analyzer(Ando AQ6317) and the transmitted and reflected power is recorded as a func-tion of wavelength. A laser power of 5 dBm was used and the OSA bandwidthwas set to 2 nm. The chip was temperature stabilized at 25 ◦C by a Peltier ele-ment. We refer to the signal going from the first lensed fiber to the second lensedfiber as ‘forward’, and to the signal at port 3 of the circulator as ‘backward’. Apolarization controller was used to ensure that only TE polarized light was cou-pled into the chip. Port 1 and port 3 of the MMI are led to straight facets usingmono-mode waveguides. MMI port 2 is led to an angled facet, which stronglysuppresses reflections from that point.

42


DUT

CirculatorPolarizationController

TLSOSA

LFLF1 2

3

Figure 3.13: Measurement setup. TLS: tunable laser source, LF: lensed fiber, DUT: de-vice under test, OSA: optical spectrum analyzer. The optical spectrum analyzer is syn-chronized to the TLS. This strongly suppresses ASE noise from the laser and enables highdynamic range.

0 5 10 15 20−40

−30

−20

−10

0

Cavity length [mm]

Rel

ativ

e in

tens

ity [d

B]

Q1 AQ1 E

P+QP+R

P

Q

R

Q+R

Figure 3.14: Example length domain signals for devices A and E from quarter Q1. Theinset shows the possible paths (P,Q,R) through the chip. The bars above the peaks showthe integration ranged used. Path Q+R is not used.

The parasitic reflections of the different devices are evaluated as follows. Firsta wavelength sweep from 1520 nm to 1580 nm with 12001 points was performed.Each uncoated straight facet gives a reflection of around 30 %. There are nowmultiple possible paths light can take through the chip. Light from each pathcan interfere with light from each other path. By taking a Fourier transform of thewavelength spectrum, a length domain signal is obtained, where each combinationof paths causes a peak to appear at the length difference between paths. The peakheight is determined by the relative total path loss in both paths. Figure 3.14shows the Fourier transformed signal, and the identified paths (P,Q,R) togetherwith their associated peaks. By integrating over a peak, its energy content canbe determined. Each peak can be normalized with respect to the peak formed bypaths P and Q. For proper normalization, the waveguide propagation loss needs tobe known. This was determined to be 2.0 dB/cm in a separate measurement. Themagnitude of the parasitic MMI reflection follows from the peak height of paths Pand R. This method can be applied to either the forward or backward signal. Onlythe response from MMI port 1 back to port 1 was characterized. The simulationsof the previous section show that the reflection level from port 1 to port 3 is verysimilar.

43


The results of the analysis of the measurement data is shown in figure 3.15.An uncertainty margin of ±1.5 dB is indicated. Around 1 dB comes from un-certainties in the MMI transmission, 0.3 dB from uncertainties in facet reflection,and 0.2 dB from waveguide losses. Devices from three quarters (Q1, Q2, Q3) ofthe same wafer that were processed separately, were characterized. Q1 and Q3were etched 650 nm below the core, while Q2 was intentionally etched deeperto 880 nm below the core. Figure 3.15 clearly shows that quarters Q1 and Q3behave similarly. For some devices from Q2 the measured value deviates fromQ1 and Q3. The LR devices from Q2 perform either the same or better, whichindicates that they are more tolerant to variations in etch-depth. In all cases, thevalues obtained for the forward and backward measurements are very similar. ForQ1 and Q3, the regular and cut devices perform better than expected from sim-ulation. This can be explained by the fact that the waveguide sidewalls are notperfectly vertical, which is assumed in the simulation. The simulation showedonly a small difference in reflection level between α2 = 20◦ and α2 = 10◦. Themeasurements indicate a stronger dependence on this angle, with α2 = 10◦ per-forming significantly better. The measured values for the design with α1 = 30◦

also differ notably from the simulated values. This is quite surprising, becausewhen looking at figure 3.10b, it is clear that the influence of α1 on the geometry ismuch less than that of α2. A possible explanation for the observed difference withsimulation results is a change in fabrication tolerance from device to device. Asimulation, in which all widths were increased by 0.1 µm showed a slightly lowertolerance for the new design (3 dB higher reflection vs 1 dB), but no dependencyon α1. Taking the average over all measurements, device E performs the best with−34.8 dB. The best of the Cut MMIs is C with −27.5 dB on average. This is a7.3 dB improvement, and a 17.5 dB improvement when compared to the regularMMI.

3.3.5 Conclusion

It was shown experimentally that the reflection level in deep-etched, high-contrastMMIs can be reduced to−34.8 dB by optimizing the MMI geometry. This meansa strong reduction in parasitic reflections can be accomplished with respect to thestandard MMI. The improvement with respect to MMIs with angled back-walls is7.3 dB. This approach can be applied to technologies that use trenches to definewaveguides.

3.4 MMI based 90◦ optical hybrid

A key component in optical coherent receivers is a 2×4 90◦ optical hybrid. Sucha hybrid combines a local oscillator signal (LO) with a received signal (S) and

44

MMI based 90◦ optical hybrid

A B C D E F G−40

−35

−30

−25

−20

−15

−10

Design

Ref

lect

ed [d

B]

Q1 backwardQ1 forwardQ2 backward

Q2 forwardQ3 backward

Q3 forward

Figure 3.15: Measurement results of reflection level from MMI port 1 to port 1. Theforward points are obtained by analyzing the transmitted signal, the backward points byanalyzing the reflected signal. Q1, Q2, and Q3 indicate three separately processed quar-ters of an InP wafer. Q1 and Q3 have an etch depth of 3.16 µm. Q2 was intentionallyetched deeper, down to 3.33 µm.

presents them with special phase relations at its output. At the four outputs, thephase differences between the two signals are 0, 90, 270 and 180 degrees re-spectively. By applying balanced detection to the pairs (0,180) and (90,270), thein-phase and quadrature parts of the signal can be detected. Balanced detectionallows for suppressing common distortions and improves the signal-to-noise ra-tio. Several method exists for creating 90◦ hybrids, one of which is using a 4×4MMI [77]. Such a MMI is shown in figure 3.16.

3.4.1 Design

The ideal phase relations of a 90◦ hybrid are shown in figure 3.16. It can beshown that an ideal 4× 4 MMI has exactly these phase relations [78]. Several4× 4 MMIs were designed and fabricated in a MPW at Oclaro. The designs areoptimized for TE polarization using the following procedure. The width of theMMI is chosen first. In order to have sufficient modes for good quality imaging,the width of the MMI was set to 12 µm. The optimum offset is then close toWMMI/8 ≈ 1.5 µm, and numerical optimization shows 1.504 µm to be optimal.The numerical optimization is done using the model described in section 3.2, andminimizes the following cost function.

J = 1−|S16|2−|S26|2−|S36|2−|S46|2

This corresponds to maximizing the MMI power transmission from port 6 to alloutputs. The length of the MMI was thus found to be 300 µm. Fabrication devia-

45


Table 3.2: 4×4 MMI designs

Design W L wa oID µm µm µm µmA 11.9 300 2.35 1.504B 12.0 300 2.35 1.504C 12.05 300 2.35 1.504D 12.1 300 2.35 1.504

Figure 3.16: Schematic representation of a 4×4 MMI, with port numbers shown in red.When the S and LO signals are presented at ports 8 and 6 respectively, the indicated outputrelations are obtained in an ideal device.

tions can cause the width of the fabricated MMI to vary up to a hundred nanome-ters. The constant part of this variation can be compensated for in the design. Atotal of four MMIs with widths of 11.9 µm, 12.0 µm, 12.05 µm and 12.1 µm areincluded on the final mask. Table 3.2 shows their design parameters.

The performance of a 90◦ hybrid is normally quantified by the phase errorsin the device, and by the Common Mode Rejection Ratio (CMRR). Looking atfigure 3.16, the following equations for the phase errors can be derived. In asystems application, phase errors need to be below 5◦ [79].

ε0 = (6 S16− 6 S18)− (6 S46− 6 S48)−180 (mod 360) (3.14)

ε1 = (6 S26− 6 S28)− (6 S36− 6 S38)−180 (mod 360) (3.15)

ε2 = (6 S16− 6 S18)− (6 S26− 6 S28)−90 (mod 360) (3.16)

Similarly, the CMRR can be expressed in terms of the device S-parameters aswell. The CMRR describes the balance of the signals that would be detected bya balanced photo detector at ports 1 and 4, and at ports 2 and 3. For adequateperformance in a system, the CMRR values need to be larger than 20 dBe [79].The following equations relate the CMRR, expressed in electrical decibels (dBe),

46


11.5 12 12.5−20

−10

0

10

20

MMI width [µm]

Pha

se e

rror

[°]

ε0

ε1

ε2

(a)

11.5 12 12.50

10

20

30

40

50

60

70

MMI width [µm]

CM

RR

[dB

e]

CMRR

Q1

CMRRI1

CMRRI2

CMRRQ2

(b)

Figure 3.17: Phase errors and CMRR versus MMI width.

to the S-parameters.

CMRRI1 =−20log10

(|S16|2−|S46|2

|S16|2 + |S46|2

)(3.17)

CMRRQ1 =−20log10

(|S26|2−|S36|2

|S26|2 + |S36|2

)(3.18)

CMRRI2 =−20log10

(|S18|2−|S48|2

|S18|2 + |S48|2

)(3.19)

CMRRQ2 =−20log10

(|S28|2−|S38|2

|S28|2 + |S38|2

)(3.20)

Only TE polarization was considered, even though hybrids are also used inpolarization diversity schemes. The strong birefringence of InP waveguides usu-ally requires separate handling of both polarizations. This splitting is commonlydone off-chip, after which the TM polarization is rotated to TE. The S-parametersof the device were simulated for TE at a wavelength of 1550 nm as a functionof MMI width. Equations (3.14) through (3.20) were used subsequently to findthe phase errors and CMRR values. Figure 3.17a shows that phase error of lessthan 5◦ are obtained for widths between 11.7 µm and 12.25 µm. From figure 3.17bwe see that CMRR exceeds 20 dBe for widths between 11.85 µm and 12.15 µm.The design is therefore tolerant to width deviations in the order of 100 nm. Suchperformance is considered good in system applications.

3.4.2 Test structure

In a S-parameter simulation, the phases of output signals can be inspected directly.In a measurement in the lab this is not feasible due to the very high frequency ofthe optical signals. Interferometric techniques are therefore used to measure phase

47


Figure 3.18: The test structure for 4×4 MMIs.

differences between coherent optical signals. The structure we employ is an im-balanced Mach-Zehnder interferometer that is formed out of a 1×2 MMI and the4× 4 hybrid, like in [80]. The outputs of the 1× 2 are connected to the S andLO ports of the 4× 4, using two different lengths of waveguide. A length dif-ference of 100 µm gives rise to a wavelength dependent phase difference betweenlight entering the S and LO ports. This causes interferences at the four outputsof the 4×4 with a Free Spectral Range of 6.5 nm. The relative phase differencesbetween the S and LO signal at the outputs of the 4× 4 can then be determinedby performing a wavelength sweep and recording the output powers. The teststructure is shown schematically in figure 3.18. A simulation of the wavelengthresponse of this structure is shown in figure 3.19. This test structure is well suitedfor determining the phase errors of the 4× 4. Because the test structure excitestwo inputs of the 4× 4 simultaneously, the amplitude response from individualinputs to outputs cannot be determined accurately. We will therefore focus on thephase properties of the devices.

The simulated typical transmission spectrum of the test structure for a 12 µmwide MMI is shown in figure 3.19. The interference pattern is clearly visible.Power varies sinusoidally over the output waveguides. By fitting sinusoids to thecurves, the phase errors can be estimated.

3.4.3 Fit method

As mentioned, a fit procedure is necessary to extract the phase errors from a trans-mission measurement, such as the one shown in figure 3.19. Because some effectsare ignored during fitting, there will be an inherent error in the found phase errors.To evaluate the magnitude of this error, we first fit simulated data and compare theresults with the input to the simulation. The simulated data is fitted with a totalof 14 fit coefficients, which are indicated by cx in the following equations. These

48


1520 1530 1540 1550 1560 1570 15800

0.1

0.2

0.3

0.4

0.5

Wavelength [nm]

Tra

nsm

issi

on

Out 1Out 2Out 3Out 4

Figure 3.19: Typical simulated transmission spectrum of a test structure for a 12 µm wide4×4 MMI hybrid.

equations represent expressions for the transmitted power at each port.

P1(λ) = c20 + c2

1 +2c0c1 cos(c2 +∆φ(λ)) (3.21)

P2(λ) = c23 + c2

4 +2c3c4 cos(c5 +∆φ(λ))

P3(λ) = c26 + c2

7 +2c6c7 cos(c8 +∆φ(λ))

P4(λ) = c29 + c2

10 +2c9c10 cos(c11 +∆φ(λ))

∆φ =2πc12

λ

(N0 +(λ−λ0)

∆N∆λ

+(λ−λ0)2c13

)(3.22)

It is important to realize that the same values for ∆φ must be used for each ex-pression. In practice this means all expressions have to be fitted simultaneously.The phase errors can be estimated from the fit coefficients c2, c5, c8, and c11 asfollows:

ε0 = c11− c2−180 (mod 360)

ε1 = c8− c5−180 (mod 360)

ε2 = c2− c5−90 (mod 360)

Generally there is a residual error when fitting data. This limits the accuracyof this method. In a simulation of a bare 4×4, the output phases can be inspecteddirectly. The complete test structure can also be simulated, and then fitted. Bycomparing the phase errors obtained through direct inspection and through fitting,the accuracy of the fit method can be determined. A comparison between phaseerrors obtained directly from S-parameters and from a fitting algorithm is shownin figure 3.20. All estimated phase errors are within 2◦ of the actual phase error.

49


1520 1530 1540 1550 1560 1570 1580−4

−2

0

2

4

6

8

10

Wavelength [nm]

Pha

se e

rror

[°]

Ref ∠0 − ∠3 − 180

Ref ∠1 − ∠2 − 180

Ref ∠0 − ∠1 − 90

Est ∠0 − ∠3 − 180

Est ∠1 − ∠2 − 180

Est ∠0 − ∠1 − 90

Figure 3.20: Actual phase error versus estimated phase error based on fitting algorithm.

The described model is now fitted to measured data through a least squaresbased algorithm [81]. For this particular algorithm a good initial estimate is re-quired for convergence. When the considered measured data contains at least oneperiod of the response it is relatively straight forward to obtain a reasonable startestimate. Looking at (3.21), it is apparent that the expressions for each output portin the presence of noise are of the form

Pi(λ) = a2 +b2 +2abcos(c+∆φ(λ))+n(λ)

where n(λ) is assumed to be zero mean measurement noise. Estimates for a andb are readily calculated as

a =

√µ+σ+

√µ−σ

2

b =

√µ+σ−

√µ−σ

2

with

µ =

∫λbλa

Pi(λ)dλ

λb−λa

σ =maxPi−minPi

2

These expressions are only valid if the measured signal contains at least one fullperiod of the response. In that case, the value for c can be estimated by locatingthe position at which the maximum occurs. Let

λmax = arg{

maxλ

Pi(λ)

}50


It follows then thatc =−∆φ(λmax)

Applying this to all four measured output signals results in estimates for c0 throughc11. This leaves just the two coefficients used to describe ∆φ. Recalling (3.22), wealso have to specify N0, λ0, and ∆N/∆λ. These values can be easily obtained froma mode solver. We choose λ0 = 1550 nm. The mode solver reported a phase indexN0 of 3.25 and a group index Ng of 3.69 at this wavelength. From these values itis straight forward to calculate ∆N/∆λ:

∆N∆λ

=−Ng−N0

λ0

The start value for c12 follows from the mask design and is equal to the lengthdifference in the unbalance MZI arms. The last coefficient c13 describes the groupvelocity dispersion and can be initialized to zero when small wavelength rangesare considered.

3.4.4 Measurements

After fabrication by Oclaro in a MPW run, a total of 10 chips were character-ized. Each chip features four different 4×4 devices. Unfortunately, a step in thefabrication failed, causing severe roughness and pitting of the side of the wave-guides. Reported losses were 20 dB cm-1 for waveguides parallel to the majorflat, and around 40 dB cm-1 for waveguides perpendicular to the flat. Addition-ally, the processing issues caused a relatively high number of defects, renderingsome structures unmeasurable. The transmission spectrum of the working struc-tures was recorded on an optical spectrum analyzer, while coupling light from anEDFA into the input waveguide. A free space polarization filter was used at theinput side to be able to record either the TE or TM spectrum. Input coupling wasperformed using a 40× objective. For output coupling, a lensed fiber with a spotsize of 3 µm was used.

After the transmission spectrum was obtained, we applied the described fittingmethod to extract the phase errors. Though the data was collected in a singlemeasurement, the analysis used spectral slices of 5 nm in width at a time. Thisallows to gain some insight into the wavelength dependence. From among 10different chips, we found two with a full working set of devices. A second chiphad working devices A, C and D. Data from a fourth chip was used as a thirdinstance of device B. We then proceeded by averaging the fitted phase error for alldevices of the same type. The result for ε0 is shown in figure 3.21. A clear trend isbetter performance at shorter wavelengths (1530 nm) than at longer wavelengths(>1560 nm). For the wider designs (C, D) this difference was reduced, leading

51


1525 1530 1535 1540 1545 1550 1555 1560 1565 1570−10

0

10

20

30

40

Wavelength [nm]

Pha

se e

rror

[°]

ABCD

Figure 3.21: Fitted phase error from measurement data. Only ε0 is shown, the other twophase errors behave similarly, but are smaller in magnitude.

1525 1530 1535 1540 1545 1550 1555 1560 1565 1570−10

0

10

20

30

40

Wavelength [nm]

Sim

ulat

ed p

hase

err

or [°

]

ABCD

Figure 3.22: Fitted phase error from simulation data. Only ε0 is shown, the other twophase errors behave similarly.

to a flatter phase error across wavelength. Figure 3.22 shows the simulated phaseerror for the same device types. The simulated phase error does not show theincrease with wavelength. We were unable to reproduce this particular behaviorby changing the width, length and access waveguide width in the simulation. Itmay very well be that the very large waveguide roughness has something to dowith the increased phase error at long wavelengths.

3.4.5 Conclusion

Simulations show that good 4×4 MMI performance can be obtained in InP basedintegration technology. For the Oclaro layer stack, simulation showed phase errorsbetween +5◦ and −5◦, and CMMR between 20 dBe and 50 dBe can be achieved.

52


A number of devices was fabricated, though extreme roughness occurred due to afailed etch step. The measured phase errors were considerably larger than simu-lations suggested. They ranged from −3◦ up to 35◦.

53

4Multi-mode interferencereflectors

The content of this chapter was previously published in a peer reviewed journal.Reprinted, with permission, from E. Kleijn, M. Smit, and X. Leijtens, “Multi-mode interference reflectors: a new class of components for photonic integratedcircuits,” Journal of Lightwave Technology, vol. 31, no. 18, pp. 3055–3063, ©2013 IEEE. It is included here verbatim.

4.1 Multimode interference reflectors: a new class ofcomponents for photonic integrated circuits

Abstract

Multimode interference devices are very versatile components that are often usedas components for power splitting or combining in larger circuits. In this paper wepresent a new class of multimode interference couplers that are designed to reflectall or part of the light. The components can act as on-chip mirrors with partial out-coupling, or they can act as compact mirrors with full reflection. We present anoverview of such devices, the basic theory and practical design guidelines. Theirsimple layout makes these devices easy to fabricate and tolerant to fabricationerrors. We fabricated devices of several types and present the experimental results.

4.1.1 Introduction

Reflective elements are important in photonic integrated circuits. They are essen-tial parts in Fabry-Pérot lasers and in many resonator structures. In indium phos-phide photonic integrated circuits (PICs), broadband reflective elements are con-ventionally formed by cleaved facets of the semiconductor [82], by deep-etchedshort Distributed Bragg Reflector (DBR) gratings [83] (also known as slots in thewaveguide) or by loop mirrors [84]. Each of these reflector types has its meritsand drawbacks.

Cleaved facets are relatively easy to obtain by cleaving the semiconductor.They can be used as reflectors, but any transmitted light is no longer available onchip. The reflection coefficient can be set through coating with metal or dielectric

55

Chapter 4. Multi-mode interference reflectors

layers [82], but this introduces extra non-trivial process steps. Furthermore, thecleaving process is not very accurate (±10µm). This causes uncertainty in thecavity length of a laser formed by two cleaved facets. This in turn causes themode spacing to differ between different fabrication runs.

DBRs can be placed anywhere on the chip, unlike cleaved facets. The lighttransmitted through a DBR is still available on chip. This property allows forcreating integrated filtered-feedback lasers [85]. Two main types of DBRs exist:shallow and deep. Shallow DBRs have low index contrast, while deep DBRs havea high index contrast. Only deep-etched DBRs have a broadband response [86].They can be short, with periods in the order of a few hundred nm to a fewµm [83, 87]. Their fabrication is quite demanding due to the sub-wavelengthfeature sizes and high aspect ratios required. Integrating DBRs with other com-ponents imposes restrictions to the fabrication process [83]. Furthermore, deep-etched DBRs require a very high degree of process control to obtain the desiredreflection/transmission ratio.

Integrated loop mirrors are formed by connecting the outputs of a splitter witha waveguide [84, 88, 89]. There are no restrictions on their on-chip position andtransmitted light is still available on chip. When using Multi Mode Interferencecouplers (MMIs) as the splitter, loop mirrors are easy to fabricate and have a largefabrication tolerance. Unfortunately, these structures are usually quite large as atleast a 180◦ bend is needed to connect the splitter outputs [90].

In [91], we demonstrated a new type of broadband reflector, the so called Mul-timmode Interference reflector (MIR). MIRs can also be placed anywhere on thechip, and the transmitted light is still available on chip. They have a broadbandresponse. They can therefore be a substitute for deep-etched DBRs and loop mir-rors. With typical sizes ranging from 20 µm to 100 µm they are a lot smaller thanloop mirrors, but larger than deep DBRs. The main advantage of MIRs over DBRsis their ease of fabrication. MIRs have high fabrication tolerances with respect tothe length and width of the device. Because MIRs are defined during the deepwaveguide lithography and etch steps, they require no extra processing steps fora process that includes deep-etched waveguides with vertical sidewalls. Due tothese advantages they have already been applied in several circuits [92, 93]. Inthis paper we describe the theory, provide design rules and formulas, and indicatethe achievable performance when using MIRs.

We begin in section 4.1.2 by deriving MIRs from MMIs. In section 4.1.3 thelocation of the MIR mirrors for low loss operation is calculated. We continueby investigating the losses introduced by the mirrors. Section 4.1.5 describes anumber of practical MIR designs. Simulation methods are discussed in section4.1.6. A description of the measurements and the setup used can be found insection 4.1.7.

56

Multimode interference reflectors: a new class of components for photonicintegrated circuits

Figure 4.1: A 1× 1 MMI forms the basis for a 1-port MIR. The dashed shape showsthe original MMI. The shaded shape is the resulting MIR. The mirror rounding due tolimited lithographical resolution is depicted. Self-imaging ensures no light is imaged onthe rounded area. This means low loss operation can be achieved.

4.1.2 Basic operation principle

Suppose a regular single mode waveguide is terminated by ending the waveguidewith two 45◦ etched facets. The two facets meet exactly in the center of thewaveguide forming a 90◦ tip. We will refer to this position as the mirror tip.Ideally, the waveguide mode is fully reflected by the mirrors. In reality, the mirrortip will be rounded due to limited lithographical resolution. This leads to poormirror quality, exactly on the position with the highest field intensity. Therefore itis difficult to obtain low loss reflectors in this way. In our approach, we exploit theself-imaging properties of multi-mode waveguides to ensure a low field intensityon the position of the corner where the mirror quality is poor.

Essentially, MIRs are designed by adapting an MMI. The simplest example ofthis is the 1-port MIR, shown in figure 4.1. This reflector is based on a 1×1 MMI.Two deep-etched 45 degree mirrors are placed in such a way that the point wherethey meet is exactly in the center of the MMI. Light coupled into the multimodesection of the MIR will now reflect off the 45 degree mirrors and propagate backtowards the input. The reflection loss can be low when total internal reflectiontakes place. For this, the critical angle has to be sufficiently larger than 45 degrees.Assuming that the surrounding material is air, this condition is satisfied in manywaveguiding materials such as semiconductors like indium phosphide and silicon(≈ 70◦). The principle can also be applied to low index contrast materials such asglass, but care should be taken that every mode satisfies the total internal reflectioncondition. By using MMIs with a higher port count as a basis, N-port MIRs canbe obtained.

Similar to MMIs, MIRs show high fabrication tolerances, polarization insen-sitivity and operation over large wavelength ranges [51,94]. Furthermore, they areeasy to fabricate as the technology only has to support deep-etched waveguideswith reasonably vertical sidewalls. This facilitates easy integration with other

57


components. Existing active-passive integration schemes can be used to integrateMIRs with optical amplifiers to form lasers.

Not every MMI can be adapted to form a low loss MIR. The next sectionderives the requirements that need to be fulfilled to obtain a well performing MIR.

4.1.3 Central image

Ideally, one would like to place the MIR mirror tip in the center of the under-lying MMI. In this area, light is focused into twice the number of images as atthe output of the MMI [51]. This focusing is maintained under the introductionof the mirrors. Therefore, generally speaking, an MIR is half the length of theoriginal MMI. Unfortunately, the tip of the mirror is usually a bit rounded due tolithographical effects. Consequently, if there is light imaged there, it will not bereflected perfectly and a loss penalty is incurred. Using MMI theory, the positionof the images can be calculated. Here we derive general conditions for which acentral image exists. To this end we first describe all MMI types as an instance ofa general MMI. This allows to find general equations that are valid for any MMItype.

The equivalent MMI

In [51], the general, paired and symmetric interference mechanisms of MMIs areidentified. MMIs based on a specific interference mechanism may have restric-tions to the number and placement of inputs. It can be shown [78] that all thoseMMIs can be modelled as an instance of the N′×N′ MMI shown in figure 4.2.This equivalent MMI has inputs i and outputs j. The parameter a can be chosenfreely within the bounds 0 ≤ a ≤W/N′. The length of the MMI approximatelyequals 3Lπ/N′, where [51]

Lπ =π

β0−β1≈ 4NeffW 2

e

3λ(4.1)

with Neff the effective slab index and We the effective MMI width.Table 4.1 shows how the parameters of the equivalent MMI should be config-

ured to model a certain MMI type.

Phase relations

In [78] the phase relations between inputs i and outputs j were derived for thegeneral MMI. These relations can be used to calculate for which combination ofN′, a and i, a central image does not exist. In the appendix we derive that a central

58


Figure 4.2: General N′×N′ MMI coupler. The parameter a can be freely chosen withinthe bounds 0≤ a≤W/N′.

Table 4.1: Equivalent MMI parameters for the MMI types described in [51] and [95]

Type N′ i1 a1

General N⌈ xN′

W

⌉+1

2±12 for a ∈ {0,W/N′} W

N′(1−∣∣1− ( xN′

W mod 2)∣∣)

N×N⌈ xN′

W

⌉elsewhere

Overlapping N 1≤ i≤ N′ 0 for i evenbN

2 c×bN2 c W/N′ for i odd

Paired 3N N′6 (3±1) 0 for i even

2×N W/N′ for i odd

Symmetric 4N N′/2 01×N

1 with x the input waveguide position relative to the MMI bottom edge.

59


image does not occur for

N′ oddN′ even and a 6=W/N′

(4.2)

Many MMIs can therefore be used to form a compact MIR. Some MMIs with acentral image can still be used as a basis for a MIR. The mirror tip then has to beplaced at the end of the MMI, between the output waveguides. This will doublethe length of the MIR.

It should be mentioned that there is no strict lateral guiding in the area betweenthe mirrors. This influences the imaging properties of the device. Especiallyfor high port count devices, imaging losses will increase under introduction ofthe mirrors. The image closest to the edge in the original MMI will be mostinfluenced by this effect. In a General N×N MMI with equidistant inputs, thisimage is a distance W

2N from the edge. When adding mirrors to form a MIR,lateral guiding is lost for this image along a length W/2. These two distancestogether define an angle θlim = arctan

(W/2

W/2N

)= arctan(N−1). The image will

not be disturbed much by the presence of the mirror if its diffraction angle θ0 issufficiently below θlim. The diffraction angle is related to the numerical apertureof the image. Approximating the waveguide modes by a Gaussian field we thusobtain the following requirement:

Neff sin(θ0) = NA =λ0√

2πweff� Neff sin

(arctan(

1N))

(4.3)

with Neff the effective slab index and weff the effective Gaussian width of the inputwaveguide mode. Rewriting this, we obtain the following condition for N:

N�

√2πw2

effN2eff

λ20

−1 (4.4)

Equation (4.4) shows that the limit on N increases with increased modefield diam-eter. As tolerances also become more relaxed with increased modefield diameter,it is advisable to make the input waveguides as wide as possible [51].

4.1.4 Mirror losses

So far the mirrors were assumed to be perfectly vertical and perfectly smooth.However, due to fabrication imperfections, in reality the mirrors will not be ex-actly perpendicular to the substrate and will have some roughness. The angle themirrors make with the substrate is influenced by the etch method used. A devia-tion from the ideal angle will cause a loss. Plane wave expansion methods have

60


(a) Top view (b) Side view

Figure 4.3: The above geometry was used to simulate the influence of the sidewall angleα on the mirror reflectivity. The distance d is used to correct for the Goos-Hänchen effect.The refractive index of the layers and their thicknesses are indicated. The top claddinglayer is formed from p-doped indium phosphide. The core layer is a multiple quantumwell quaternary material. The substrate is n-doped indium phosphide. The surroundingmaterial is air.

been widely employed to simulate the effect of similar angle deviations in cornermirrors. Those results can be used to estimate the effect in MIRs.

We analyzed the geometry shown in figure 4.3 using the method proposedby Besse in [96]. The angle α between the sidewall and the normal was swept.To compensate for the Goos-Hänchen effect, the mirror was shifted by a smallamount d. The optimum value of d for TE polarization in our layer stack wasfound to be 0.021 µm. This is an order of magnitude smaller than the analyticalvalue for the Goos-Hänchen effect. We believe that diffraction effects may causethe optimal value to differ. The waveguide width w was fixed at 1.5 µm. Thesurrounding medium was air. The mirror loss of a single mirror as a function of α

is shown in figure 4.4. As α approaches zero losses do not disappear completely.This is due to diffraction effects at the point where the two waveguides meet.This effect is an artifact of the model and is not present inside MIRs. The 0.5 dBtolerance is approximately 4◦. This corresponds to a 1 dB tolerance when usingtwo mirrors to form a MIR.

4.1.5 Practical MIR examples

We expect that 1-port and 2-port MIRs will find the most wide spread use out ofall possible MIRs. We therefore discuss the possible designs of these devices indepth.

61


−5 −4 −3 −2 −1 0 1 2 3 4 50

0.5

1

1.5

Sidewall angle [ °]

Mirr

or lo

ss [d

B]

TETM

Figure 4.4: Simulated maximum device reflectivity as a function of sidewall angle. Sur-face roughness is not taken into account.

Table 4.2: 1-port MIR types

Type Length input location input symmetry schematic

General 3Lπ/2 any anySymmetric 3Lπ/8 W/2 even

Paired 3Lπ/6 W/3, 2W/3 even

1-port MIR

A number of different options exist for making 1-port MIRs. The options can beobtained from table 4.1 by setting N to 1. We then see that a general interference1×1, a symmetric interference 1×1 and a paired interference 2×1 can be usedas basis. None of these MMIs has a central image. We can therefore set LMIR =LMMI/2. Table 4.2 list the properties of the different 1-port MIRs. It shows thatthe shortest device is symmetric interference based. This type only works foreven symmetric input fields. This causes a 1-port MIR based on this principle towork as a reflective mode filter [97]. The paired interference based 1-port MIRalso only works properly for even symmetric input fields. It therefore does notadd anything in terms of functionality, as the device is bigger than the symmetricinterference based device. The general interference based device, however, doesfunction well for odd symmetric input fields. This means it will reflect any inputfield.

2-port MIR

By offering not only reflection but also transmission, 2-port MIRs are able to re-place many existing on-chip integrated reflectors. They are based on 2×2 MMIs.From table 4.1 it can be seen that a number of different 2× 2 MMIs exist. Themost obvious are the general interference and paired interference based devices

62


Table 4.3: 2-port MIR types

Type Wmin Length input input ratio schematiclocation symm. R:T

General 2Wwg+g 3Lπ/4 Wwg2 , W−Wwg

2 any 50:50Paired 3(Wwg+g) 3Lπ/12 W/3, 2W/3 even 50:50

C 2(Wwg+g) 3Lπ/4 W/4, 3W/4 even 50:50D 5

2(Wwg+g) 3Lπ/10 W/5, 3W/5 even 72:28

with N = 2. Two overlapping image 2×2 MMI devices also exist. They are de-scribed in detail in [95] and allow for non-equal split ratios. Known from [65] asbasic type C and D, they have parameters N = 4, i ∈ {1,3} and N = 5, i ∈ {2,3}respectively. Their split ratios are 85:15 and 72:28 for C and D respectively.

Applying the central image check derived in section 4.1.3, we find that thetype C device has a central image. We therefore place the mirrors not at 3Lπ/8,but at 3Lπ/4. This also changes the split ratio of the C type reflector to 50:50,instead of the original 85:15.

Table 4.3 list the properties of the different 2-port MIRs. The minimum widthWmin is set by the width of the input waveguides Wwg and the required lithograph-ical gap g to ensure proper etching. Equation (4.1) shows that Lπ is proportionalto W 2. Using this relation, it can be shown that the General interference based de-vice is the shortest for Wwg/g < (1+

√10)/3. For larger input waveguide widths,

the type D device is shorter. When a 50:50 split ratio is essential, then the pairedinterference based device is shorter for Wwg/g > 1+

√3.

The split ratios are not necessarily restricted to 50:50 and 72:28, as table 4.3might suggest. Tapering the MIR, similar to what has been done for MMIs in [65],can change the split ratio to in principle any possible value.

4.1.6 Simulation methods

Due to the reflector element in MIRs, the propagation inside the devices is omnidi-rectional. As a result, some of the simulation methods suitable for MMIs cannotbe directly applied to MIRs. If the mirrors are assumed to be perfect, then anequivalent geometry can be found that can be simulated using bidirectional andunidirectional methods.

Suppose a mode that is guided by the multi-mode section of a MIR is incidenton the two 45 degree mirrors. After reflecting off both mirrors, the direction ofpropagation of the mode will have been reversed. Due to total internal reflection,there will also be a mode dependent phase shift [98]. We will ignore this phase

63


shift for now in the analysis. An additional effect of the corner mirror is thatthe mode shape will have been mirrored over the center line of the MIR (the zaxis in figure 4.1). This means that the field Ψ−(x,y,z) of a mode that has beenreflected by the mirrors can be expressed in terms of the field Ψ+(x,y,z) of aforward propagating mode:

Ψ−(x,y,z) = Ψ+(−x,y,2LMIR− z) for 0≤ z≤ LMIR (4.5)

with LMIR the length of the MIR, where we assume that z = 0 corresponds to theentrance of the MIR and that x = 0 marks the center line of the MIR. Equation(4.5) shows that the backward propagating field at the entrance of the MIR can beobtained by evaluating the forward propagating field at (−x,y,2LMIR− z). Thisfield can be obtained by using the regular simulation methods for MMIs, suchas Modal Propagation Analysis or Beam Propagation Method (BPM). We usedBPM to evaluate the performance of MIRs and compared the results to a hybridsimulation method that is able to take effects from the mirrors into account.

BPM

We used a commercial 2D BPM program [43] to analyze the equivalent unidi-rectional structure derived above. The simulated two-port MIR is of type C andwas designed for a layer stack with and effective index of 3.25. It has a width of6.0 µm and a length of 78.5 µm for a central wavelength of 1550 nm for TM pola-rization. The input waveguides are 2 µm wide and are located at±1.5 µm from theMIR center line. The results of this simulation are shown in figure 4.5, togetherwith the results for the hybrid simulation method, which is described below. Thedevice shows a 1 dB bandwidth of more than 100 nm. The normalized reflectionRnorm, defined as R/(R+T ), has a practically constant value of 0.5±0.03.

Using BPM, the tolerance to width deviations can also be simulated. Theresult of this simulation is shown in figure 4.6.

Hybrid BPM and FDTD

FDTD is an omnidirectional method and can thus simulate the full mirror struc-ture. It is also very computation intensive, which limits the size of the structuresthat can be simulated. By dividing the MIR into parts and selectively applying ei-ther BPM or FDTD, both the speed of BPM and the omnidirectionality of FDTDcan be exploited. Such a simulation is possible using a commercial software pack-age from Phoenix [43]. Figure 4.7 shows how the device is partitioned in thismethod.

An optimization of the length of the same type D device as described earlierwas performed using the hybrid method. It shows an optimum length of 77.9 µm,

64


1500 1520 1540 1560 1580 16000

0.5

1

1.5

λ [nm]

Loss

[dB

]

1500 1520 1540 1560 1580 16000.4

0.45

0.5

0.55

Rno

rm

λ [nm]

BPMHybrid

Figure 4.5: Comparing BPM to the hybrid method. The optimal length of the devicewas found to be 78.5 µm using BPM. When using the hybrid method the optimum lengthwas 77.9 µm. This difference is thought to be due to the Goos-Hänchen effect. The lossfound by both methods matches very well. The ratio between reflection and transmissionis hardly influenced by the mirrors.

5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.50

1

2

3

Device width [µm]

Loss

[dB

]

5.5 5.6 5.7 5.8 5.9 6 6.1 6.2 6.3 6.4 6.50.2

0.4

0.6

0.8

1

Rno

rm

Device width [µm]

Figure 4.6: BPM simulation of the device tolerance to width deviations. The nominaldevice width is 6.0 µm. For width deviations up to ±100 nm there is less than 1 dB ad-ditional loss. The normalized reflection coefficient deviates less than 0.02 from the idealvalue of 0.5 in this range.

65


Figure 4.7: The MIR is divided into three parts. The first part is simulated using BPM.The field is then stored and launched into an FDTD simulation. The output field of theFDTD is launched in a BPM simulation. The overlaps with the access waveguide modesare then calculated to obtain device reflection and transmission coefficients. The dottedshape indicates the area that is simulated during the different steps. ML: mode launcher,FS: field saver, FL: field launcher, MO: mode overlap. Arrows indicate the direction ofthe launchers.

which deviates a bit from the 78.5 µm found earlier using solely BPM. The dif-ference is caused by the mode dependent phase shift that occurs on total internalreflection [98]. A wavelength sweep was also carried out. Figure 4.5 comparesthis sweep to the results obtained from the BPM simulation. The losses accordingto the hybrid method are somewhat higher; on average 0.2 dB. This is to be ex-pected as more nonidealities are included in the simulation. Both simulation typesshow the same device bandwidth and split ratio.

4.1.7 Measurements

Device design

A number of devices were manufactured in a multi-project wafer run, on an InPplatform developed by Oclaro, as part of the European research project Paradigm.All waveguides were deep-etched with air as the surrounding material and a slabindex of 3.25 at λ = 1.55 µm. A total of 5 MIR designs were made: two 1-portand three 2-port devices. The design parameters are listed in table 4.4. The accesswaveguide width, Wwg, was chosen to be 2 µm for most devices, both becausesimulations indicated acceptable losses and to keep short taper lengths to the stan-dard 1.5 µm wide waveguides. The gap between the access waveguides was setto 1 µm to ensure the gap could be opened lithographically. This choice fixes the

66


Table 4.4: Fabricated MIRs

ID Ports Type W (µm) L(µm) Wwg(µm)M1 1 Symmetric 6.0 36.2 2.0M2 1 Symmetric 7.5 57.4 2.5M3 2 General 5.0 54.4 2.0M4 2 Paired 9.0 57.0 2.0M5 2 C 6.0 78.4 2.0

minimum width for the two port devices to 5 µm, 9 µm and 6 µm for types Gen-eral, Paired and C, respectively. The width of the 1-port devices was chosen tobe in the same range. To minimize internal reflections in the devices the cornerson the input side were cut, as described in [66]. The devices were optimized forTM polarization. The input and output waveguides leading to the facets have a7 degree angle with respect to the facet normal to suppress reflections. The chipwas not anti-reflection coated.

Measurement setup

Several structures, shown in figure 4.8, were specifically designed to enable char-acterization of MIRs. The structures either build an interferometer out of MIRs, orinsert a MIR in an interferometric structure. We identify them by their similarityto known interferometers: Fabry-Perot, Mach-Zehnder and Michelson. The ad-vantage of such structures is that the measurement result is largely independent ofthe input and output coupling coefficients. The operating principle of the Fabry-Perot interferometer in loss measurements is described in [99]. We repeat it herefor clarity.

The transmission of a Fabry-Perot interferometer built out of MIRs on reso-nance is given by

FPon =Pout

Pin=

T 2G(1−RG)2 (4.6)

with T,R the MIR power transmission and reflection coefficient, G = exp(−αL)the cavity loss assuming a cavity length L and a loss coefficient α ≥ 0. The off-resonance transmission is given by

FPoff =Pout

Pin=

T 2G(1+RG)2 (4.7)

Combining both equations gives an expression for the on/off resonance transmis-sion ratio, which we label D

FPon

FPoff= D =

(1+RG)2

(1−RG)2 (4.8)

67


Rewriting this gives use the following solution for R

R =1G

√D−1√D+1

(4.9)

The value of D can be obtained by performing a wavelength sweep. When chang-ing the wavelength the response will vary between the on- and off-resonance re-sponse. The operating principle of the other structures is closely related.

The Michelson structure is used only for measuring the reflection coefficientof a 1-port reflector. The Fabry-Perot structure is used only to determine the re-flection coefficient of the 2-port MIRs. The Mach-Zehnder measurement structureis used to determine the transmission coefficient of the 2-port MIRs. Therefore,two separate measurements of two separate structures are used to determine thesplit ratio and loss of the 2-port MIRs.

A tunable laser based setup (see figure 4.9) was used to obtain the spectral re-sponse of the characterization structures. The laser module (Agilent 81600B) andthe power meter (Agilent 81632A) were installed in the same mainframe (Ag-ilent 8164A). The narrow line width of the laser combined with its small stepsize allows us to see fine details in the spectrum. In the measurements, the laserwas swept in a continuous mode from 1530 nm to 1570 nm and 4001 points wererecorded. figure 4.10 shows an example of a recorded spectrum of a Fabry-Perottype characterization structure, which was normalized to the laser input power.From the top figure it is clear that the fast Fabry-Perot fringes are present. How-ever, some additional modulation is present. This modulation was not present ina measurement of a straight reference waveguide. The modulation indicates spu-rious reflections and other parasitic effects in the characterization structure. Dueto this, the calculated reflectivity values fluctuate somewhat. In the presentationof the measurement results below, we display the average (µ) of all these points inthe spectrum, as well as the standard deviation (σ), as follows: µ±σ.

Discussion

After analyzing the fringes in the measured spectra of the Michelson, Mach-Zehnder, and Fabry-Perot structures, we obtained the results shown in table 4.5.The mean and standard deviation are shown as µ± σ respectively. This tableshows that the devices operate with less than 2 dB insertion loss for the optimumpolarization. Typical insertion losses for MMIs in this technology are less than1 dB [51]. MIRs have some additional losses associated with the mirrors. Thereis little polarization dependence and the amount that is there is mainly caused bythe birefringence of the layer stack. The measured split ratio matches theoreticalpredictions very well for device M4 and reasonably well for device M3. DeviceM5 shows a split ratio that deviates somewhat from the expected 50:50 value. This

68


Figure 4.8: The on-chip characterization structures. The device under test is highlightedin grey. MMIs are used as splitters and combiners. The Fabry-Perot and Michelsoninterferometer methods are used to determine the reflection coefficient of a MIR. TheMach-Zehnder interferometer method is used to determine the transmission coefficient.Differences in arm lengths or the presence of a cavity gives rise to fringes in the wave-length response. From the ratio of the maxima and minima of these fringes, the MIRproperties can be calculated. Only the Michelson method is suitable for 1-port MIRs.

Figure 4.9: The measurement setup. TLS: tunable laser source; PMF: polarization main-taining fiber; PC: polarization controller; SMF: single mode fiber; MO: microscope ob-jective; PBS: polarizing beam splitter; LWD: long working distance lens; DUT: deviceunder test; LF: lensed fiber; PM: power meter.

could be caused by a fabrication imperfection in the Mach-Zehnder test structurefor that device.

The uncertainties in the presented data mainly stem from parasitic effects.Especially the Mach-Zehnder test structure showed large modulations of the ex-pected fringe spectrum. The main cause is the non-ideal performance of the 1×2MMI in combination with the reflection of the MIR. What happens is that the in-put power is split over the two arms. A large fraction of light in the device armis reflected back to the 1× 2 MMI. Some of this reflected light couples into thereference arm due to parasitic effects in the 1×2 MMI. We estimate this couplingcan be as large as −16 dB. Circuit level simulations have shown that such cou-pling levels can have a pronounced influence on the MZI response. This effect isstrongly suppressed when using 2×2 MMIs as splitters and combiners. Anotherimprovement is to deliberately increase the losses in the MZI reference arm. Thiswill increase the fringe visibility.

69


1530 1535 1540 1545 1550 1555 1560 1565 15700

0.2

0.4

0.6

0.8

λ [nm]

Inte

nsity

[A.U

.]

1530 1535 1540 1545 1550 1555 1560 1565 15700

0.25

0.5

0.75

1

λ [nm]

Ref

lect

ivity

Estimated reflectivityAverage

Figure 4.10: Top: example of a measured transmission spectrum of a Fabry-Perot typecharacterization structure formed from two MIRs of design M5. The ratio between themaxima and minima of the fringes is used to calculate the MIR reflectivity. The reflectioncoefficient is very constant over the wavelength, indicating the large bandwidth of MIRs.Some modulation of the fast fringes is present. We believe these to be caused by parasiticeffects like spurious reflections, coupling with the substrate, etc. Bottom: correspondingcalculated reflection coefficients.

Table 4.5: MIR characterization results

ID Loss TE [dB] Loss TM [dB] R:T TE R:T TMM1 0.9±0.3 0.4±0.8M2 0.7±0.3 0.7±0.5M3 2.3±0.6 1.7±0.6 49 : 51±7 58 : 42±9M4 1.5±0.5 1.8±0.7 49 : 51±6 50 : 50±11M5 2.5±0.5 1.4±0.5 61 : 39±8 62 : 38±9

70


4.1.8 Conclusion

A new class of on-chip reflectors, dubbed MIRs (Multi-mode Interference Re-flector), was introduced. MIRs have many desirable properties. They have largefabrication tolerances, can be placed anywhere on chip and provide a large re-flection bandwidth. For the first time, we described their operating principles anddesign method in detail. We have identified several sub-types and discussed theirproperties. A number of MIRs were fabricated. Measurements show excellentdevice performance with losses as low as 0.4 dB for 1-port and as low as 1.4 dBfor 2-port devices. These results lead us to believe that MIRs are valuable com-ponents for use in integrated optical circuits.

4.1.9 Appendix

Here we derive the conditions under which a central image exists in a generalMMI, such as the one shown in figure 4.2. The optimal length of this generalMMI is 3Lπ/N′. The center of an N′×N′ MMI can therefore be analyzed byinspecting the output images of a 2N′×2N′ MMI.

We now have two MMIs. The original N′×N′ MMI with free parameter a,inputs i and outputs j, and a second 2N′× 2N′ MMI, which we label B just forclarity. We label all parameters belonging to MMI B by adding a hat. We thereforehave N = 2N′, free parameter a, inputs i and outputs j.

Through inspection of the geometry of B, see figure 4.2, it can be seen that acentral image can only exist if a = 0. The location of the output image j in B isthen given by

x j =W2−⌊ j

2

⌋2WN

Where x j is the distance of the center of the image to the center of the MMI. Acentral image therefore has position x j = 0. This means that in B, an output imagej can only be central if it satisfies

⌊ j2

⌋=

N4=

N′

2(4.10)

Equation (4.10) can only be satisfied if N′ is even. Therefore, there is no centralimage for odd N′.

The values of a and a are linked by requiring that the inputs and outputs of theoriginal MMI align with those of B. The requirement that 0≤ a≤ W

2N′ also has tobe fulfilled. This leads to the following expression

a =W2N′−∣∣a− W

2N′∣∣

71


Equating this to zero and solving for a provides the following solutions

a =W2N′± W

2N′

When a has these values, the MMI becomes a so called overlapping image MMI.In such an MMI two virtual waveguides end up at the same physical position.

Using the relations from above, we can determine which inputs i map to thesame position as the inputs i of the original MMI. The inputs images of a generalMMI are at positions

xi =−W

2+⌊ i

2

⌋2WN′

+(2a(i mod 2)−a)

Applying this equation to both the original MMI and to MMI B, we obtain thefollowing equality requirement, where a = 0 has been entered already⌊ i

2

⌋2WN

=⌊ i

2

⌋2WN′

+(2a(i mod 2)−a) (4.11)

Now solving (4.11) for i

i =

2i+ 1±1

2 for i even and a = 02(i−1)+ 1±1

2 for i even and a =W/N′

2i+ 1±12 for i odd and a =W/N′

2(i−1)+ 1±12 for i odd and a = 0

(4.12)

From [78] we have the following phase relations between input i and output jof an N× N MMI

φi j =

{φ0 +π+ π

4N( j− i)(2N− j+ i) for i+ j even

φ0 +π

4N( j+ i−1)(2N− j− i+1) for i+ j odd

The field transmission at an output j due to an input i is then given by

Ti j =1√N

exp( jφi j)

where j is the imaginary unit, which from now on forward will only refer to theimaginary unit.

In an overlapping image MMI, inputs (outputs) overlap with adjacent inputs(outputs). The vector sum of Ti j over i and j is taken to calculate the transmissionbetween physical waveguides.

Equation (4.10) shows that the two output images of B that map to the centerhave j = N′ and j = N′+1. Because of image overlapping two inputs are always

72


excited simultaneously. For B these are inputs i and i+1. The central image fieldstrength is therefore given by

Ec = Ti,N′+Ti,N′+1 +Ti+1,N′+Ti+1,N′+1

From (4.1.9), ignoring the common phase φ0 and realizing that N = 2N′ weobtain

Ti,N′=1√N

exp( j[π+π

8N′(i−N′)(5N′− i)]) = e jφA

Ti,N′+1=1√N

exp( j[π

8N′(i+N′)(3N′− i)]) = e jφB

Ti+1,N′=1√N

exp( j[π

8N′(i+N′)(3N′− i)]) = e jφB

Ti+1,N′+1=1√N

exp( j[π+π

8N′(i−N′)(5N′− i)]) = e jφA

It follows then that Ec can only equal zero if φA = φB +(2n+ 1)π, with n aninteger. This can be reworked into the following

(i−N′)(5N′− i) = (i+N′)(3N′− i)+16N′nπ

Expanding brackets and reordering terms

i = 2N′+4n

We now enter the solutions for i from (4.12)

2N′+4n =

2i+ 1±1

2 for i even and a = 02(i−1)+ 1±1

2 for i even and a =W/N′

2i+ 1±12 for i odd and a =W/N′

2(i−1)+ 1±12 for i odd and a = 0

(4.13)

In (4.13), N′, i and n are integer. This means that the minimum step to match bothsides of the equation is two. The value of 1±1

2 is either 0 or 1. When it has value1, the equality cannot hold. We are therefore left with just the following cases

N′+2n =

i for i even and a = 0(i−1) for i even and a =W/N′

i for i odd and a =W/N′

(i−1) for i odd and a = 0

(4.14)

We already established that N′ must be even for a central image to exist. The righthand side of (4.14) must therefore also be even. Equation (4.14) thus reduces to

N′+2n =

{i for i even and a = 0(i−1) for i odd and a = 0

To summarize, the requirements for a central image to be absent are therefore:

73


• N′ odd

• N′ even and a 6=W/N′

This means that only when N′ is even and a =W/N′, a central image exists.

74

5Arrayed waveguidegratings

Since their invention in 1988 [100], arrayed waveguide gratings (AWGs) have be-come the number one filtering element in integrated optics for many different ap-plications. Its most important function is as a multiplexer or demultiplexer, wheredifferent wavelength channels are split over different outputs of the device. Whenthe device is designed with multiple inputs, much more complex functionality canbe achieved. Just to illustrate how important this device is; in the 6th COBRAfoundry run, 10 out of 12 designs used AWGs. It is no wonder then, that a lotof attention went into developing the COBRA AWG library. This development istwo fold. On the one hand a layout module is needed that ‘draws’ the AWG shape.Though routines to draw AWGs have existed, we developed the first module thatis able to work within the PDAflow framework1 and offers support for multiplefoundries. Our layout library also provides suppression of reflections thay mightoccur inside the AWG. Secondly, it is also very important to be able to simulatethe response of these generated AWGs. A new analytical AWG model was de-veloped that can simulate the response orders of magnitude faster than numericalmethods. In this chapter we describe the layout part of the library in section 5.2,and the simulation part in section 5.3. As a third part, the effect of polarizationrotation in AWGs is discussed in section 5.4. However, the design and operationof AWGs needs to be described a bit more first.

5.1 Operation

The operation of AWGs is best explained using a schematic representation of thephysical layout. Such a schematic is shown in Figure 5.1. An AWG has a numberof input waveguides, Nin, a number of output waveguides, Nout, and a number ofarray waveguides, Na. The input and output waveguides are both connected toa star coupler, which consists of a Free Propagation Region (FPR). Light fromthe input waveguide enters the FPR, at which point diffraction occurs and light isprojected along the output aperture. There it is coupled to the array waveguides.There is a fixed length difference between each consecutive array waveguide so

1for more information on the PDAflow, see chapter 6 and appendix A.

75

Chapter 5. Arrayed waveguide gratings

Figure 5.1: Layout of an AWG. When light from a broadband source is launched at theinput, the dispersive properties of an AWG cause light of different colors to be focusedon different output waveguides.

that the length of the ith waveguide obeys Li = L0 + i∆L. This length differenceis chosen equal to an integer number m times the central wavelength λc dividedby the mode index neff. The integer m is referred to as the array order. Thelength difference gives rise to a wavelength dependent phase difference ∆Φ =2πneff∆L/λ. It is this phase difference that causes the phase front of the field atthe output aperture to tilt for λ 6= λc. Because there is a wavelength dependence ofthe phase difference, different wavelengths will be deflected over different anglesin the output FPR. The deflection angle can be approximated as [101]

θ =∆Φ−m2π

2πnsda/λ=

neff∆L−mλ

nsda(5.1)

with ns the slab index inside the FPR, and da the pitch of the array waveguides.Equation (5.1) equals zero when the numerator equals zero. This happens at thecentral wavelength of the array, λc, which is typically specified by the designer of

76

Layout specifics

Figure 5.2: Close up of the output FPR. The same labeling of AWG parameters as in [101]is used.

the AWG. Using the deflection angle θ we can define an array dispersion D at thecentral wavelength as

D = Radθ

d f=

∆L dneffd f +m λc

fc

ns∆α=

∆L dneffd f +∆Lneff

1fc

ns∆α=

1fc

∆L∆α

ng

ns=

dsd f

(5.2)

with ng the group index, and s defined in Figure 5.2.

5.2 Layout specifics

The library routines that were created as part of the work described in this thesistake a number of user parameters and generate a layout based on them. The mainuser parameters, and a short description, are shown in table 5.1. Based on theseparameters a general design of the AWG is made, which is valid for any particularlayout. The values that are calculated are ∆L, m, D, ∆α, Ra, Na, and Li. Theyare calculated using the approach described in [101]. These values are the inputfor the next stage of the AWG generation routines. These routines are differentfor different AWG layouts. With layout we mean a particular way of arrangingthe arms of an AWG. The layouts that have been implemented in the library arenamed here the “Orthogonal” layout2, which was introduced by Takahashi [102],the “Smit” layout, introduced by Smit [103] and Dragone [104], and the “Alcatel”layout, introduced by Bissessur [105]. All layouts are shown in figure 5.3. It isnot always trivial to calculate the lengths, radii of curvature and angles of thearray waveguide for a particular layout. However, a structured procedure can befollowed that generally is the same for all layouts. In broad terms it consists of

2Also known as Manhattan or horseshoe layout.

77


Name Function Default value, Range Units TypeNin Number of inputs 4, > 0 intNout Number of outputs 4, ≥ 0 intlambda_c Central wavelength 1.55 [1.5,1.6] µm doublepol Polarization “TE”, [“TE”,“TM”] stringdf Channel spacing 400e9, > 0 Hz doublefsr Free Spectral Range 1600e9, > 0 Hz doublew_io I/O waveguide width 1.5, > 0 µm doubled_r I/O waveguide pitch 3.0, >w_io µm doublew_a Array waveguide width 1.5, > 0 µm doublegap_a Array waveguides gap 0.4, > 0 µm doubleAAF Array Acceptance Factor 3.0, (0,6] µm doublegamma Chirp factor 0.0 [0,3] µm doublechirp_type Single or double chirp 0, [0,1] introwland Rowland I/O mounting 1, [0,1] int

Table 5.1: The user parameters for the AWG library.

Figure 5.3: The three available different layouts. The dark gray areas indicate typicallydeep-etched regions. (a): Orthogonal, (b): Alcatel, (c): Smit.

creating a system of equations and solving that for a number of free parameters inthe AWG. For some layouts there are more free parameters than constraints, andtherefore many solution exists. A solution can usually be found by minimizing forsize by iterating over additional free parameters. Because a detailed descriptionof creating AWG layouts is often lacking in the literature, we will briefly outlineit here.

78

Layout specifics

Figure 5.4: Schematic layout of an orthogonal AWG.

5.2.1 Layout procedure

The first step in creating an AWG layout is identifying which geometric free pa-rameters there are in a particular layout. Here we will use the orthogonal layoutas an example. This particular layout has a symmetry line that splits the AWGin two equal halves. Two major constraints can be written down: geometricaland optical. The geometrical constraint ensures that the two halves connect in thecenter of the AWG. The optical constraint ensures all waveguides have the properoptical length. In figure 5.4 the geometrical parameters of an orthogonal AWGare shown. This figure shows that the layout consists of a straight, followed by acurve, another straight, another curve and a last straight. In this layout we assumethat the width of all waveguides is the same. This means that a straight has justa single parameter, its length. A curve has a radius, an angle and an offset, ofwhich the latter can be calculated from the radius of the curve. All parameters arelabeled X j, where X refers to the type and j to the position in the array. So the ra-dius of the first curve is indicated by R1. All parameters with an over-bar representnumerical arrays of size Na. Individual elements of these arrays are indexed usingsquare brackets: R1[i], where i indicates the ith element. Figure 5.4 also showstwo other parameters: ∆s and ∆x. The first ensures that the array waveguides areon a equidistant lateral grid. It is supplied by the user by specifying a minimumgap between array waveguides. The second parameter is used to make sure allwaveguides end at the same vertical plane. Using all the parameters we can writedown the following relations

[LT +L0]βs = [L1 +L2 +L3]βs +βr(R1)|A1|+βr(R2)|A2| (5.3)

∆x = [Ra +Lmin]sin(A1)+ [R1 +O1](1− cos(A1))+R2 +O2 +L3 (5.4)

79


s[i] = −Na−12

+ i∆s (5.5)

LT[i] = L0 + i∆L (5.6)

with βs the propagation constant in a straight waveguide, and βr(r) the angularpropagation constant in a curved waveguide of radius r. Equation (5.3) is anoptical constraint that ensures all array waveguides have the correct optical length.Equation (5.4) is a geometrical constraint. Next to these constraints there are anumber of general constraints that will also create the smallest possible shape.These can be deduced from some parameters set by the technology, such as theminimum radius of curvature, Rmin, and the associated offset, Omin. The minimumlength for L1 can be used to accommodate a shallow to deep transition, and islabeled Lmin here.

L1 ≥ Lmin (5.7)

L2[0] = 0 (5.8)

L3[0] = 0 (5.9)

R2 = Rmin (5.10)

O2 = Omin (5.11)

A2 = π/2 (5.12)

If the equidistant grid for s is chosen too tight, the values of R1 for the outerarray waveguides will violate the minimum bending radius. The first check per-formed is thus entering Rmin as a value for R1, and calculating the maximum ∆s.The offset O1 is neglected in this analysis.

∆s′ = max

{∆s,2

[Ra +Lmin]sin(A1[0])+ [Rmin +Omin](1− cos(A1[0])

)Na−1

}(5.13)

Now using (5.5) and the new value for ∆s, the following equation for R1 can bederived

R1 =s− (Ra +Lmin)sin(A1)

1− cos(A1)−O1 (5.14)

Unfortunately (5.14) is a transcendental equation in R1, because O1 is a functionof R1. Solutions can be obtained by using a root finder, but it is also possible toneglect the contribution of O1 because it is orders of magnitude lower than thetypical radii used. The only error this introduces is a deviation from a equidistantgrid s. This method does not introduce phase errors as the real value of R1 is usedin subsequent calculations. This is the approach we take here. The solution for R1is subsequently used to calculate O1. Now using (5.4) and (5.9) through (5.12),

80

New analytical arrayed waveguide grating model

the values for L3 can be calculated. We are thus left with determining values forL2. We use the last unused constraint (5.3) for this. In this constraint there is afinal parameter we have not discussed, L0. Its value follows from (5.8).

L2 = LT +L0−βr(R1)

βs|A1|−

βr(R2)

βs|A2|−L1−L3 (5.15)

Equation (5.15) immediately highlights a potential problem with the orthogonallayout. If the length difference between arms is very small, then the increase inL2 from arm to arm also becomes small. This may cause waveguides to overlapin the L3 section. On the other hand, if ∆L is very big, then this layout has thetendency to become very high as L2 values become big. This can be controlled byselecting a larger ∆s, which will make the layout more square like. Other layouts,such as the “Smit” or “Alcatel” layouts, may still give suitable geometries in caseswhere the “Orthogonal” layout fails.

5.2.2 Suppressing reflections

When making lasers, controlling reflections is very important as they may disturblaser operation [106]. Because AWGs are frequently used as multiplexers or asthe wavelength selective element in multi-wavelength lasers [107–110], ensuringlow reflections in AWGs is essential. The interfaces between the FPR and theinput/output waveguides or the array waveguides may give rise to reflections. Inthose areas, high index to low index interfaces are present. Similar to MMIs(see chapter 3), the reflection mechanisms involved may be very efficient becausefocused beams of light are involved. This is of course no problem when the beamis focused onto the output waveguide. However, for other wavelengths the beammay be focused on the trench region next to the waveguide. To suppress thesereflections, the trenches can be tapered. Parasitic reflected light is then directedaway from the input, leading to a reduction of the reflection level. Figure 5.5shows the generated shape. It can be controlled through parameters α1, α2 andα3. The other parameters are taken from table 5.1.

5.3 New analytical arrayed waveguide grating model

The following section describes a new analytical arrayed waveguide grating model.It was previously published in a peer reviewed journal. Reprinted, with permis-sion: E. Kleijn, M. Smit, and X. Leijtens, “New analytical arrayed waveguidegrating model,” Journal of Lightwave Technology, vol. 31, no. 20, pp. 3309–3314,© 2013 IEEE. It is included here verbatim.

81


(a) (b)

Figure 5.5: (a) A FPR design with etched regions shown in gray. The trench edge atthe array aperture is angled by α1. (b) Each individual I/O waveguide is created from aninversion base (green) and a waveguide base (blue). The final trench shape is obtained bysubtracting the two bases. Because adjacent waveguide bases can overlap, the complexshape in (a) is obtained.

Figure 5.6: Fabricated input FPR.

Abstract

An analytical model of star couplers in arrayed waveguide gratings (AWG) isderived. By retaining the real 1D mode shapes, the model is able to calculatethe star coupler response to fundamental modes, as well as higher-order modes.This is desirable for modeling passband flattened AWGs. The model can calculatethe response of an AWG very fast, because no numerical root finding or integralcalculation is involved. This allows it to be used in circuit level simulations.

5.3.1 Introduction

Arrayed Waveguide Gratings (AWGs) are key devices in many optical systems.They are used extensively as multiplexers and demultiplexers [101]. Because theycan be integrated on a chip, they are also frequently used in Photonic Integrated

82


Circuits (PICs) as wavelength filtering devices. As the complexity of PICs in-creases, there is a need for detailed circuit level simulations. Because such circuitscan contain many components, the time needed to simulate a single componentmust be kept low. Due to the large physical size of AWGs, the calculation times ofrigorous physical simulation methods, such as Beam Propagation Method (BPM)or Finite Difference Time Domain (FDTD), are prohibitive. Therefore, there is aclear need for fast AWG models.

One of the difficulties in modeling AWGs is analyzing the star couplers. Pre-vious work [104, 111] has mainly focused on finding design equations for thesecouplers rather than providing an accurate simulation model. In this paper wepresent a new analytical star coupler model, and by extension an AWG model,that is suitable for circuit level simulation as described in [112]. Similar to ex-isting analytical models we use a paraxial approximation [113, 114]. Instead ofusing a Gaussian approximation of the fundamental mode, we choose to retainthe real mode field, with exponential tails and a cosine function in the core. Weshow that this approach results in increased accuracy at a minimal increase of cal-culation time. A further advantage of our model is its ability to include higherorder modes. This can be used, for example, to simulate passband flattening usingmultimode interference couplers (MMIs) [115].

We start in section 5.3.2 by describing the profile of the considered modes. Wethen continue by describing the diffraction integral, which we apply to calculatethe coupling coefficients of an AWG star coupler. In section 5.3.3 we find a closedsolution to the integral. In section 5.3.4 the coupling to the array waveguides iscalculated. These individual pieces are put together in section 5.3.5 where thefull AWG model is described. Section 5.3.6 then compares this model to othersimulation methods. We conclude in section 5.3.7.

5.3.2 Theoretical model

Mode profile

We consider a three layer slab waveguide with an index profile n0|n1|n2 and widthd, as shown in Figure5.7. Such a structure can be obtained after application ofthe Effective Index Method to the index profile of a 2D waveguide cross-section.A slab waveguide mode solver is used to find the guided modes in this structure.Without loss of generality we define the center of the waveguide to be at x = 0.The field profiles U(x) of the guided waveguide modes then have the form of(5.16), where U(x) is either Ey (quasi-TE polarization) or Hy (quasi-TM pola-

83


rization) [61].

U(x) =C

cos(u/2−φ)exp( v

2+vxd ) for x <−d

2

cos(ux/d+φ) for |x| ≤ d2

cos(u/2+φ)exp(w2−

wxd ) for x > d

2

(5.16)

with

v = k0d[N2−n22]

1/2

u = k0d[n21−N2]1/2

w = k0d[N2−n20]

1/2

φ =12

{arctan(w/u)− arctan(v/u)+mπ for TE

arctan(n21w

n20u )− arctan( n2

1vn2

2u)+mπ for TM

Where k0 = 2π/λ0, m the mode number, defined as b uπc, and N the mode index.

The mode is normalized through the coefficient C. Its value can be calculated bysatisfying the following equation

1 =∫

∞

−∞

U(x)U∗(x)dx

C =

√2d

[1+

cos(u/2−φ)2

Re(v)+

sin(u)cos(2φ)

u+

cos(u/2+φ)2

Re(w)

]−1/2

In order to decrease the calculation time needed by our model, we precalcu-lated the mode index N for many wavelengths and tabularized the results. In thisway we avoid having to run a mode solver during the AWG simulation.

AWG star coupler

In AWGs the coupling from the input waveguide to the array waveguides is takencare of by a star coupler. The typical geometry of such a coupler is shown inFigure5.8. In this figure, the input waveguide is shown on the left, at an angleαin = δ/2. A single array waveguide is shown on the right at an angle θ. Thearray waveguides are positioned on a circle with radius Ra. The input waveguidesare positioned on the Rowland circle with radius Rin = Ra/2. Defocussing, suchas is used in some chirped AWGs [116], can be included through the parameterd f , which equals zero for normal AWGs. The presented geometry is that of anasymmetric star coupler. The model can also be applied to different input geome-tries, for example symmetric, by choosing different values for (x0,z0) and αin.

84


Figure 5.7: Three layer slab waveguide geometry. The waveguide has width d. Thefundamental and first order modes are shown. The refractive indices of the three layersare shown as n0, n1 and n2, where it is assumed that n1 is the highest of the three.

Figure 5.8: A schematic of a free propagation region in an AWG. An input waveguideis visible on the left, ending at (x0,z0). A single array waveguide is drawn on the right,beginning at (x, z).

85


The model can be applied to propagate any field which can be described asa linear combination of modal fields in the input waveguides, thus also allowingfor weakly coupled waveguides. Here we consider a single mode of any orderin one input waveguide ending at a point (x0,z0) at an angle αin. The ξ axis isperpendicular to the centerline of this input waveguide. At the same time weconsider a single output waveguide at an angle θ, which begins at a point (x0, z0).The ζ axis is perpendicular to the centerline of the output waveguide. We nowlaunch a mode with a profile Uin(ξ) and we wish to calculate the coupling to anoutput mode Uout(ζ). This can be any mode of the considered input waveguide.

When light exits the input waveguide, diffraction occurs. The field at the otherside of the star coupler along the ζ axis is therefore described by the 2D Fresnel-Huygens diffraction integral [114]

U(x, z) =

√k√

j2π

∫∞

−∞

Uin(ξ)z′

rexp( jkr)√

rdξ (5.17)

with k = nsk0 the wavenumber in the material, ns the slab index, U(x, z) thediffracted field, and

r =√

[x(ζ)− x(ξ)]2 +[z(ζ)− z(ξ)]2

The coupling between the modes is given by the overlap integral between theoutput mode and the diffracted field

O =∫

∞

−∞

U(x(ζ), z(ζ))Uout(ζ)dζ (5.18)

No closed solutions exist for the integrals in (5.17) and (5.18). However,it is possible to find an approximate closed expression when it is assumed thatthe angles αin and θ are small and that r is much larger than the effective modewidths of the input and output modes along ξ and ζ, respectively. In most practicalAWGs these assumptions are valid. This approximation is related to the paraxialapproximation described in [114], the validity of which is discussed in detail in[117].

An inspection of (5.17) shows that the integral argument contains a slowlyvarying amplitude component and a fast varying phase component. Under theabove outlined assumptions, we approximate r linearly in ξ for the phase com-ponent. For the amplitude component we retain only the constant term in r. Weapply this to (5.17) and obtain the following expression

U(x, z)≈ z′√

k exp( jkr0)

r0√

j2πr0

∫∞

−∞

Uin(ξ)exp( jkr1ξ)dξ (5.19)

86


with r0 and r1 the constant and linear terms of the Maclaurin series of r in ξ:

r = r0 + r1ξ+O(ξ)2

r0 =√[x(ζ)− x0]2 +[z(ζ)− z0]2

r1 =[x0− x(ζ)]cos(αin)+ [z0− z(ζ)]sin(−αin)

r0

andz′ = cos(αin)[z(ζ)− z0]+ sin(αin)[x(ζ)− x0]

5.3.3 Solving the diffraction integral

With the approximation of r outlined above, it is possible to get a closed expres-sion of the integral in (5.19). We insert the field expression of (5.16) and treat thethree regions separately. This results in the following integrals

I1 = C0(r0)∫ −din/2

−∞

Avin exp(vinξ/din)exp( jkr1ξ)dξ

I2 = C0(r0)∫ din/2

−din/2cos(uinξ/din +φ)exp( jkr1ξ)dξ

I3 = C0(r0)∫

∞

din/2Awin exp(−winξ/din)exp( jkr1ξ)dξ

with

C0(r0) = Cinz′√

k exp( jkr0)

r0√

j2πr0

Avin = cos(uin/2−φin)exp(vin/2)

Awin = cos(uin/2+φin)exp(win/2)

Closed solutions exist for all these integrals, as derived in the appendix. Theclosed expressions are

I1=C0(r0)Avindin

vin− jγexp(− jγ/2− vin/2) (5.20)

I2=C0(r0)

[din exp(− jφin)

uin− γsin(

uin− γ

2

)+

din exp( jφin)

uin + γsin(

γ+uin

2

)](5.21)

I3=C0(r0)Awindin

win− jγexp( jγ/2−win/2) (5.22)

87


Figure 5.9: Three neighboring array waveguides are shown schematically in gray, withtheir individual mode profiles indicated. The modes of adjacent waveguides may overlap.This leads to an overestimation of the power coupled to the array. By limiting the inte-gration bounds to −ζ0 to ζ1 and renormalizing the array mode, no overestimation takesplace.

with γ=dinkr1.

The diffracted field at coordinate (x, z) is thus approximated as

U(x, z)≈ I1 + I2 + I3 (5.23)

5.3.4 Coupling to the array waveguides

Equation (5.23) describes the field value at a single point (x, z) due to the diffrac-tion of an input field Uin(ξ). As mentioned, an overlap integral between the outputmode and the diffracted field gives the coupling to the output mode. This integralis given in (5.18). However, this equation is only valid for an array of isolatedwaveguides. In an AWG the array waveguides can be in close proximity and theybehave as a system of coupled waveguides. In such a situation, the exponentialtails of the individual array waveguide modes overlap significantly. This meansthat applying (5.18) to every array waveguide leads to an overestimation of thepower coupled to the array waveguides. Instead of applying coupled mode theoryand considering the array waveguides as a whole, we propose a simpler approach.We modify the boundaries of every overlap integral so that instead of running from−∞ to +∞, it runs from −ζ0 to ζ1. These two points correspond to the center be-tween waveguide i and i−1, and between i and i+1. This is shown schematicallyin Figure5.9. The array waveguide’s mode profile is renormalized so that the en-ergy contained in the region between −ζ0 and ζ1 equals 1. The modified overlap

88


integral thus equals

O′i =∫

ζ1

−ζ0

U ′i (ζ)U(x(ζ), z(ζ))dζ (5.24)

U ′i (ζ) =

[∫ζ1

−ζ0

Ui(ζ)U∗i (ζ)dζ

]−0.5

Ui(ζ)

In the limit of an infinite gap between array waveguides, ζ0 and ζ1 both tend toinfinity, and the original equation for an isolated waveguide is obtained. When thegap equals zero, the array waveguides form a single wide waveguide and essen-tially all power is coupled to this waveguide. In our approximation, the mode ineach waveguide is then approximated as a pure cosine function. In this limit ourmodel therefore gives an overestimation of the insertion loss.

To get to a closed analytical solution of the complete star coupler, the integralin (5.24) needs to be solved. Unfortunately, no closed solutions exists. This is dueto the ζ dependence of x and z, and through them the ζ dependence of r0 and r1.If we assume that the effective width of the mode profile Ui(ζ) is small comparedto r0 at ζ = 0, then we can apply a linear approximation of r0.

r0 = r0,0 + r0,1ζ+O(ζ2)

with

r0,0 =√

R2a + x2

0 + z20−2Ra (z0 cos(θ)+ x0 sin(θ))

r0,1 =z0 sin(θ)− x0 cos(θ)

r0,0

Also r1 has to be approximated to be able to find a closed expression. When theangles αin and θ are small, or in other words if x0� Ra and x� Ra, then r1 canbe approximated by a constant.

r1 = r1,0 +O(ζ)

with

r1,0 =x0 cos(αin)+ z0 sin(−αin)−Ra sin(−αin +θ)

r0,0

When these approximations are valid, also z′ can be approximated as follows:

z′ ≈ z′0 = Ra cos(αin−θ)− z0[cos(αin)+ sin(αin)]

When the approximations detailed above are applied to (5.20), (5.21), and(5.22), then the only ζ dependent part of the integral solutions I1, I2 and I3, is

89


C0(r0). Similar to before, C0 contains a slow varying amplitude component anda fast varying phase component. For the amplitude component, we replace allinstances of r0 by r0,0. For the phase component we replace r0 by

[r0,0 + r0,1ζ

].

We obtain the following integrals that have to be solved to get the value of O′i in(5.24)

B1 = KAvout

∫ −dout/2

−ζ0

exp( jkr0,1ζ)exp(voutζ/dout)dζ

B2 = K∫ dout/2

−dout/2exp( jkr0,1ζ)cos(uoutζ/dout +φout)dζ

B3 = KAwout

∫ζ1

dout/2exp( jkr0,1ζ)exp(−woutζ/dout)dζ

with

K = CinCoutz′0din√

kr0,0√

j2πr0,0exp( jkr0,0)

(K1 +K2

)K1 =

Avin exp(−vi/2)jγ0 + vin

exp(− jγ0/2)+Awin exp(−win/2)− jγ0 +win

exp( jγ0/2)

K2 =exp(− jφin)

uin− γ0sin(

uin− γ0

2)+

exp( jφin)

−uin− γ0sin(−γ0−uin

2)

γ0 = dinkr1,0

These are exactly the same integrals for which we found closed expressions ear-lier. We thus find

B1 =KAvoutdout

jdoutkr0,1 + vout

[exp(− jdoutk

r0,1

2− vout

2)

−exp(− jkr0,1ζ0−ζ0vout/dout)

](5.25)

B2 = Kdout exp(− jφout)

doutkr0,1−uoutsin(

doutkr0,1−uout

2)+

Kdout exp( jφout)

doutkr0,1 +uoutsin(

doutkr0,1 +uout

2) (5.26)

B3 =KAwoutdout

− jdoutkr0,1 +wout

[exp( jdoutk

r0,1

2− wout

2)

−exp( jkr0,1ζ1−ζ1wout/dout)

](5.27)

90


O′ = B1 +B2 +B3 (5.28)

5.3.5 Full AWG model

An AWG consists of two star couplers that are connected by array waveguides ofincreasing length. We consider an AWG with Nin input waveguides, Nout outputwaveguides and Na array waveguides. The goal of the model is to obtain the en-tries t ji of the transmission matrix T , which describe the transmission from inputi to output j. This can be written as a matrix multiplication of three transmissionmatrices.

T = FoutΦFin (5.29)

where Fin is the response of the input star coupler which is a Na×Nin matrix, Φ

is a Na×Na diagonal matrix representing the amplitude and phase response of thearray waveguides, and Fout is the response of the output star coupler which is aNout×Na matrix. The response of both input and output star couplers is modeledin exactly the same way. The transmission matrix T has dimensions Nout×Nin.

5.3.6 Comparison to existing models

To evaluate the performance of our new model we simulated a regular AWG anda passband flattened AWG with three different methods. The first method is a2D Beam Propagation Method (BPM) simulation using a commercial softwarepackage [43]. The BPM was configured to have a lateral step size of 10 nm. Thelongitudinal step size was 50 nm. A Padé(3,3) approximation was used for propa-gating the fields. The total BPM simulation was built up by first exciting an inputof the input star coupler and taking the mode overlap with the array waveguidemodes sufficiently far away from the star coupler so negligible coupling betweenarray waveguides occurred. A phase shift corresponding to each array waveguidelength was then applied. Finally, the output star coupler was simulated to get thetransmission of the device. This approach thus follows the principle from (5.29).It should be mentioned that BPM has limited accuracy for strongly guiding wave-guides [118]. The second simulation type is a paraxial approximation using Gaus-sian mode fields [113]. In this Gaussian model we apply the overlap integral in(5.24), but using Gaussian mode fields. Finally, the new model described in thispaper is applied.

Regular AWG

The parameters of the regular AWG are shown in table 5.2. The device is a 1×4 AWG with a channel spacing of 1.6 nm. The layer stack used is an indium

91


Table 5.2: Simulated AWG parameters

Parameter ValueNin 1Nout 4Central wavelength 1550 nmChannel spacing 3.206 nmFree spectral range 12.83 nmArray order 106Number of arms 20Arm length increase 51.17 µmShortest arm length 319.1 µmIO waveguide width 1.50 µmArm waveguide width 1.50 µmGap between array waveguides 0.40 µmSlab index 3.253Lateral cladding index 1.0Substrate index 3.16Top cladding index 3.17Ra 55.87 µmAngle between array arms 1.949◦

Angle between IO waveguides 3.590◦

MMI width1 3.00 µmMMI length1 13.75 µm1 only for passband flattened device

phosphide stack with high lateral index contrast.

Figure 5.10 shows the simulation results of the three models. The passbandsare centered around 1550 nm. We see an excellent match between our analyticalmethod and the BPM results to such an extent that they are virtually indistinguish-able. Both show an insertion loss of 3 dB and a crosstalk floor between −50 dBand −55 dB. The periodicity of the crosstalk also matches very well. The onlyvisible deviation is a small sidelobe directly adjacent to the passband, which theBPM predicts to be at −39 dB while our method predicts −45 dB. For the Gaus-sian model there are much stronger deviations to the numerical results. First ofall, the Gaussian model overestimates the width of the passband, and secondlythe crosstalk level is under estimated at −60 dB. The Gaussian model also givesa higher insertion loss of 4.9 dB. In terms of calculation times, our new methodfinished in 1.6 seconds for 2000 points, the Gaussian model in 1.3 seconds for

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Figure 5.10: The response as predicted by the three different models. The analyticalresults match extremely well with the BPM results. The Gaussian model clearly deviatesfrom the other methods. The inset shows a close-up of the passbands. The roll-off in thepassband height due to diffraction effects is clearly visible.

2000 points, while the BPM took around 9.5 hours for only 200 points. Thus, ourmethod is approximately 5 orders of magnitude faster than the BPM.

Flattened AWG

As mentioned, our model is able to simulate the response of passband flattenedAWGs. We again use the 1× 4 AWG whose parameters are shown in table 5.2,but now an MMI is placed at the input. The MMI has a width of 3 µm, a lengthof 13.75 µm, and an input waveguide width of 1.5 µm. The length of the MMIwas optimized to provide a flattened field at the output. A linear combination ofthe first three even modes was used in the analytical model to represent the fieldat the end of the MMI coupler. The weighting coefficients and relative phases ofthese modes were determined through Modal Propagation Analysis of the MMI.Because in our model, the AWG response is calculated separately for each mode,the calculation time scales linearly with the number of input modes. The analyt-ical simulation finished in 4.6 seconds for 2000 points and 3 input modes. TheBPM now took 8.5 hours for 200 points. The transmission of the passband flat-tened AWG as calculated by BPM simulations and the analytical model are shownin Figure 5.11. This figure shows an excellent match between the two methods.There is some deviation in the crosstalk behavior. There the BPM shows crosstalk

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BPMAnalytical

Figure 5.11: Flattened AWG response as predicted by BPM and by the analytical model.A very good match between the BPM and the analytical model is obtained.

levels of around −45 dB, where our method predicts −55 dB. The maximum de-viation in the passbands is limited to 0.5 dB.

5.3.7 Conclusion

A new analytical model for AWGs was derived. Other analytical AWG modelsexist, of which the paraxial approximation with Gaussian mode fields is probablythe most well known [113, 114]. That Gaussian model suffers from a number ofinaccuracies, of which many are avoided in our model. First of all, the Gaus-sian approximation of the mode can only be applied to the fundamental mode.Our method works equally well for both the fundamental mode and higher or-der modes. This allows our model to simulate passband flattening using mul-timode output waveguides [119], MMI couplers in the input [115] or parabolictapers [120] more accurately than adaptations of the Gaussian model such asin [121]. Secondly, the Gaussian approximation of the mode has a big mismatchwith the actual mode shape in the exponential tails of the mode. This results ina poor prediction by the Gaussian model of the AWG crosstalk [113]. In termsof speed, our model has similar performance as the Gaussian model because bothpresent fully analytical expressions for the coupling coefficients of the star cou-pler. The new model was compared to BPM simulations and an excellent matchwas obtained. Given its capabilities, speed and accuracy, we feel that this modelis very well suited for use in circuit level simulations.

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5.3.8 Appendix

We provide a derivation here of the closed expression for integrals I1, I2, and I3 ofsection 5.3.3. We start with I1. Integral I3 is completely equivalent to I1 and wewill therefore not show its derivation.

I1 =C0

∫ −d/2

−∞

Av exp(vξ/d)exp( jkr1ξ)dξ

I1 =C0Av

∫ −d/2

−∞

exp((v+ jγ)ξ/d)dξ

I1 =C0Avd

v+ jγexp((v+ jγ)ξ/d)

∣∣∣−d/2

−∞

I1 =C0Avd

v+ jγexp(− jγ/2− v/2)

with γ=dkr1.Integral I2 is slightly more complicated and involves expanding the cosine into

its complex exponential parts.

I2 =∫ d/2

−d/2cos(uξ/d +φ)exp( jγξ/d)dξ

I2 =12

∫ d/2

−d/2

[exp(− j(uξ/d +φ))+ exp( j(uξ/d +φ))

]exp( jγξ/d)dξ

I2 =exp(− jφ)

2

∫ d/2

−d/2exp(− juξ/d)exp( jγξ/d)dξ+

exp( jφ)2

∫ d/2

−d/2exp( juξ/d)exp( jγξ/d)dξ

I2 =exp(− jφ)

2

∫ d/2

−d/2exp(− jξ/d(u− γ))dξ+

exp( jφ)2

∫ d/2

−d/2exp( jξ/d(u+ γ))dξ

I2 =d exp(− jφ)−2 j(u− γ)

exp(− jξ/d(u− γ))∣∣∣d/2

−d/2+

d exp( jφ)2 j(u+ γ)

exp( jξ/d(u+ γ))∣∣∣d/2

−d/2

I2 =d exp(− jφ)

u− γsin(

u− γ

2)+

d exp( jφ)u+ γ

sin(γ+u

2)

95


5.4 Sidelobes in the response of arrayed waveguidegratings caused by polarization rotation

The following section describes the impact of polarization rotation on AWG per-formance. It was previously published in a peer reviewed journal. Reprintedwith permission: E. Kleijn, P. Williams, N. Whitbread, M. Wale, M. Smit, andX. Leijtens, “Sidelobes in the response of arrayed waveguide gratings caused bypolarization rotation,” Optics Express, vol. 20, no. 20, pp. 22660-22668, © 2012OSA.

Abstract

Earlier it was observed that polarization rotation in an AWG built from birefrin-gent waveguides can result in sidelobes in its response. This effect was measuredin a polarization sensitive AWG with an orthogonal layout. Now we investigatethrough detailed simulation whether this effect also exists in polarization desen-sitized AWGs. It is shown that a dispersion compensated AWG does not sufferfrom a polarization sidelobe. Alternatively, the AWG can be designed to minimizepolarization rotation to suppress the sidelobe.

5.4.1 Introduction

Arrayed waveguide gratings (AWGs) are commonly used components in inte-grated optics. In most applications the crosstalk performance offered by these de-vices is very important, with large sidelobes adversely affecting crosstalk levels.Sidelobes in AWG responses have so far been reported to originate from finitearray aperture sizes [101], phase errors due to fabrication imperfections [122],coupling between array waveguides [123], higher-order mode propagation [124],and unwanted scattering. Using relatively simple measurements, it can be shownthat sidelobes can also be caused by polarization rotation in the AWG. We refer tothese sidelobes as polarization rotation sidelobes or ‘PR-sidelobes’ for short.

In birefringent waveguides the TE and TM polarized modes have differentpropagation constants. An AWG constructed out of such waveguides will havedifferent dispersion for either polarization. As such, the AWG pass band posi-tions for different polarization will be shifted in frequency with respect to eachother. There are several methods to make AWGs polarization insensitive. We willinvestigate whether these methods also reduce or eliminate the PR-sidelobes.

We first noticed PR-sidelobes experimentally in a device whose layout isshown in Figure 5.12(a). It was discovered that the output signal of this AWGcontained a mix of TE and TM polarization, whereas only one polarization statewas launched at the input. It was further noticed that the main transmission peak

96

Sidelobes in the response of arrayed waveguide gratings caused by polarizationrotation

had the same polarization as the input signal. The highest sidelobe however, hadan orthogonal polarization with respect to the input signal.

The layout type of the investigated device uses the same bend radius and anglefor all the tight bends in the array. This reduces the systematic phase errors asso-ciated with different bend radii and angles [125]. Unfortunately, this also causesthe polarization conversion to be the same for every bend in the array, which cre-ates a coherent effect. If the bends are different, averaging takes place, makingthe effect less pronounced. Here we will only discuss the effect in the orthogonalAWG layout of Figure 5.12(a).

The work presented here expands on earlier work presented at a conference[126]. First we will discuss the devices in which the PR-sidelobes were observed.After that we continue in section 5.4.3 with a detailed description of the mea-surements. These are then compared in section 5.4.4 to simulations. A similarsimulation is used in section 5.4.5 to see which polarization desensitising meth-ods can remove the PR-sidelobe. We conclude in section 5.4.6.

5.4.2 Device design

The measured devices were manufactured in a well established process from thecompany Oclaro Ltd., based in the United Kingdom. The stack consists of alightly doped 2 µm thick p-InP top cladding and a 0.36 µm thick MQW (MultipleQuantum Well) core on a n-InP substrate. The resulting slab index is 3.246 at awavelength of 1.55 µm. All waveguides were 1.5 µm wide and deep-etched, withan etch depth of 3.6 µm. The surrounding material is air. An SEM picture of theresulting cross-section is shown in Figure 5.12(b). The indicated sidewall-anglein this figure equals 87 degrees.

Figure 5.12(a) shows the layout of the device. The used bend radius was150 µm for all curved waveguides. Lateral offsets of 16 nm were applied at junc-tions between straight and curved waveguides. The designed four channel AWGhad a free spectral range of 1600 GHz and a channel spacing of 400 GHz. Thedevices were processed by Oclaro.

5.4.3 Measurements

The devices were characterized and sidelobes on one side of the transmissionpeaks were observed. Figure 5.13 shows their location in the spectrum. Furthermeasurements were carried out to determine the source of these sidelobes. Themeasurement setup used is shown in Figure 5.14. In this setup the light from abroadband light source is TE polarized by the input polarizer. After the light haspassed through the device under test, a second polarizer can be set to transmiteither TE or TM polarized light, or be removed to allow any polarization to pass.

97


free propagationregions

arraywaveguides

inputs outputs

star-couplers

center line

(a) Layout (b) Cross-section

Figure 5.12: (a) Layout of the manufactured AWG. (b) Scanning Electron Microscope(SEM) image of a waveguide cross-section of the manufactured AWG. The indicatedangle is 87 degrees, which means the sidewall angle equals 3 degrees.

Three measurements were performed. In the first measurement the outputpolarizer was set to transmit the TE part of the output signal. In the second mea-surement the TM part of the output was transmitted. In the last measurementthe output polarizer was removed and the total transmitted power was recorded.The results of these measurements are shown in Figure 5.15. This figure clearlyshows a sidelobe on the shorter wavelength side of the main transmission peak.This sidelobe is not present in the filtered, TE-only, output signal. However, itis present in the TM part of the output. Because only TE polarized light waslaunched, the TM output must be the result of polarization rotation in the sample.

On closer inspection of Figure 5.13 it becomes clear that for TE input, thesidelobe is on the shorter wavelength side. For TM input, the sidelobe is on thelonger wavelength side. This is consistent with polarization conversion takingplace in the array. Suppose that the TE mode is launched and that it has a higherpropagation constant than the TM mode (βTE > βTM), as is the case for our device.The phase of the light that is converted to TM then increases more slowly duringpropagation. The TM light thus experiences a virtual red-shift. This means that,to end up in the same output waveguide as the original TE light, its wavelengthhas to be shorter. The same argument holds for TM polarized input, but then avirtual blue-shift occurs. The rotated light in the output waveguide then has alonger wavelength. The sidelobe thus appears at shorter wavelengths for TE andat longer wavelengths for TM.

The layout of Figure 5.12(a) can be divided into three general areas: the input

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Figure 5.13: Typical response of the characterized devices for TE input (black) and TMinput (grey). The arrows indicate the PR-sidelobes.

ASE

SMF

Microscope objectives

Inputpolarizer

DUT OSA

SMFOutputpolarizer

Figure 5.14: Schematic of the experimental setup. The input polarizer is present in allmeasurement; in some measurements no output polarizer was used. ASE: AmplifiedSpontaneous Emission source, SMF: Single Mode Fiber, DUT: Device Under Test, OSA:Optical Spectrum Analyzer.

waveguides, the array, and the output waveguides. Figure 5.13 shows that the dis-tance in wavelength between the sidelobe and main peak (≈ 2.4 nm) is less thanthe observed shift between the TE main peak and TM main peak (≈ 4.3 nm). Ifthe rotation were to occur in the input waveguide, the full TE/TM shift should beobserved. If the rotation occurred in the output waveguide, no effect should be ob-served. The rotation must therefore happen in the array itself. The rotation mostlikely occurs in the curved array waveguides, as curved waveguides have been re-ported to cause polarization rotation [127]. In the next section, the measurementswill be compared to detailed simulations to further support this hypothesis.

5.4.4 Simulation

A transmission matrix based approach was used to simulate the device that wasmeasured in the previous section. In the model, the AWG is split into two starcouplers and individual straight and curved waveguides. For every part a trans-

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No polarizerTE polarizedTM polarized

Figure 5.15: OSA trace of the filtered, TE polarized ASE spectrum for: no output polar-izer (solid), output polarizer set to TE (dashed), output polarizer set to TM (dotted). Thetraces have been normalized, correcting for the nonuniform shape of the ASE spectrum.

mission matrix is calculated. Concatenation of the transmission matrices thenresults in the transfer of the full AWG. The model includes polarization rotation.

The star-couplers are modelled using the “leading-order paraxial approxima-tion”, as described in [114]. This approximation is valid for small angles in thestar-coupler and allows the use of a Fourier transform to calculate the diffractedfield. The mode field of the fundamental mode in the input waveguide of the star-coupler is approximated by a Gaussian. This allows for a fully closed analyticalexpression for the field at the other side of the star-coupler. The slab-index, thatis necessary for this method, was calculated for each polarization independentlyand fitted with a second order polynomial. Using this method we calculated thecoupling coefficients between the input and output waveguides to the array wave-guides. It was assumed that the coupling between array waveguides can be ne-glected.

The array waveguides each have two inputs and two outputs; one for TE andone for TM. In the straight waveguides, the transmission matrix is as follows:

Ts =

(exp(− jβTEL) 0

0 exp(− jβTML)

)(5.30)

with β the polarization dependent propagation constant. The propagation constantwas calculated at several wavelengths by using a 2D Film Mode Matching methodand then fitted with a second order polynomial for TE and TM separately. FromEq. (5.30) it is clear that we assume there is no polarization rotation in the straightwaveguides. Instead, this is modeled in the curved waveguides.

The curved waveguides are modeled by two hybrid modes with their princi-ples axes rotated by an angle φ with respect to the straight waveguide modes. The

100


transmission matrix thus becomes:

Tc =

(sinφ cosφ

cosφ −sinφ

)(exp(− jβ0Rθ) 0

0 exp(− jβ1Rθ)

)(sinφ cosφ

cosφ −sinφ

)(5.31)

with φ the polarization rotation angle, R the bend radius and θ the bend angle.For the propagation constants of the hybrid modes, we assume that β0 = βTMand β1 = βTE. Because these two propagation constants are different, the state ofpolarization will rotate during propagation through the curved waveguides.

To match the height of the polarization sidelobe in the simulation with theexperimental results, a polarization rotation angle of 2.7◦ is needed. This is areasonable value as the sidewall angle was measured to be 3◦. As Figure 5.12(b)shows, the sidewall angle increases closer to the substrate. The curvature of thewaveguide causes the field to shift outward and slightly down. This increases theinfluence of the sidewall on the field profile.

An additional change was made in the simulation to better match the mea-surements. The fitted TE and TM mode indices were changed slightly to matchthe measured polarization dispersion of 4.3 nm in the array. This was done bysubtracting 0.008 (around 0.25 %) from the TM mode index. The need for thiscorrection can be explained by the fact that the layer stack uses a MQW core,whereas a bulk model was used for the calculation. This difference can induceadditional polarization dispersion.

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TE+TMTE polarizedTM polarized

2.2 nm

Figure 5.16: Simulation of an AWG with polarization rotation occurring in the curvedarray waveguides. The result of the simulation matches well with the measurement resultsshown in Figure 5.15

A simulation was carried out with fully TE polarized light at the input on thesame layout as shown in Figure 5.12(a). In the simulation result the PR-sidelobehas shifted 2.2 nm with respect to the main lobe. In the measured response thisis 2.4 nm. Please remember that only the polarization dependence of the whole

101


layer stack was fitted to experimental results. The position of the PR-sidelobewas not matched to experimental results. Keeping this in mind, we obtain a verygood match between the result of the simulation, shown in Figure 5.16, and themeasured response.

5.4.5 Eliminating the sidelobe

When using birefringent waveguides, an AWG is polarization sensitive. Severalapproaches exist for making such AWGs polarization insensitive. Smit namesthe following in [101]: insertion of a half-wave plate, compensating polarizationdispersion, order matching, and launching TE and TM polarizations from differentinput waveguides (input polarization splitting). The discussion in this sectionstrictly limits itself to AWGs with the same layout as shown in Figure 5.12(a).It will be shown that, for this particular layout, only a specific form of dispersioncompensation can eliminate the negative effect of the PR-sidelobe. The simulationmethod described in section 5.4.4 was used to show this. The simulation wasmodified to use one of the various polarization desensitising methods.

Decreasing polarization rotation

The PR-sidelobe will be reduced by decreasing the amount of polarization rotationtaking place in the curved sections. This could be done by changing the waveguidegeometry or by increasing the bending radius of the curved array waveguides.Alternatively, the length of the curved sections could be chosen in such a waythat the hybrid modes have the same relative phase at both the end of the curveas at the beginning. In that case the state of polarization will be the same at thebeginning and end of the curve. The curves then essentially become full-waveplates. For 90 degree bends in our InP layer stack, this condition is fulfilled bytaking the bend radius equal to an integer multiple of 97 µm. To meet minimumbend radius requirements, the radius would become 194 µm.

Half-wave plate

By inserting a half-wave plate (HWP) at the center line, a polarization insensitivedevice was obtained in [128]. Its effect on the PR-sidelobe can be understood asfollows. Suppose TE polarized light is launched at the input. After propagatingthrough the first curve, the polarization state is mixed. Dispersion then occursin the straight waveguide, with the phase of TE increasing faster than that of theTM polarized light. At the center of the array the HWP interchanges the twopolarizations. The phase difference between the two polarizations is then reducedagain, until the second curve is reached. At that point the phase profile is thesame as after the first curve. However, the main lobe is now TM polarized and the

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sidelobe is TE polarized. Propagation through the second curve causes additionalpolarization rotation. Applying the same reasoning as in section 5.4.3, dispersionin the last straight part of the array will cause a red shift of the sidelobe withrespect to the main peak. The dispersion will now only occur in the last straightof the AWG. The shift of the sidelobe is therefore slightly smaller when using aHWP. We therefore expect to see a TM polarized mainlobe and a red shifted TEpolarized sidelobe.

This behavior was verified using a modified version of the simulation de-scribed in section 5.4.4. The half-wave plate was modelled as interchanging theTE and TM content. In the simulation, the input was TE polarized. The resultsare shown in Figure 5.17. As was expected, the mainlobe is now TM polarizedand the TE polarized sidelobe is on the longer wavelength side.

Figure 5.17: Simulated response of an AWG with an inserted half-wave plate subject topolarization rotation in the curved waveguides. The PR-sidelobe is not removed by thismethod, but only displaced in frequency.

Dispersion compensation

In a commonly used dispersion compensation method, a waveguide section witha different birefringence is inserted in the center of the array [129]. The sectioncompensates for the polarization dispersion that occurs when propagating throughthe whole array. When polarization rotation occurs within the array, the requiredamount of dispersion compensation will be less. A single compensation section inthe center of the array can therefore never both remove the PR-sidelobe and makethe AWG polarization insensitive. The simulation result, shown in Figure 5.18(a),confirms this. Another dispersion compensation method, described in [130], ap-plies two compensation sections. The sections are positioned before and afterthe curved waveguides. The polarization rotated light now propagates throughonly one compensation section. Mixed polarized light at the input of the AWG

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propagates through both compensation sections. The amount of dispersion com-pensation is therefore different in the two cases. Figure 5.18(b) shows the resultof a simulation, including polarization rotation, of such a dispersion compensatedAWG. It can be seen that there is a PR-sidelobe, but its position is now the sameas the main transmission lobe. This means that though the sidelobe exists, it doesnot have a negative influence on the AWG response.

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(a)

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(b)

Figure 5.18: (a) Simulated response of an AWG subject to polarization rotation in thecurved waveguides, with one dispersion compensation section in the center. (b) Simu-lated response of an AWG subject to polarization rotation in the curved waveguides, withdispersion compensation sections before the curved waveguides. The TE trace is coveredby the TE+TM trace.

Order matching

The response of an AWG is periodic, with every transmission peak being sep-arated by one free spectral range. In the order matching approach, explainedin [131], the free spectral range of the AWG is matched to the frequency shiftbetween the TE and TM transmission peaks after propagating over the full lengthof the array. As mentioned in section 5.4.3, the observed frequency shift betweenthe main transmission peak and the PR-sidelobe is less than that of the main TEand TM transmission peaks. The order matching method therefore cannot botheliminate the PR-sidelobe and make the AWG polarization insensitive at the sametime.

Polarization splitter

In the polarization splitter approach, TE and TM polarized input light are launchedfrom different positions in the input star coupler. The displacement between the

104


two positions matches the frequency shift due to polarization dispersion. Thespectral response of both polarizations thereby becomes the same. Launchingfrom a different position can only be done if both polarizations can be separatedat the input of the AWG, which cannot be done for polarization rotated light in thearray.

5.4.6 Conclusion

It was shown through simulation and through measurements that polarization ro-tation in the curved waveguides of an AWG may cause a sidelobe in the responseof the device, provided that the device is polarization sensitive. AWGs using thesame curved waveguides in every arm seem particularly sensitive to this effect.Several methods exist for making AWGs polarization insensitive. The half-waveplate, order matching, and input polarization splitting methods will not removethe PR-sidelobe. When using certain variants of the dispersion compensationmethod, the PR-sidelobe is shifted to the same position as the main transmissionlobe, cancelling negative effects. Reducing the amount of polarization rotation inthe device will lower the PR-sidelobe level. The amount of polarization rotationcan be reduced by choosing the length of the curves such that they become full-wave plates. For the discussed AWG layout and layer stack, this would require abend radius of 194 µm. In practice, the best way to avoid a PR-sidelobe may be tochoose a different layout of the AWG, specifically a layout using different bendsin different array arms.

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6Component Libraries forMPW runs

Proper design tools are essential in reducing the development effort of PICs. Inthis chapter we explore the steps taken as part of this thesis work, together withsoftware and foundry partners in the PARADIGM project, towards realizing com-prehensive component libraries. Within the project, an Application ProgrammingInterface (API) was designed. In this chapter the requirements for such an APIare discussed on a high abstraction level. The details surrounding the actual im-plementation can be found in appendix A.

6.1 What is a library?

In essence, a library is a collection of information. When applying this to photoniccomponent libraries, this means that there is information on components in thelibrary. Three aspects of this can be recognized [41]. The first is the informationnecessary for generating a mask. The information could be a fixed geometricalshape. If we consider an example of a straight waveguide, the mask informationcould be a rectangle of 1 µm wide and 10 µm long. This example immediatelyshows that in photonics it is often not convenient to make this mask informationfixed. Therefore, it should also be possible to generate the mask information basedon user input. In our example, much more functionality is offered if the user isable to choose the width and length of the straight waveguide. A third possibility isthat the mask information is kept private by the foundry. In this case an abstractedlayout could be included in the library, which just shows locations where a usercould connect other components or specify the position of the component.

The second kind of information included in the library relates to behavior ofthe component. Verification of circuit level behavior by circuit simulation canshow the performance in general, but also whether design flaws are present. Acircuit simulator needs behavioral information on all the included components tobe able to generate a circuit response. This information can be generated by phys-ical solvers that take material parameters and geometries as input parameters. Itis also possible to use an abstracted mathematical model, which calculates cer-tain properties of the component as a function of several variables. Measurementresults can also be used to provide the behavioral information.

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Chapter 6. Component Libraries for MPW runs

Figure 6.1: General API environment. Third party programs are made aware of availablefoundry libraries and design house libraries, and their capabilities by using the API. Thearrows indicate communication between parts.

Finally, the last bit of information the library provides, is a symbol, which isused for representing the component in a schematic. This symbol also presents away for users to edit the component’s parameters. The symbol is not necessarilystatic. Some components have a varying number of inputs and outputs, dependingon the values selected by a user. Dynamically updating the component symbolshould therefore be possible. Together, the three mentioned aspects define a com-ponent.

A library can describe a large number of components or Building Blocks(BBs), and they can be provided by different suppliers. A foundry would typicallysupply a library containing the basic building blocks for an offered technology. Itis also possible for design houses to supply a library containing extra BBs, or sub-circuits. With many possible suppliers, it is necessary to define a framework toguarantee interoperability between different software components.

6.2 Framework

Users do not interact directly with component libraries. Users will rather use a cer-tain software program, while libraries form an extension of the capabilities of thatsoftware program. In a typical photonics design flow, many different tools areused. Examples are physical solvers for calculating mode indices, temperaturegradients etc., but also mask layout software, frequency domain circuit simula-tors, and time domain simulators. If a library can be used in all these differentprograms, potential conflicts and repetition of information can be avoided. Toachieve such functionality, strict rules on communication between libraries andsoftware programs need to be defined. In software engineering these rules aretypically specified in an Application Programming Interface (API). Widespreadadoption of an API can be stimulated by allowing open access to it.

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Framework

A high level schematic environment of a possible API is shown in figure 6.1.The environment for which the API is defined is very diverse. There will bemajor differences from user to user in which libraries and software programs areavailable. A plug-in architecture solves this by dynamically loading availablelibraries. Figure 6.1 shows third party software programs on the top. This couldbe simulators or mask layout tools etc. The API layer in the center facilitatescommunication between foundry libraries, design house libraries, and the thirdparty programs. Each library contains a number of BBs. Each BB can have anumber of associated views. Views are ways of interpreting the BB. A physicallayer solver will need different information from a BB than a mask layout tool.These differences are reflected in the different views. Programs have access toall views and decide which ones they can use in the current context. Because theviews define the way communication should take place between different partsof the environment, they are contained in the API description. In the rest of thissection we will briefly investigate the requirements of these views and proposea possible implementation path. It was mentioned that a BB should provide alayout, a symbol, and behavioral views. Each of these will be discussed.

6.2.1 Layout view

All components are manufactured using a technological process with one or morelithography steps. Each lithography step has associated mask layers in whichcertain areas are exposed while other areas are covered. The available mask layersand their function are determined by the technological process of the foundry.With the layout of a component we mean the ensemble of geometrical shapesin all mask layers that are related to the component. Any layout view shouldtherefore at least be able to write a shape to a mask layer. By repeatedly addingshapes the total layout can be created. A situation where an already added shapeshould be removed again might also occur. Some form of remove functionalityshould therefore also be offered. To be able to do this, the shape to be removedmust be identifiable.

The current industry standard for mask files is the Graphic Database Systemversion 2 (GDSII) file format. This format offers support for filled polygons,and paths. It therefore makes sense for a layout view to support at least thesetwo geometric primitives. Other mask file formats, such as OASIS, are able tosupport more geometric primitives, like circles. The layout view should thereforebe flexible enough to allow it to be extended. In its most basic form, the layoutview therefore looks similar to the following.

LayoutView {ShapeID AddShape(shape, position);RemoveShape(ShapeID);

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(a) (b) (c)

Figure 6.2: An example of a symbol for a straight waveguide, a curved waveguide, andfor a 1× 2 splitter. All ports are shown as red squares and are labeled pi. Below thesymbol is a list of the BB type, the BB name, and its parameters. The splitter has no usereditable parameters in this example.

}

6.2.2 Symbol view

A basic property of hierarchical design is that many details are hidden on the high-est levels of abstraction to prevent cluttering. Symbolic circuit layout is a verypowerful method implementing this. In this method, BBs are represented by sym-bols. These symbols show an abstracted representation of the BB together withthe location of the available BB ports. A symbol should also provide a method forediting the parameters of the BB. Figure 6.2 shows a number of possible exam-ples of symbols for different BBs. It is important to realize that symbols need notbe static. Such BBs exist where the number of ports depends on user input. Anexample of this is the arrayed waveguide grating. Taking these requirements intoconsideration, we can derive the following pseudo code as a basic interface of thesymbol view.

SymbolView {AddPort(portID, position);RemovePort(portID);ShapeID AddShape(shape, position);RemoveShape(ShapeID);

}

At this point we have not specified what kind of shapes are supported. Rectanglesand polygons seem obvious choices, but circles and arcs could also be supported.

6.2.3 S-matrix view

For passive linear components the scattering matrix approach is a convenient for-malism for defining the frequency domain response [68]. In this approach it is

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Framework

assumed that a BB has a finite number of well defined ports through which it in-teracts with components connected to it. Complex scattering parameters relate anincoming wave at any port to outgoing waves at all ports. In this description, eachmode at each port needs to be considered separately. All ports are bidirectional.Consider a BB with N ports. A port i supports a total of mi modes. The totalnumber of modes M through which the BB interacts is found by summing all mi:

M =N−1

∑i=0

mi

For a BB with M interacting modes, there are therefore M2 scattering parameters.This is conveniently represented by a M×M matrix, where entry (m,n) relatesincoming mode n to the outgoing mode m. In a calculation of S-parameters, theport with which a mode is associated needs to be known. We therefore introducea data structure that encapsulates both the properties of the port and of the mode.This data structure is labeled a PortMode. This data structure contains an identi-fier, which should be unique with respect to all other PortModes belonging to thesame BB.

We now need a unique way of sharing a S-matrix. The first issue that shouldbe addressed is how the S-matrix is stored in computer memory. S-matrices are2 dimensional, but computer memories are 1-dimensional. A standard methodfor storing 2D matrices is the row-major order method1. Using this method, theS-matrix of a BB with two PortModes is encoded as an array as follows:[

S11 S12S21 S22

]→ [S11,S12,S21,S22]

From this it is clear that Smn for a M port BB is stored in the 1D array at position(m− 1)M +(n− 1), with zero based indexing. An alternative solution would beto use an array of pointers that point to column data locations. This approachrequires more memory allocation calls, which is slower. The software frameworkdoes not specify how the actual values for the S-parameters should be obtained.This can be a model, or measured values. It is desirable that they can be obtainedin times on the order of milliseconds as S-matrices are mainly used in circuit levelsimulation, where many BBs can be present. To this end, models such as the onespresented in chapters 3 through 5 can be used. Though the layout in memoryof the S-matrix has now been determined, a memory position where the matrixshould be stored has not yet been assigned. C++ programming offers two possibleroutes. The first is to directly return the S-matrix by value. On older compilersthis might result in extra copy operations, which cost time to execute. To avoid

1Another option is the column-major order method. The choice between these is arbitrary

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this, large objects are often written to a memory location that has been specifiedby the calling program through a pointer. By using this method, the regular returnvalue can be used to indicate if an error occurred during the calculation of theS-matrix. The latter method is the preferred approach.

Matrices are ordered structures. The library that generates the matrix, andthe software that receives the matrix therefore need to agree upon the PortModeorder, i.e. which PortModes are associated with entry (m,n) of the S-matrix. Thecalling program is aware of all the PortModes of the BB. By letting the callingprogram create a list of PortModes, it has the possibility to ignore certain modes.This would allow a reduction in calculation load if certain PortModes are notneeded. It also allows the calling program to reorder the PortModes, which mightbe advantageous when using the S-matrix in further calculations.

The scattering parameter approach works in the frequency domain. The fre-quency under consideration needs to be communicated to the BB because gen-erally S-matrices are frequency dependent. This could be achieved by setting aBB parameter, but it is more transparent and intuitive to pass this as an argumentdirectly.

Given the requirements discussed above, we can derive a pseudo code inter-face for the S-matrix view.

int GetSmatrix(Complex destination&, List PortModes, double frequency)

6.2.4 Time domain view

When simulating optical amplifiers, it is often important to include non lineareffects. These effects cannot be simulated using frequency domain scattering pa-rameters, because this method assumes the component is linear. Time domainmethods can model non linear effects though. Time domain methods such as Fi-nite Difference Time Domain (FDTD) are able to simulate a very wide range ofstructures, but they are also very computationally intensive. This limits their useto relatively small structures. The size of the computational domain is typicallylimited by computer memory, with 2 GB of RAM resulting in a maximum domainsize of 300×300×300 cells [132]. This makes FDTD unsuitable for circuit levelsimulation. Other time domain methods exist that are much more efficient at han-dling large circuits, such as the Time Domain Traveling Wave (TDTW) method.

In the 1D Time Domain Traveling Wave method each component is dividedinto a number of sections along the propagation direction. The electric field ineach section is modeled as two complex values: one for the forward travelingwave, and one for the backward traveling wave. At each step in time, the electricfield values are updated based on the previous value and the value in the adjacentsections. The electric field of a plane wave with a frequency ω and propagation

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Framework

constant β conforms to the following expression:

E(z, t) ∝ exp( jωt− jβz) (6.1)

We now consider only frequencies close to ω0. We thus set ω = ω0 +∆ω andβ ≈ β0 +∆ω

∂β

∂ω= β0 +

∆ω

vg, with vg the group velocity. We obtain the following

expression:

E(z, t) ∝ exp( j∆ωt− j∆ω

vgz)exp( jω0t− jβ0z) (6.2)

Equation (6.2) is only valid if ∆ω � ω. This approximation is known as theslowly-varying envelope approximation. As mentioned, the TDTW method con-siders sections and time steps. The length of the sections is ∆z, and the size ofthe time step is ∆t. If we now choose ∆z = vg∆t, then the electric field can beconveniently expressed as:

E(z, t) = A(z, t)exp( jω0t− jβ0z) (6.3)

In (6.3), A(z, t) is a slowly-varying amplitude coefficient that propagates at thegroup velocity. In TDTW the fast varying phase coefficient ( jω0t− jβ0z) is re-moved. This is the main difference between TDTW and FDTD. This is what al-lows TDTW to be used on entire circuits. Similar to the scatter matrix approach,interaction with the BB is limited to a discrete number of ports.

Now that the basic properties of TDTW have been described, we can considerwhat the interface between a TDTW simulator and a library BB should look like.We will come up with a prototype time domain view. Because all componentshave internal memories (the value of the forward and backward propagating fieldin all its sections), the simulator needs a way to reset this value at the beginningof the simulation. If a set function for this memory is available, it is possible tocontinue a simulation after halting it. The size of the internal BB memory needsto be known to be able to do this. In a TDTW simulator, the time step ∆t is thesame for all components. The time domain view should therefore have a way ofcommunicating this to a BB. At every time step, the simulator should supply theBB with an incoming field value at all its ports. In turn, the BB should providean outgoing field value at all its ports. Similar to the S-matrix view, both the BBand the simulator should agree on the port order. To resolve this, the simulatorsends an ordered list of ports to the BB. There is also the issue of where theoutput field values of the BB should be written. Again, a pointer to a memoryaddress is supplied as the destination for the generated outputs. We thus come tothe following interface for the time domain view:

int GetFieldResponse(double timestep, List Ports,List InputValues, Complex destination&)

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unsigned int GetMemorySize();void ResetMemory();void SetMemory(List ForwardValues, List BackwardValues);

6.2.5 PDAFlow

The previous sections showed our view of a general outline of the requirementsof an API framework aimed at creating interoperability between component li-braries and third party software. Within the European FP7 programs EuroPIC andPARADIGM, a framework with this aim was created. This framework is calledthe PDAFlow [133]. The implementation of the PDAFlow differs from what wasdescribed above. It lacks a time domain view, and the symbol and s-matrix viewsare currently proprietary to one of the project partners. More details on the imple-mentation of the PDAFlow can be found in appendix A.

6.3 Design Rule Checking

The libraries described above help the designer by supplying standardized build-ing blocks. Another important functionality that software can offer is design rulechecking. To be able to fabricate a design, certain rules need to be adhered to.These are specified by the foundry and are known as design rules. Because adesign can be very complex, it is important to automatically check whether anyrule is violated. This process is known as a Design Rule Check (DRC). Theserules are usually geometrical rules, because in the end a user delivers a geometryin the form of a mask file to the foundry. Currently, the industry standard fileformat is typically GDSII, which stands for Graphic Database System version 2.Some rules originate from fabrication requirements, such as minimum line widthand minimum gap size. Others come from optical requirements, such as mini-mum bending radii to ensure low loss. Rules that only involve a single BB, suchas minimum radius and width requirements, can be checked directly while plac-ing the BB. Rules involving more than one BB have to be checked after all BBshave been placed. Most geometrical rules are checked using Boolean operationson polygons. Figure 6.3 shows a number of these Boolean operations applied topolygons. Now suppose we have two BBs: A and B. A common rule of a foundryis that BBs are not allowed to overlap. Translated into Boolean operations, thismeans that the and operation between the outlines of A and B should result in theempty set. A more stricter rule of the foundry might be that there should be aminimum gap g between A and B. An initial solution might be to grow the out-lines by g/2 in all directions, and performing the and operation again. However,such an approach is only valid for isolated BBs. Usually there are waveguides

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Design Rule Checking

Figure 6.3: Boolean operations on polygons

Figure 6.4: General method for ensuring minimum gap between BBs. A waveguidecomes in from the left and right side, and a metal track from the top. The BB outline,in green, is grown by half the allowed gap size. Each access port is also grown by thisamount. From the grown BB outline, each grown access port is subtracted to obtain thefinal shape shown in purple.

leading to the BB, which are of course allowed to connect to the BB. As part ofthe BB definition, it is known at which position a waveguide is allowed to con-nect, and what width w that connection has. A general correct solution thereforeis the following. A line of the same width as the waveguide is defined at eachport position. This line is then grown by g/2 in each direction so a rectangle ofsize (w+ g;g) is formed. The original BB outline is also grown by g/2 in eachdirection. The grown connection line shapes are then subtracted from the grownBB outline. This final shape is then used in an and operation to find overlaps. Thisprocess is shown schematically in figure 6.4. Currently, the implemented DRC isusing a different approach, which only grows the BB laterally. This is only validfor BBs where waveguides only connect from opposite sides. Many BBs satisfythis requirement. Laterally growing a structure is only possible if its central pathis well defined. The difference between isometrically grown shapes and laterallygrown shapes is shown in figure 6.5. This approach was chosen because it is mucheasier to implement while it still functions correctly for most BBs.

Next to overlap and distance design rules, a fab may also assign valid ranges

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Figure 6.5: Grown polygons. The original polygon is shown in green with a dashedoutline. The grown shape is shown in purple. Polygon centerlines are colored red. (a):Isometrically grown polygon. (b)-(d): Laterally grown polygons.

to the widths of shapes and the bending radii used. In the previous paragraphwe already introduced the central path. When geometric shapes are defined bya parametrized central path and a parameterized width, it is straight forward tocheck for minimum bending radii and minimum width violations. Such paths areconstructed by combining functions describing the coordinates of points along thepath. Without loss of generality, we define a parametric path ~P(t) as

~P(t) = x(t)~ux + y(t)~uy (6.4)

Here t is a running variable, and~ui denotes the unit vector in the i direction. Byalso defining a width as a function of t, a 2D shape can be defined. This is shownschematically in figure 6.6. There are a few restrictions that apply to describinga shape in this fashion. The most notable is that x(t) and y(t) have to be twicecontinuously differentiable in t. Under these restrictions, the normal vector ~N andtangent vector ~T are well defined at all points [134]:

~T (t) =x(t)√

x(t)2 + y(t)2~ux +

y(t)√x(t)2 + y(t)2

~uy (6.5)

~N(t) = − y(t)√x(t)2 + y(t)2

~ux +x(t)√

x(t)2 + y(t)2~uy (6.6)

with x(t)= dx(t)/dt and y(t)= dy(t)/dt. When using such a description of a path,the minimum width can be easily found. It is also possible to find the bendingradius along such paths. The radius of curvature R is defined in [134] as

R(t) =

(x(t)2 + y(t)2

)3/2

|x(t)y(t)− y(t)x(t)|(6.7)

The minimum bending radius can thus be checked by requiring

R(t)> Rmin ∀ t

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Multi Project Wafer runs

Figure 6.6: A parameterized geometrical shape. The central path is given by ~P(t). Thelocal width is given by w(t). Combining these with the normal ~N(t) gives rise to a fullydefined shape.

An additional benefit of parametric curves is the fact that the path length sab ofa segment between t = a and t = b can be calculated by integrating the absolutevalue of the differential displacement vector [134].

sab =∫ b

a|x(t)~ux + y(t)~uy|dt =

∫ b

a

[x(t)2 + y(t)2]1/2

dt (6.8)

Generally, the optical length is of interest rather than the geometrical path length.When the bending radii are big and the width of the curve is constant, then theoptical length can be approximated by

Lopt,ab =∫ b

aβ(t)

[x(t)2 + y(t)2]1/2

dt ≈ βsab (6.9)

with β the propagation constant.

6.4 Multi Project Wafer runs

So far we have briefly touched upon the concept of Multi Project Wafer (MPW)runs. In these runs, many designs from different users are combined in a singlewafer. In this way, the total production costs are shared among many users. Thisallows low cost access to fabrication services, typically for prototyping and re-search applications. The COBRA research institute has taken a leading role inoffering MPW services on InP. Initially, for the first three runs, processing wasdone per wafer quarter. The same lithographic pattern was then imaged on eachof the four quarters separately. Each quarter had 6 user cells and 3 test cells, allwith dimensions 4.3×4.0 mm2. Users would thus receive 4 copies of their design.The following two runs still used the quarter based layout, but instead processedall quarters at the same time as a single wafer. Many processing steps were nowapplied to the whole wafer at once, instead of four separate times for each quarter.This led to a reduction in equipment load. In 2012 a decision was made to changethe layout to maximize the use of the full 2" wafer. This led to a large increasein available user cells because the space on the wafer could be allocated much

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(a) (b)

Figure 6.7: (a): Design of MPW run COBRA 6. The largest diameter circle shows thewafer edge. The smallest circle indicates the area 5 mm or more from the wafer edge. (b):Photograph of the realized wafer, reproduced with kind permission from the photographer,Nando Harmsen.

more efficiently. The cell size was increased slightly to 4.6×4.0 mm2. A total of67 user cells and 9 test cells could now be fitted on the same wafer. Of the usercells, 46 are positioned five millimeter or more from the wafer edge. These aredesignated as being reliable, because process quality cannot be guaranteed within5 mm from the wafer edge. This leaves 21 cells that may not meet specifications.After processing, each user receives 3 to 4 cells from the reliable area and 1 or 2cells from the other cells. This means the new full 2" scheme can accommodatearound 11 users; almost double the previous quarter based approach. Figure 6.7shows the design of the wafer layout and the fully processed wafer of the sixthCOBRA MPW run in 2012.

The time schedule of MPW runs is roughly organized as follows. A run isfirst announced to users of the platform, who then have the opportunity to submita design. Once all the user designs have been received and checked, the foundryproceeds with the assembly of the wafer layout. This process is highly automatedbecause at COBRA we plan to offer many MPW runs and we wish to have turn-around times in the order of 3 months. The latter implies that the wafer shouldbe assembled and all mask plates ordered within days from the design submissiondeadline. When the masks are received, processing begins. After processing, thechips are cleaved, coated, and shipped to the users.

6.4.1 Mask assembly

Before fabrication can start, the multiple designs in a MPW run have to be com-bined into a single mask. This is typically done by a broker, as foundries ratherwish to focus on fabrication rather than interaction with dozens of users. The bro-

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ker collects the designs from all the users and places them at designated positionson the wafer. At COBRA this is done by a separate script that uses a fixed wafermap to place all the designs. This script also places a mask-set identifier on eachlayer, together with the name of that layer. This makes it easy for clean-roomtechnical staff to identify the glass mask plates. Finally, it places alignment mark-ers and some test-structures for the surface profiler. The whole assembled maskdesign is now written to a GDSII file. The second step done by the broker is tohandle the placement of private BBs. When offering MPW services, foundriesmay not want to reveal the design of their BBs. To use a BB, designers only needsome basic information, such as the BB function, port placement, size, etc. Thisinformation can be easily separated from the actual mask layout of the BB. Inthe library approach this is accomplished by using so called private BBs. In thisapproach a designer only sees a placeholder for the BB, but is not aware of itsactual contents. An example of this is the SOA BB in the COBRA library. Theuser is aware of a cbSOA BB, but this component only shows a bounding box ofthe resulting SOA. The exact mask shapes needed for fabrication are only knownby COBRA and are contained in a private BB. The cbSOA is only a placeholder.These placeholders are replaced by the foundry with the actual BB layout duringmask assembly. The locations of the placeholder components are communicatedto the foundry as a single text file. The broker therefore writes the locations of allthe private BBs specified by all users into a single file. The private BB locationfile and the GDSII file are then handed over to the foundry.

After receiving the mask files, the foundry will replace the placeholders withthe actual private BBs. Some processing of the mask may still be necessary. In theCOBRA process for example, waveguides are defined by trenches on either side ofthe waveguide. The trench is generated by subtracting the waveguide shape from awidened version of the same shape. The waveguide shape and the widened shapeare on different mask layers. Similar operations have to be carried out to generatethe p-metal layer from the plating layer, and the planarization layers. These oper-ations are all carried out on the fully assembled mask. Again, to avoid errors andreduce the required labor, we automated this process. The changes are stored tothe wafer GDSII file, which concludes the design process. The GDSII file is sentto the mask-shop, which uses Electron-Beam Pattern Generators to create a set ofchrome on quartz mask plates. During mask assembly the operator only has toperform three manual actions. Because of this high degree of automation, maskassembly can be completed within hours.

6.4.2 COBRA MPW library

In order to support the MPW activities at COBRA, we developed a componentlibrary. It defines the components that can be placed by PIC designers, but it also

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contains the routines necessary for automated mask assembly. The contents of thislibrary, along with comparable libraries from other foundries, are shown in table6.1 through 6.3. All libraries are able to provide designers with layouts of individ-ual components. At COBRA we also worked a lot on support for simulations. Inthe overview in tables 6.1 and 6.2, we distinguish four levels of simulation capa-bilities: none (-), basic (+), parametrized (++), advanced (+++). Basic simulationtypically models components as a single constant, for example a 1× 2 MMI canbe modeled as a constant 0.5 split-ratio. Parametrized simulation captures somewavelength dependence, or dependence on another variable. Advanced simula-tion typically includes many variables, and also models reflections. The modelsderived in this thesis fall in the last category. Designers for the COBRA platformcan use the library to simulate a circuit of dozens of components within secondson a regular PC. The COBRA library also features the most Design Rule Checks.These efforts have made the COBRA library the most advanced library used inInP integrated optics design. The COBRA library is available under a licensingscheme, currently against no cost. More than 400 licenses to over 50 organiza-tions have been distributed. They have used the COBRA library to create over 70PIC designs.

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COBRA HHI OclaroLayout Sim. Layout Sim. Layout Sim.

Straight C ++ H + O +Curved C ++ H + O +S-bend C - H - O -Taper C - H - O +Parabolic Taper C - C - C -Crossing C - H - O -Isolation C - H - O -Arc-Line-Arc C - C - C -Line-Arc-Line C - C - C -Generic Bend C - C - C -Spot Size Converter - - H - O -Directional Coupler - - H - - -Polarization Conv. - - C + - -1×1 MMI C +++ C - C -1×2 MMI C +++ H,C +,- O,C ++,-1×4 MMI - - H + - -2×2 MMI C +++ H,C ++,- O,C ++,-85/15 MMI C +++ - - - -72/28 MMI C +++ - - - -1-port MIR C +++ - - C -2-port MIR C +++ - - C -AWG C,B +++,++ C,B +++,++ C,B +++,++

Table 6.1: Passive components present in the libraries for the three platforms in thePARADIGM project. The letters indicate the provider of the component: C=COBRA,H=HHI, O=Oclaro, B=BrightPhotonics.

COBRA HHI OclaroLayout Sim. Layout Sim. Layout Sim.

DC pad x - x - x -RF pad x - x - x -EOPM x - - - x +++TOPM - - x - x -SOA x - x - x +++DBR - - x - x -PIN x - x - x -

Table 6.2: Active components present in the libraries for the three platforms in thePARADIGM project.

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COBRA HHI OclaroRadius of curvature x x xWaveguide width x x xWaveguide gap x - -Overlapping BBs x - -Waveguide overlap BB x x xOutside Cell x - xActives pitch x - -Actives orientation x x xShallow/deep separation x - -Metal gap x - -Metal overlap BB x - x

Table 6.3: Design Rule Checks present in the libraries for the three platforms in thePARADIGM project.

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7Conclusions and outlook

7.1 Conclusions

There are many application areas that can benefit from photonic integration tech-nology. Generic Integration Technology provides a common platform that canserve many applications. Indium phosphide based platforms are very suitable tobe used in this way because they offer a wide selection of features. Indium phos-phide allows to integrate optical gain, phase modulation, detection and passivecomponents on a single monolithic chip. Low cost prototyping access to thistechnology has been pioneered at COBRA and in the PARADIGM project by of-fering Multi Project Wafer runs. Such a run combines many different designs ona single wafer. Overhead costs can be shared over many parties in this way.

In a Generic Integration Technology the fabrication process is fixed. Thisallows for designs made for such a technology to be shared and reused. A BuildingBlock (BB) based design methodology arises naturally from this property. In thisthesis we have described the development of new BBs, creating behavioral modelsfor BBs, improving existing BBs, and how BBs can be effectively shared betweenusers by employing component libraries. The main accomplishments of this thesisare

• a novel approach to model optical properties of layer stacks.

• approximate simulation methods to model reflections at junctions.

• a new geometry for MMIs that strongly suppresses parasitic reflections.

• a new kind of reflective component: the Multimode Interference Reflector.

• a new analytical model for Arrayed Waveguide Gratings.

• a component library for indium phosphide based Photonic Integrated Cir-cuits.

Some of these results could also be applied to other photonic integration plat-forms, notably Silicon-on-Insulator (SOI) and TriPlex. It is expected that espe-cially the MIR and improved MMIs could transfer well to these two platforms.

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Chapter 7. Conclusions and outlook

Whether the derived models can be used on these platforms depends mainly onthe applicability of the effective index method, which is known to be inaccuratefor SOI.

The results of this thesis have been used in five MPW runs so far: COBRA 6& 7, and SMART Photonics 8 through 10. The library created as part of this thesiswork allows designers to focus on the higher abstraction level of circuit design.Designers no longer need to be aware of process technology and the layer stack.Due to the fast and detailed models derived in the thesis, designers can use circuitsimulation to design their circuit, rather than to verify it. So far, already around50 users have used the COBRA library to create more than 70 designs.

7.2 Outlook

When the work described in this thesis began, there was one indium phosphideMPW run per year in the world that was open to external partners. Now thatthis thesis is printed, this has increased to 7: three by SMART Photonics, two byOclaro and two by HHI. This shows there is a clear demand for such services, withmany users wanting to prototype their designs. All these users currently mainlyuse software from three companies to layout and simulate their designs. For thelayout part this is MaskEngineer by PhoeniX. This company also supplies physi-cal level simulation tools like mode solvers and BPM based propagation simula-tion. On the circuit level, a time domain simulator is provided by PhotonDesignin the form of PICWAVE [135], and a frequency domain simulator by Filaretecalled Aspic [136]. With the introduction of the PDAFlow, there is some inter-operability between these programs. At the moment though, this functionality iseither quite limited or very specific to the mentioned software programs. To getan idea of the currently supported features we take the COBRA library as exam-ple. It is possible to use the COBRA library to generate a layout in MaskEngineerwith advanced design rule checking. It is also possible to simulate straight andcurved waveguides, MMIs, MIRs, and AWGs in Aspic. Though this is quite a lotof functionality already, the following features are still missing:

• frequency domain simulation of shallow-to-deep transitions, electro-opticmodulators, tapers, semiconductor optical amplifiers, and PIN detectors

• including loss in the layer stack models

• time domain simulation support

• mask export using the PDAFlow

• interoperability with programs from vendors outside PARADIGM

124

Outlook

Based on the presented layer stack models in chapter 2, it should be quitestraightforward to include support for shallow-to-deep transitions. Using the Mil-ton and Burns model [137], parabolic tapers could be included. EOPMs, SOAsand PINs are not passive components, and as such they were not studied in thisthesis. When their optical response is linearized, they can be included in fre-quency domain simulations. As with the models for the other components, it isimportant to keep simulation times low for each individual component, otherwisecircuit simulation becomes prohibitively slow. If measurement data is available,polynomial models like the one in [138] may be used. However, polynomial mod-els tend to give unphysical trends when used for interpolation.

To include loss in the layer stack models, the imaginary part of the propagationconstant should be fitted as well. This will require different fitting models thanthe ones presented in chapter 2.

Including support for time domain simulations will take close cooperationwith software companies offering time domain simulation tools, because currentlythere is no well defined open interface for describing the communication betweena library and a time domain simulator. Once such an interface is defined it shouldbecome part of the PDAFlow. More progress has been made in this area forfrequency domain simulation. There is an interface describing how a S-matrixshould be communicated, but it is proprietary to Filarete. There are plans to makethe S-matrix interface part of the PDAFlow though. Defining interfaces is typi-cally done by foundations with members from the industry. An example of sucha foundation in electronics is Si2 [139], which targets Electronic Design Assis-tance and maintains the OpenAccess Database format. Recently the PDAFlowFoundation [133] was created with a similar goal for integrated optics.

Aspic and PICWAVE currently offer very basic support to export a design toMaskEngineer. Upon export, a script is generated that can be loaded in MaskEngi-neer to create the layout. The way this script is generated is determined by Aspicand PICWAVE. This method is currently not part of the PDAFlow. The exportfunctionality should be generalized. A possibility is using the following method.The MaskEngineer script could be generated by the individual BBs in the design,with the third party program iterating over each BB in the design and managingconnectivity.

The PDAFlow API was developed recently within the PARADIGM project. Itis therefore logical that only the programs from the three software vendors in theproject currently offer some support for the PDAFlow. The PDAFlow is meant asan open standard, however. To see whether it achieves this goal, a number of othersoftware vendors should try to incorporate PDAFlow support in their products. Atthe moment, only VPI is working actively on this. Lumerical has also shown aninterest though, and both have become members of the PDAFlow Foundation.

125

Chapter 7. Conclusions and outlook

7.3 Commercial MPW

After the EuroPIC and PARADIGM research projects, integrated optics researchbased on InP has switched up gears. After almost a decade of research level accessto MPW services, the first semi-commercial MPW runs first appeared late 2013.For the MPW runs offered within the research projects there was a large interest,which exceeded the available capacity. Access to these research MPWs was freeof charge, access to (semi)-commercial MPWs will not be. It remains to be seenhow many users are willing to pay for a design. Prices currently range from 300to 500 AC mm−2. It will be difficult for foundries to survive on running MPWsalone. Luckily it will be easy for a user to populate an entire wafer with hisdesign originally made for an MPW because the technology is the same. At themoment it is unclear though when such production runs can be expected. Let ushope the prediction made by Smit [140] is correct, and small volume productionstarts in 2015 and reaches a 500 MAC market in 2017.

126

APDAFlow

In chapter 6 a framework for defining the communication between libraries andsoftware programs was introduced. Within the European Union FP7 projects Eu-roPIC and PARADIGM such a framework was created. This framework is namedthe PDAFlow. At some points the PDAFlow currently differs notably from theframework described in chapter 6. Here we discuss in some detail the way thePDAFlow currently works.

A.1 Connecting to the PDAFlow

The PDAFlow forms the connecting framework through which libraries and soft-ware programs can communicate. This communication is initiated by a softwareprogram. To illustrate the different steps in the communication, we will use anS-matrix simulator by Filarete, Aspic [136], as an example.

Figure A.1 shows the communication steps that take place when loading alibrary for use with Aspic. First the library is loaded and the BBs inside thelibrary are registered in the PDAFlow. In this registration step, a list of BBs andtheir properties is constructed. The BB properties are for example the BB nameand which views it supports. In the second step, Aspic connects to the PDAFlowand obtains this list of BBs. Based on the BB properties Aspic determines whichBBs it can use, as some BBs may not support simulations at all. In the third stepAspic loads the symbol of a particular BB supplied by the library. Currently thiscommunication takes place directly between the library and Aspic. The details ofthis communication are specified by the 3rd party software vendor, Aspic in thiscase, and are not part of the PDAFlow due to intellectual property issues. Thesame is true for step 4, where simulation data is communicated between Aspicand the library. There are, however, proposals to make these views part of thePDAFlow. The next section shows how this communication is implemented.

A.2 Implementation

When a software program connects to the PDAFlow, the steps shown in figureA.2 are performed. A configuration file, PDAConfig.ini, specifies which libraries

127

Appendix A. PDAFlow

Figure A.1: Communication from a library to a 3rd party software program.

to load. It also specifies a set of paths where library files can be stored. Thosepaths are then searched for library files. The version of the libraries is checked tosee if it is compatible with the active PDAFlow version. If this is the case, load-ing continues by running the initLibraryFoundry function of the libraries. Thisfunction registers a foundry object with the PDAFlow. By loading this object, thelayout software gets access to the cross-section definition and layout information.This is accomplished through a phxIncludeView. The cross-section and layout in-formation is stored as encrypted Phoenix-script code. The phxIncludeView is re-sponsible for decrypting the data, provided the proper license is available. If thisis indeed the case, then a plain-text string with Phoenix-script code is returnedto the querying layout software. In practice this will always be MaskEngineeras no other software is currently able to interpret Phoenix-script. Most BBs arecurrently defined using the script route. There are two types of BBs that can be de-fined in Phoenix-script: layouts and classes. The main difference between them isthat layouts behave like C++ functions, while classes behave like C++ classes. In-herently classes are more complicated than layouts. The Phoenix script interpreteris run on all the script code supplied by that library. Whenever the interpreter en-counters a layout, it automatically registers this as a BB with the PDAFlow. Dueto the complexity of classes, the interpreter is not able to do this at the moment.We will now briefly describe what the implementation of a typical layout view,symbol view, and S-matrix view look like.

Layout

A basic example of a layout is shown in listing A.1. The code starts with definingthe name of the layout, and its arguments. In this case, cbStraight, and length andwidth respectively. On line 3 the keyword dlgname then specifies how the layoutshould be displayed in the BB tree overview dialog, namely under COBRA, in the

128

Implementation

Figure A.2: These steps are performed when loading a library.

1layout cbStraight(double length=100. RangeSpec >= 0.0,2 double width=mask::CSattr("wgWidth"))3 dlgname "COBRA/Curve"4 pdaViews "tueStraight_AspicView,tueStraight_SmatrixView"5{6 techTUE.csCheck(this,1,1,1);7 mask::setLayoutPort(this,"in0","out0");8 ml::Straight(cin->this@in0,cout->this@out0 : wfix(width),length)elm;9 this=Curve2BuildingBlock(this,elm,width,width,0);

10}

Listing A.1: cbStraight layout definition in SPT

Curve branch. Line 4 then specifies which views are associated with this particu-lar layout. These views are names of C++ classes. When parsing the layout, thePhoenix-script interpreter creates an instance of these views and adds them to theregistered BB. Before this can be done, the views themselves have to be registeredwith the PDAFlow. This is done upon loading of the library, in the initLibraryBBC++ function. In this particular example, tueStraight_AspicView defines a sym-bolic representation of the BB, while tueStraight_SmatrixView defines the wave-length response for simulation. These two will be described in more detail in thefollowing two sub-sections. The initial parsing of the layout stops here. The bodyof the layout code is only parsed while making a mask design.

When the layout is placed during mask design, the body of the layout codeis executed. First, on line 6, a check whether the BB is allowed in the currentlyactive cross-section is performed. The three numerical arguments of this functionspecify whether the BB is allowed in the shallow, deep and metal cross-sections.The next line then defines the default input and output ports of the BB. Line 8then draws the BBs by calling a MaskEngineer built-in geometric shape. Finally,line 9 adds some default properties like input and output width, and bounding boxports to the layout.

129

Appendix A. PDAFlow

1class PDA_DLLAPI tueStraight_AspicView : public filGeneralView2{3 public:4 tueStraight_AspicView(pda::BB* bb);5 pda::String getLibraryName() const;6 pda::String getTreeName() const;7 pda::String getParameterScript() const;8 pda::String getParameterScript (pda::String blockName) const;9 pda::String getHandleScript() const;

10 pda::String getSmartDrawScript() const;11 pda::String getDrawScript() const;12 pda::String getLocalAttributesScript() const;13 pda::String getLocalAttributesScript(pda::String blockName) const;14 pda::String getPortPositionScript() const;15 pda::String getAltName() const;16 pda::String docVersion() const;17 pda::Int getSupportedBlockCount() const;18 pda::String getSupportedBlockName (pda::Int index) const;19};

Listing A.2: tueStraight_AspicView definition in C++

Symbolic representation

When using a BB in a circuit level simulator, a representation of the BB is nec-essary. Usually, a stylized symbol is used to avoid clutter from physical layoutdetails at the higher abstraction level of the circuit. The available ports of theBB also have to be defined by the symbol. Unfortunately there is currently nostandardized way to represent this in the PDAFlow. However, for Aspic there isa vendor specific definition. Listing A.2 shows this definition. It is a class withvirtual member functions that are overridden in derived BB specific classes. ThegetDrawScript function supplies a string of Aspic-script code. This script codeis then parsed and executed by Aspic. In the case of this straight waveguide, itsimply draws a rectangle of width and length equal to the waveguide width andlength. Another important function is the getPortPositionScript. This returns anAspic script that defines how many ports are available and where they are located.

Scattering parameters

The third aspect of a BB representation in a library is the behavioral information.For passive linear components the scattering matrix approach is a convenient for-malism for defining the response [68]. In this approach it is assumed that a BB

130

Implementation

1class PDA_DLLAPI tueStraight_SmatrixView : public filBBSmatrixView2{3 public:4 tueStraight_SmatrixView(pda::BB* bb);5 ~tueStraight_SmatrixView(){;}6 bool Transfer( const std::vector<PortMode>::const_iterator& Begin,7 const std::vector<PortMode>::const_iterator& End,8 const pda::Double& lambda, pda::Complex* ret);9};

Listing A.3: tueStraight_SmatrixView definition in C++

has a finite number of well defined ports through which it interacts with compo-nents connected to it. Complex scattering parameters relate an incoming wave atany port to outgoing waves at all ports. For a BB with N ports there are thereforeN2 scattering parameters. This is conveniently represented by a N ×N matrix,where entry (m,n) relates the incoming wave at port n to the outgoing wave atport m. A software representation of such S-matrices was developed by Filaretein the form of a base class: filBBSmatrixView. To implement a S-matrix view fora specific BB, a derived class should be defined. The declaration of the derivedclass for a straight waveguide is shown in listing A.3. The Transfer(..) functiongenerates the S-matrix based on the arguments specified. These arguments are alist of PortModes in the form of a begin and an end point of an iterator over a list.A PortMode is a C++ object that is associated with a port of the BB, but whichalso carries information about which mode it represents, i.e. mode order andpolarization. The list of port modes defines the order in which the ports are tra-versed. The third argument is the wavelength, lambda, that is considered. Finally,the fourth argument specifies the memory location where the generated S-matrixshould be stored. This is a pointer to the beginning of a C++ array of complexnumbers. Row-major encoding is used to store the matrix to this location.

131

BEffective Index Methodvalidity

The Effective Index Method (EIM) is used throughout this thesis to reduce theconsidered cross-sections from a 2D structure to a 1D structure. This may give riseto errors due to invalid assumptions. EIM works well for low-contrast structures,and was found to work reasonably well for medium contrast structures as well [58,141,142]. A derivation that includes the assumptions made can be found in manytextbooks [57, 143]. In this appendix we will compare the results as predictedby EIM to those calculated by a rigorous 2D method. We consider two differenttechnology platforms. The first is the COBRA deep-etched waveguide structurein indium phosphide. The second is a typical silicon on insulator photonic wire.

The rigorous 2D mode solver is based upon a Film Mode Matching (FMM)technique [43]. For both platforms we use 120 film modes. No difference wasobserved when increasing the number of film modes to 180, which indicates thesolver converges to a stable result. The considered wavelength and polarizationwere 1550 nm and TE, respectively. We compare the two methods by looking atthe found mode indices and by looking at the overlap between the found modefield and a laterally shifted copy along the x-axis. By looking at the overlap wetry to obtain a qualitative measure for the accuracy of the field profiles.

B.1 Indium phosphide

The deep-etched COBRA waveguides have the cross-section shown in figure B.1.The results of both the EIM and FMM are shown in figure B.2. The results for themode index match well. The largest deviation is on the order of 10−3 and occursfor the narrowest width. The overlap results also match quite well. Deviations canbe seen for large offsets, where the EIM predicts a faster roll-off. Based on theseresults we can conclude that the effective index method is a valid approximationfor the COBRA waveguide structure.

133

Appendix B. Effective Index Method validity

Figure B.1: COBRA deep-etched waveguide cross-section.

1.5 2 2.5 33.23

3.235

3.24

3.245

3.25

3.255

3.26

3.265

Width [µm]

Nef

f

EIMFMM

(a)

0 0.5 1 1.5−40

−35

−30

−25

−20

−15

−10

−5

0

Offset [µm]

Ove

rlap

[dB

]

EIMFMM

(b)

Figure B.2: Indium phosphide waveguide results. (a): Effective mode index versus wave-guide width. (b): Self overlap of the mode profile in a 1.5 µm wide waveguide versuslateral offset.

B.2 Silicon on insulator

For the silicon on insulator wires we used the structure from [144]. The cross-section is shown in figure B.3. Figure B.4 compares the EIM and FMM. Largedeviations can be seen in both the mode index and in the self-overlap. The devi-ation in the mode index is on the order of 10−1 at the narrowest width. The EIMfield profile is too narrow compared to FMM. Clearly the EIM is unsuitable forvery narrow photonic wire structures.

134

Silicon on insulator

Figure B.3: Silicon on insulator photonic wire waveguide cross-section.

0.4 0.45 0.5 0.55 0.6 0.65

2.1

2.2

2.3

2.4

2.5

2.6

Width [µm]

Nef

f

EIMFMM

(a)

0 0.2 0.4 0.6 0.8−40

−35

−30

−25

−20

−15

−10

−5

0

Offset [µm]

Ove

rlap

[dB

]

EIMFMM

(b)

Figure B.4: Silicon on insulator photonic wire waveguide results. (a): Effective modeindex versus waveguide width. (b): Self overlap of the mode profile in a 400 nm widewaveguide versus lateral offset.

135

Bibliography

[1] S. Miller, “Integrated optics: An introduction,” The Bell System TechnicalJournal, vol. 48, no. 7, pp. 2059–2069, September 1969.

[2] S. Nicholes, M. Masanovic, B. Jevremovic, E. Lively, L. Coldren, andD. Blumenthal, “An 8× 8 InP monolithic tunable optical router (motor)packet forwarding chip,” Journal of Lightwave Technology, vol. 28, no. 4,pp. 641–650, 2010.

[3] N. K. Fontaine, R. P. Scott, and S. Yoo, “Dynamic optical arbitrary wave-form generation and detection in InP photonic integrated circuits for Tb/soptical communications,” Optics Communications, vol. 284, no. 15, pp.3693–3705, 2011.

[4] M. K. Smit, “A breakthrough in photonic integration,” Fotonica Magazine,vol. 34, no. 1, pp. 5–10, January 2009.

[5] R. P. Nagarajan and M. Smit, “Photonic integration,” IEEE LEOS Newslet-ter, vol. 21, no. 3, pp. 4–10, June 2007.

[6] M. K. Smit, “Toward a breakthrough in photonic integration,” in TechnicalDigest of the fifteenth MicroOptics Conference, MOC’09, October 25-28,2009, Tokyo, Japan., October 2009, pp. 18–21.

[7] M. Smit, X. Leijtens, E. Bente, J. van der Tol, H. Ambrosius, D. Robbins,M. Wale, N. Grote, and M. Schell, “A generic foundry model for InP-basedphotonic ICs,” in Optical Fiber Communication Conference and Exposition(OFC/NFOEC), 2012 and the National Fiber Optic Engineers Conference,2012, pp. 1–3.

[8] W. Green, S. Assefa, A. Rylyakov, C. Schow, F. Horst, and Y. Vlasov,“CMOS integrated silicon nanophotonics: An enabling technology for ex-ascale computing,” in Advanced Photonics. Optical Society of America,2011.

[9] M. Romagnoli, P. Galli, G. Grasso, E. Iannone, and A. Bogoni, “Opticalintegration: Enabling technology for photonic switching,” in Photonics inSwitching, 2009. PS ’09. International Conference on, 2009, pp. 1–4.

[10] J. Ko and Y. Ni, “Technology developments in structural health monitoringof large-scale bridges,” Engineering Structures, vol. 27, no. 12, pp. 1715–1725, 2005.

137

Bibliography

[11] A. Minardo, R. Bernini, L. Amato, and L. Zeni, “Bridge monitoring usingBrillouin fiber-optic sensors,” Sensors Journal, IEEE, vol. 12, no. 1, pp.145–150, 2012.

[12] B. J. A. Costa and J. A. Figueiras, “Fiber optic based monitoring systemapplied to a centenary metallic arch bridge: Design and installation,” Engi-neering Structures, vol. 44, pp. 271–280, 2012.

[13] P. Antunes, H. Lima, N. Alberto, L. Bilro, P. Pinto, A. Costa, H. Rodrigues,J. Pinto, R. Nogueira, H. Varum, and P. André, “Optical sensors basedon fiber Bragg gratings for structural health monitoring,” in New Develop-ments in Sensing Technology for Structural Health Monitoring, ser. LectureNotes in Electrical Engineering, S. Mukhopadhyay, Ed. Springer BerlinHeidelberg, 2011, vol. 96, pp. 253–295.

[14] X. Bao and L. Chen, “Recent progress in optical fiber sensors based on Bril-louin scattering at university of Ottawa,” Photonic Sensors, vol. 1, no. 2, pp.102–117, 2011.

[15] E. Mendoza, Y. Esterkin, C. Kempen, and Z. Sun, “Multi-channel mono-lithic integrated optic fiber Bragg grating sensor interrogator,” PhotonicSensors, vol. 1, no. 3, pp. 281–288, 2011.

[16] M. Felicetti, J. van der Tol, R. K. Breteler, D. Szymanski, and M. K. Smit,“InP photonic integrated circuit for BOTDR fiber sensing,” in AdvancedPhotonics. Optical Society of America, 2013.

[17] D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson,W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fuji-moto, “Optical coherence tomography,” Science, vol. 254, pp. 1178–1181,1991.

[18] V. D. Nguyen, B. I. Akca, K. Wörhoff, R. M. de Ridder, M. Pollnau, T. G.van Leeuwen, and J. Kalkman, “Spectral domain optical coherence to-mography imaging with an integrated optics spectrometer,” Optics Letters,vol. 36, no. 7, pp. 1293–1295, April 2011.

[19] B. Tilma, Y. Jiao, J. Kotani, X. Leijtens, R. Nötzel, M. Smit, and E. Bente,“Monolithically integrated continuously tunable InP-based quantum-dotlaser source in the 1.6 to 1.8 µm wavelength region,” in Proceedings ofthe 15th Annual Symposium of the IEEE Photonics Benelux Chapter, 2010,pp. 81–84.

[20] B. Tilma, Y. Jiao, P. J. Van Veldhoven, B. Smalbrugge, H. P. M. M. Am-brosius, P. Thijs, X. Leijtens, R. Nötzel, M. Smit, and E. A. J. M. Bente,“InP-based monolithically integrated tunable wavelength filters in the 1.6-1.8 µm wavelength region for tunable laser purposes,” Journal of LightwaveTechnology, vol. 29, no. 18, pp. 2818–2830, 2011.

[21] A. M. Weiner, “Ultrafast optical pulse shaping: A tutorial review,” OpticsCommunications, vol. 284, no. 15, pp. 3669–3692, 2011, special Issue on

138

Bibliography

Optical Pulse Shaping, Arbitrary Waveform Generation, and Pulse Charac-terization.

[22] M. Heck, P. Muñoz, E. Bente, Y. Barbarin, Y. Oei, R. Nötzel, D. Lenstra,and M. Smit, “Tunable integrated pulse shaping devices,” in Proceedings ofthe 10th Annual Symposium IEEE/LEOS Benelux Chapter, 1-2 December2005, pp. 75–78.

[23] E. Bente, S. Tahvili, X. Leijtens, M. Wale, E. Klein, and M. Smit, “In-tegrated optical pulse shaping devices for mode-locked lasers in the 1.5µm region,” in Transparent Optical Networks (ICTON), 2012 14th Interna-tional Conference on, 2012, pp. 1–4.

[24] F. Soares, N. Fontaine, R. Scott, J.-H. Baek, X. Zhou, T. Su, S. Cheung,Y. Wang, C. Junesand, S. Lourdudoss, K.-Y. Liou, R. Hamm, W. Wang,B. Patel, L. A. Gruezke, W. Tsang, J. Heritage, and S. J. B. Yoo, “Mono-lithic InP 100-channel × 10-GHz device for optical arbitrary waveformgeneration,” Photonics Journal, IEEE, vol. 3, no. 6, pp. 975–985, 2011.

[25] K. Mandai, T. Suzuki, H. Tsuda, T. Kurokawa, and T. Kawanishi, “Ar-bitrary optical short pulse generator using a high-resolution arrayed-waveguide grating,” in Microwave Photonics, 2004. MWP’04. 2004 IEEEInternational Topical Meeting on, 2004, pp. 107–110.

[26] N. K. Fontaine, R. P. Scott, J. Cao, A. Karalar, W. Jiang, K. Okamoto, J. P.Heritage, B. H. Kolner, and S. J. B. Yoo, “32 phase × 32 amplitude opticalarbitrary waveform generation,” Optics Letters, vol. 32, no. 7, pp. 865–867,April 2007.

[27] C.-C. Chong, K. Hamaguchi, P. F. Smulders, and S.-K. Yong, “Millimeter-wave wireless communication systems: Theory and applications,”EURASIP Journal on Wireless Communications and Networking, no. 1,2007.

[28] S. Tripathi, K. Takeya, H. Inoue, T. Hasegawa, and K. Kawase, “Non-destructive inspection of chloride ion in concrete structures using millime-ter wave attenuated total reflection technique,” in Infrared, Millimeter, andTerahertz Waves (IRMMW-THz), 2012 37th International Conference on,2012, pp. 1–2.

[29] J. Yao, “Microwave photonics,” Journal of Lightwave Technology, vol. 27,no. 3, pp. 314–335, 2009.

[30] U. Gliese, T. Nielsen, S. Norskov, and K. Stubkjaer, “Multifunctional fiber-optic microwave links based on remote heterodyne detection,” MicrowaveTheory and Techniques, IEEE Transactions on, vol. 46, no. 5, pp. 458–468,1998.

[31] A. Corradi, G. Carpintero, B. W. Tilma, M. K. Smit, and E. A. J. M. Bente,“Integrated dual-wavelength semiconductor laser systems for millimeterwave generation,” in Semiconductor Laser Conference (ISLC), 2012 23rdIEEE International, 2012, pp. 34–35.

139

Bibliography

[32] W.-P. Huang, X. Li, C.-Q. Xu, X. Hong, C. Xu, and W. Liang, “Opticaltransceivers for fiber-to-the-premises applications: System requirementsand enabling technologies,” Journal of Lightwave Technology, vol. 25,no. 1, pp. 11–27, 2007.

[33] D. Vermeulen, G. Roelkens, J. Brouckaert, D. Van Thourhout, and R. Baets,“Toward an integrated fiber-to-the-home transceiver on a silicon nanopho-tonics platform,” in Proceedings of the 13th Annual Symposium of the IEEEPhotonics Benelux Chapter, 2008, pp. 87–90.

[34] The MOSIS service. University of Southern California. [Online].Available: http://www.mosis.com/

[35] L. Conway, The MPC Adventures: Experiences with the Generation ofVLSI Design and Implementation Methodologies: Transcribed from an In-vited Lecture at the Second Caltech Conference on Very Large Scale Inte-gration, January 19, 1981. Xerox Palo Alto Research Center, 1981.

[36] Committee on Innovations in Computing and Communications: Lessonsfrom History, National Research Council, Funding a Revolution:Government Support for Computing Research. The National AcademiesPress, 1999. [Online]. Available: http://www.nap.edu/openbook.php?record_id=6323

[37] S. P. Dandamudi, Guide to RISC Processors for Programmers and Engi-neers. Springer New York, 2005.

[38] A. J. Martin, “25 years ago: The first asynchronous micropro-cessor,” January 2014. [Online]. Available: http://resolver.caltech.edu/CaltechAUTHORS:20140206-111915844

[39] M. Smit, X. Leijtens, E. Bente, J. Van der Tol, H. Ambrosius, D. Robbins,M. Wale, N. Grote, and M. Schell, “Generic foundry model for InP-basedphotonics,” Optoelectronics, IET, vol. 5, no. 5, pp. 187–194, 2011.

[40] M. Smit, “Past and future of InP-based photonic integration,” in IEEELasers and Electro-Optics Society, 2008. LEOS 2008. 21st Annual Meet-ing of the, November 2008, pp. 51–52.

[41] A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, andP. De Dobbelaere, “A grating-coupler-enabled CMOS photonics platform,”Journal of Selected Topics in Quantum Electronics, IEEE, vol. 17, no. 3,pp. 597–608, 2011.

[42] JePPIX: Joint European Platform for InP-based Photonic IntegratedComponents and Circuits. [Online]. Available: http://www.jeppix.eu/

[43] Phoenix Software B.V., FieldDesigner, MaskEngineer and OptoDesigner,Enschede, The Netherlands, 2014. [Online]. Available: http://www.phoenixbv.com

[44] W. Bogaerts, Y. Li, S. Pathak, A. Ruocco, M. Fiers, A. Ribeiro, E. Lambert,and P. Dumon, “Integrated design for integrated photonics: from the phys-

140

http://www.mosis.com/

http://www.nap.edu/openbook.php?record_id=6323

http://www.nap.edu/openbook.php?record_id=6323

http://resolver.caltech.edu/CaltechAUTHORS:20140206-111915844

http://resolver.caltech.edu/CaltechAUTHORS:20140206-111915844

http://www.jeppix.eu/

http://www.phoenixbv.com

http://www.phoenixbv.com

Bibliography

ical to the circuit level and back,” in Proceedings SPIE 8781, IntegratedOptics: Physics and Simulations, 2013, p. 878102.

[45] E. Lambert, M. Fiers, S. Nizamov, M. Tassaert, S. Johnson, P. Bienstman,and W. Bogaerts, “Python bindings for the open source electromagneticsimulator meep,” Computing in Science Engineering, vol. 13, no. 3, pp.53–65, 2011.

[46] M. Fiers, T. V. Vaerenbergh, K. Caluwaerts, D. V. Ginste, B. Schrauwen,J. Dambre, and P. Bienstman, “Time-domain and frequency-domain model-ing of nonlinear optical components at the circuit-level using a node-basedapproach,” Journal of the Optical Society of America B, vol. 29, no. 5, pp.896–900, May 2012.

[47] F. Fiedler and A. Schlachetzki, “Optical parameters of InP-based wave-guides,” Solid-State Electronics, vol. 30, no. 1, pp. 73 – 83, 1987.

[48] X. Leijtens, “JePPIX: the platform for indium phosphide-based photonics,”Optoelectronics, IET, vol. 5, no. 5, pp. 202–206, October 2011.

[49] J. H. Den Besten, M. P. Dessens, C. G. P. Herben, X. Leijtens, F. Groen,M. Leys, and M. Smit, “Low-loss, compact, and polarization independentphasar demultiplexer fabricated by using a double-etch process,” PhotonicsTechnology Letters, IEEE, vol. 14, no. 1, pp. 62–64, Jan 2002.

[50] N. Kapany and J. Burke, Optical waveguides, ser. Quantum electronics–principles and applications. Academic Press, 1972.

[51] L. Soldano and E. C. M. Pennings, “Optical multi-mode interference de-vices based on self-imaging: principles and applications,” Journal of Light-wave Technology, vol. 13, no. 4, pp. 615–627, 1995.

[52] J.-H. Jang, W. Zhao, J. W. Bae, D. Selvanathan, S. Rommel, I. Adesida,A. Lepore, M. Kwakernaak, and J. Abeles, “Direct measurement ofnanoscale sidewall roughness of optical waveguides using an atomic forcemicroscope,” Applied Physics Letters, vol. 83, no. 20, pp. 4116–4118,2003.

[53] J. W. Bae, W. Zhao, J.-H. Jang, I. Adesida, A. Lepore, M. Kwakernaak,and J. Abeles, “Characterization of sidewall roughness of InP/InGaAsPetched using inductively coupled plasma for low loss optical waveguideapplications,” Journal of Vacuum Science Technology B: Microelectronicsand Nanometer Structures, vol. 21, no. 6, pp. 2888–2891, 2003.

[54] J. Lin, A. Leven, N. G. Weimann, Y. Yang, R. F. Kopf, R. Reyes, Y. K.Chen, and F. sen Choa, “Smooth and vertical-sidewall InP etching usingCl2/N2 inductively coupled plasma,” Journal of Vacuum Science Technol-ogy B: Microelectronics and Nanometer Structures, vol. 22, no. 2, pp. 510–512, 2004.

[55] F. Payne and J. Lacey, “A theoretical analysis of scattering loss from planaroptical waveguides,” Optical and Quantum Electronics, vol. 26, no. 10, pp.977–986, 1994.

141

Bibliography

[56] A. Melloni, F. Carniel, R. Costa, and M. Martinelli, “Determination of bendmode characteristics in dielectric waveguides,” Journal of Lightwave Tech-nology, vol. 19, no. 4, pp. 571–577, 2001.

[57] C. Vassallo, Optical waveguide concepts. Elsevier, 1991.[58] K. S. Chiang, “Performance of the effective-index method for the analysis

of dielectric waveguides,” Optics Letters, vol. 16, no. 10, pp. 714–716, May1991.

[59] D. Marcuse, “Radiation losses of tapered dielectric slab waveguides,” TheBell System Technical Journal, pp. 273–290, February 1970.

[60] H. Taylor and A. Yariv, “Guided wave optics,” Proceedings of the IEEE,vol. 62, no. 8, pp. 1044–1060, Aug 1974.

[61] R. G. Hunsperger, Integrated Optics, Theory and Technology, 6th ed., ser.Advanced Texts in Physics. Springer, 2009.

[62] Wolfram Research, Inc., Mathematica Edition: Version 8.0. Champaign,Illinois: Wolfram Research, Inc., 2010.

[63] E.-G. Neumann, “Curved dielectric optical waveguides with reduced tran-sition losses,” Microwaves, Optics and Antennas, IEE Proceedings H, vol.129, no. 5, pp. 278–280, 1982.

[64] P. Besse, E. Gini, Bachmann, M., and H. Melchior, “New 1 × 2 multi-mode interference couplers with free selection of power splitting ratios,” inECOC Proceedings Firenze ’94, September 1994.

[65] P. Besse, E. Gini, M. Bachmann, and H. Melchior, “New 2×2 and 1×3multimode interference couplers with free selection of power splitting ra-tios,” Journal of Lightwave Technology, vol. 14, no. 10, pp. 2286–2293,October 1996.

[66] R. Hanfoug, L. Augustin, Y. Barbarin, J. Van der Tol, E. Bente, F. Karouta,D. Rogers, S. Cole, Y. Oei, X. Leijtens, and M. Smit, “Reduced reflectionsfrom multimode interference couplers,” Electronics Letters, vol. 42, no. 8,pp. 465–466, 2006.

[67] R. H. Dicke, “A computational method applicable to microwave networks,”Journal of Applied Physics, vol. 18, no. 10, pp. 873–878, 1947.

[68] X. Leijtens, P. Le Lourec, and M. Smit, “S-matrix oriented CAD-tool forsimulating complex integrated optical circuits,” Journal of Selected Topicsin Quantum Electronics, IEEE, vol. 2, no. 2, pp. 257–262, June 1996.

[69] M. Born and E. Wolf, Principles of Optics, 7th ed. Cambridge UniversityPress, 1999.

[70] D. Stock and L. Kaplan, “A comment on the scattering matrix of cas-caded 2n-ports (correspondence),” Microwave Theory and Techniques, IRETransactions on, vol. 9, no. 5, pp. 454–454, September 1961.

[71] G. Simpson, “A generalized n-port cascade connection,” in MicrowaveSymposium Digest, 1981 IEEE MTT-S International, June 1981, pp. 507–509.

142

Bibliography

[72] C. Bachiller, H. Gonzalez, V. Esbert, A. Martinez, and J. Morro, “Efficienttechnique for the cascade connection of multiple two-port scattering ma-trices,” Microwave Theory and Techniques, IEEE Transactions on, vol. 55,no. 9, pp. 1880–1886, Sept 2007.

[73] D. Erasme, L. Spiekman, C. Herben, M. Smit, and F. Groen, “Experimentalassessment of the reflection of passive multimode interference couplers,”Photonics Technology Letters, IEEE, vol. 9, no. 12, pp. 1604–1606, 1997.

[74] Y. Gottesman, E. Rao, and B. Dagens, “A novel design proposal to mini-mize reflections in deep-ridge multimode interference couplers,” PhotonicsTechnology Letters, IEEE, vol. 12, no. 12, pp. 1662–1664, 2000.

[75] E. Pennings, R. van Roijen, M. Van Stralen, P. De Waard, R. Koumans,and B. Verbeek, “Reflection properties of multimode interference devices,”Photonics Technology Letters, IEEE, vol. 6, no. 6, pp. 715–718, 1994.

[76] Y. Li and R. Baets, “Improved multi-mode interferometers (MMIs) onsilicon-on-insulator with the optimized return loss and isolation,” in Pro-ceedings of the 16th Annual Symposium of the IEEE Photononics BeneluxChapter, 2011, pp. 205–208.

[77] M. Seimetz and C.-M. Weinert, “Options, feasibility, and availability of2×4 90◦ hybrids for coherent optical systems,” Journal of Lightwave Tech-nology, vol. 24, no. 3, pp. 1317–1322, 2006.

[78] M. Bachmann, P. Besse, and H. Melchior, “General self-imaging proper-ties in N × N multimode interference couplers including phase relations,”Applied Optics, vol. 33, no. 18, pp. 3905–3911, June 1994.

[79] OIF-DPC-RX-01.1: Implementation Agreement for Integrated Dual Pola-rization Intradyne Coherent Receivers, Optical Internetworking ForumStd., April 2010.

[80] S.-H. Jeong and K. Morito, “Novel optical 90◦ hybrid consisting of a pairedinterference based 2× 4 MMI coupler, a phase shifter and a 2× 2 MMIcoupler,” Journal of Lightwave Technology, vol. 28, no. 9, pp. 1323–1331,2010.

[81] E. Jones, T. Oliphant, P. Peterson et al., “SciPy: Open source scientifictools for Python,” 2001–. [Online]. Available: http://www.scipy.org/

[82] M. Ettenberg, “A new dielectric facet reflector for semiconductor lasers,”Applied Physics Letters, vol. 32, no. 11, pp. 724–725, 1978.

[83] B. Docter, E. Geluk, M. Sander-Jochem, F. Karouta, and M. Smit, “Deepetched DBR gratings in InP for photonic integrated circuits,” in IndiumPhosphide Related Materials, 2007. IPRM ’07. IEEE 19th InternationalConference on, 2007, pp. 226–228.

[84] Y. Huang, Y. Xiao, G. Xu, S. Chang, Y.-G. Zhao, R. Wang, B. Ooi,and S. Ho, “A single-directional microcavity laser with microloop mirrorsand widened medium realized with quantum-well intermixing,” PhotonicsTechnology Letters, IEEE, vol. 18, no. 1, pp. 130–132, January 2006.

143

http://www.scipy.org/

Bibliography

[85] B. Docter, J. Pozo, S. Beri, I. Ermakov, J. Danckaert, M. Smit, andF. Karouta, “Discretely tunable laser based on filtered feedback fortelecommunication applications,” Journal of Selected Topics in QuantumElectronics, IEEE, vol. 16, no. 5, pp. 1405–1412, September 2010.

[86] K. Kasunic, “Design equations for the reflectivity of deep-etch distributedBragg reflector gratings,” Journal of Lightwave Technology, vol. 18, no. 3,pp. 425–429, March 2000.

[87] T. Kleckner, D. Modotto, A. Locatelli, J. Mondia, S. Linden, R. Morandotti,C. De Angelis, C. Stanley, H. van Driel, and J. Aitchison, “Design, fabrica-tion, and characterization of deep-etched waveguide gratings,” Journal ofLightwave Technology, vol. 23, no. 11, pp. 3832–3842, November 2005.

[88] Y. Ikuma, M. Yasumoto, D. Miyamoto, J. Ito, and H. Tsuda, “Small helicalreflective arrayed-waveguide grating with integrated loop mirrors,” OpticalCommunication (ECOC), 2007 33rd European Conference and Ehxibitionof, pp. 1–2, September 2007.

[89] L. Xu, X. Leijtens, P. Urban, E. Smalbrugge, T. de Vries, Y. Oei, R. Nötzel,H. de Waardt, and M. Smit, “Novel reflective SOA with MMI-loop mirrorbased on semi-insulating InP,” in Proceedings of the 13th Annual Sympo-sium of the IEEE Photonics Benelux Chapter. Enschede, The Netherlands,November 2008, pp. 43–46.

[90] W. Yuan, C. Seibert, and D. Hall, “Single-facet teardrop laser withmatched-bends design,” Journal of Selected Topics in Quantum Electron-ics, IEEE, vol. 17, no. 6, pp. 1662–1669, November 2011.

[91] L. Xu, X. Leijtens, B. Docter, T. de Vries, E. Smalbrugge, F. Karouta,and M. Smit, “MMI-reflector: A novel on-chip reflector for photonic inte-grated circuits,” in Optical Communication, 2009. ECOC ’09. 35th Euro-pean Conference on, September 2009, pp. 1–2.

[92] J. Zhao, E. Kleijn, M. Smit, P. Williams, I. Knight, M. Wale, and X. Leij-tens, “Novel lasers using multimode interference reflector,” in InformationPhotonics (IP), 2011 ICO International Conference on, 2011, pp. 1–2.

[93] J. Zhao, E. Kleijn, P. Williams, M. Smit, and X. Leijtens, “On-chip laserwith multimode interference reflectors realized in a generic integration plat-form,” in Compound Semiconductor Week (CSW/IPRM), 2011 and 23rd In-ternational Conference on Indium Phosphide and Related Materials, 2011,pp. 1–4.

[94] P. Besse, M. Bachmann, H. Melchior, L. Soldano, and M. Smit, “Opticalbandwidth and fabrication tolerances of multimode interference couplers,”Journal of Lightwave Technology, vol. 12, no. 6, pp. 1004–1009, June 1994.

[95] M. Bachmann, P. Besse, and H. Melchior, “Overlapping-image multimodeinterference couplers with a reduced number of self-images for uniformand nonuniform power splitting,” Applied Optics, vol. 34, no. 30, pp. 6898–6910, October 1995.

144

Bibliography

[96] P. A. Besse, J.-S. Gu, and H. Melchior, “Reflectivity minimization ofsemiconductor laser amplifiers with coated and angled facets consideringtwo-dimensional beam profiles,” Journal of Quantum Electronics, IEEE,vol. 27, no. 6, pp. 1830–1836, June 1991.

[97] J. Leuthold, R. Hess, J. Eckner, P. Besse, and H. Melchior, “Spatialmode filters realized with multimode interference couplers,” Optics Let-ters, vol. 21, no. 11, pp. 836–838, 1996.

[98] R. M. A. Azzam, “Phase shifts that accompany total internal reflection ata dielectric–dielectric interface,” Journal of the Optical Society of AmericaA, vol. 21, no. 8, pp. 1559–1563, August 2004.

[99] R. Walker, “Simple and accurate loss measurement technique for semicon-ductor optical waveguides,” Electronics Letters, vol. 21, no. 13, pp. 581–583, June 1985.

[100] M. Smit, “New focusing and dispersive planar component based on an op-tical phased array,” Electronics Letters, vol. 24, no. 7, pp. 385–386, 1988.

[101] M. Smit and C. Van Dam, “PHASAR-based WDM-devices: Principles, de-sign and applications,” Journal of Selected Topics in Quantum Electronics,IEEE, vol. 2, no. 2, pp. 236–250, June 1996.

[102] H. Takahashi, I. Nishi, and Y. Hibino, “10 GHz spacing optical frequencydivision multiplexer based on arrayed-waveguide grating,” Electronics Let-ters, vol. 28, no. 4, pp. 380–382, Feb 1992.

[103] M. K. Smit, “Integrated optics in silicon-based aluminum oxide,” Ph.D.dissertation, Delft University of Technology, 1991.

[104] C. Dragone, “An N×N optical multiplexer using a planar arrangement oftwo star couplers,” Photonics Technology Letters, IEEE, vol. 3, no. 9, pp.812–815, September 1991.

[105] H. Bissessur, F. Gaborit, B. Martin, G. Ripoche, and P. Pagnod-Rossiaux,“Tunable phased-array wavelength demultiplexer on InP,” Electronics Let-ters, vol. 31, no. 1, pp. 32–33, Jan 1995.

[106] K. Peterman, “External optical feedback phenomena in semiconductorlasers,” Journal of Selected Topics in Quantum Electronics, IEEE, vol. 1,no. 2, pp. 480–489, 1995.

[107] P. Muñoz, R. García-Olcina, C. Habib, L. Chen, X. Leijtens, T. de Vries,M. Heck, L. Augustin, R. Nötzel, and D. Robbins, “Sagnac loop reflec-tor and arrayed waveguide grating-based multi-wavelength laser monolith-ically integrated on InP,” IET Optoelectronics, vol. 5, no. 5, pp. 207–210,2011.

[108] M. H. Kwakernaak, W. Chan, N. Maley, H. Mohseni, L. Yang, D. R.Capewell, B. Kharas, V. Frantz, T. Mood, G. Pajer, D. Ackerman, J. G.Kim, and D. H. Lee, “Multi-frequency laser monolithically integratingInGaAsP gain elements with amorphous silicon AWG,” in Optical Fiber

145

Bibliography

Communication Conference, 2006 and the 2006 National Fiber Optic En-gineers Conference. OFC 2006, 2006.

[109] M. Zirngibl and C. Joyner, “12 frequency WDM laser based on a trans-missive waveguide grating router,” Electronics Letters, vol. 30, no. 9, pp.701–702, 1994.

[110] C. Joyner, M. Zirngibl, and J. P. Meester, “A multifrequency waveguidegrating laser by selective area epitaxy,” Photonics Technology Letters,IEEE, vol. 6, no. 11, pp. 1277–1279, 1994.

[111] C. Dragone, “Efficient N×N star couplers using Fourier optics,” Journalof Lightwave Technology, vol. 7, no. 3, pp. 479–489, March 1989.

[112] A. Melloni, A. Canciamilla, G. Morea, F. Morichetti, A. Samarelli, andM. Sorel, “Design kits and circuit simulation in integrated optics,” in Inte-grated Photonics Research, Silicon and Nanophotonics. Optical Societyof America, 2010.

[113] P. Muñoz, D. Pastor, and J. Capmany, “Modeling and design of arrayedwaveguide gratings,” Journal of Lightwave Technology, vol. 20, no. 4, pp.661–674, April 2002.

[114] A. Klekamp and R. Munzner, “Calculation of imaging errors of AWG,”Journal of Lightwave Technology, vol. 21, no. 9, pp. 1978–1986, September2003.

[115] J. Soole, M. Amersfoort, H. Leblanc, N. Andreadakis, A. Rajhel,C. Caneau, R. Bhat, M. Koza, C. Youtsey, and I. Adesida, “Use ofmultimode interference couplers to broaden the passband of wavelength-dispersive integrated WDM filters,” Photonics Technology Letters, IEEE,vol. 8, no. 10, pp. 1340–1342, October 1996.

[116] C. Doerr, M. Shirasaki, and C. Joyner, “Chromatic focal plane displace-ment in the parabolic chirped waveguide grating router,” Photonics Tech-nology Letters, IEEE, vol. 9, no. 5, pp. 625–627, 1997.

[117] J. Goodman, Introduction to Fourier Optics, 3rd ed. Roberts and CompanyPublishers, December 2005.

[118] C. Vassallo, “Limitations of the wide-angle beam propagation method innonuniform systems,” Journal of the Optical Society of America A, vol. 13,no. 4, pp. 761–770, April 1996.

[119] M. Amersfoort, C. de Boer, F. van Ham, M. Smit, P. Demeester, J. van derTol, and A. Kuntze, “Phased-array wavelength demultiplexer with flattenedwavelength response,” Electronics Letters, vol. 30, no. 4, pp. 300–302,February 1994.

[120] K. Okamoto and A. Sugita, “Flat spectral response arrayed-waveguidegrating multiplexer with parabolic waveguide horns,” Electronics Letters,vol. 32, no. 18, p. 1661, August 1996.

146

Bibliography

[121] P. Muñoz, D. Pastor, and J. Capmany, “Analysis and design of arrayedwaveguide gratings with MMI couplers,” Optics Express, vol. 9, no. 7, pp.328–338, September 2001.

[122] T. Kamalakis, T. Sphicopoulos, and D. Syvridis, “An estimation of perfor-mance degradation due to fabrication errors in AWGs,” Journal of Light-wave Technology, vol. 20, no. 9, pp. 1779–1787, 2002.

[123] S. Day, J. P. Stagg, D. Moule, S. J. Clements, C. Rogers, S. Ojha, T. Clapp,J. Brook, and J. Morley, “The elimination of sidelobes in the arrayed wave-guide WDM,” in Integrated Photonics Research. Optical Society of Amer-ica, 1996.

[124] M. Kohtoku, T. Hirono, S. Oku, Y. Kadota, Y. Shibata, and Y. Yoshikuni,“Control of higher order leaky modes in deep-ridge waveguides and appli-cation to low-crosstalk arrayed waveguide gratings,” Journal of LightwaveTechnology, vol. 22, no. 2, pp. 499–508, 2004.

[125] F. Soares, W. Jiang, N. Fontaine, S.-W. Seo, J.-H. Baek, R. Broeke, J. Cao,K. Okamoto, F. Olsson, S. Lourdudoss, and S. J. B. Yoo, “InP-basedarrayed-waveguide grating with a channel spacing of 10 GHz,” in OpticalFiber communication/National Fiber Optic Engineers Conference, 2008.OFC/NFOEC 2008. Conference on, 2008, pp. 1–3.

[126] E. Kleijn, P. Williams, N. Whitbread, M. Wale, M. Smit, and X. Leij-tens, “Sidelobes caused by polarization rotation in arrayed waveguide grat-ings,” in Information Photonics (IP), 2011 ICO International Conferenceon, 2011, pp. 1–2.

[127] W. Lui, T. Hirono, K. Yokoyama, and W.-P. Huang, “Polarization rotationin semiconductor bending waveguides: a coupled-mode theory formula-tion,” Journal of Lightwave Technology, vol. 16, no. 5, pp. 929–936, 1998.

[128] H. Takahashi, Y. Hibino, and I. Nishi, “Polarization-insensitive arrayed-waveguide grating wavelength multiplexer on silicon,” Optics Letters,vol. 17, no. 7, pp. 499–501, April 1992.

[129] M. Zirngibl, C. Joyner, and P. Chou, “Polarisation compensated waveguidegrating router on InP,” Electronics Letters, vol. 31, no. 19, pp. 1662–1664,1995.

[130] H. Takahashi, Y. Hibino, Y. Ohmori, and M. Kawachi, “Polarization-insensitive arrayed-waveguide wavelength multiplexer with birefringencecompensating film,” Photonics Technology Letters, IEEE, vol. 5, no. 6, pp.707–709, 1993.

[131] M. Zirngibl, C. Joyner, L. Stulz, T. Gaiffe, and C. Dragone, “Polarisationindependent 8×8 waveguide grating multiplexer on InP,” Electronics Let-ters, vol. 29, no. 2, pp. 201–202, 1993.

[132] Optiwave, OptiFDTD tutorials, 32 bit edition, Ottawa, Canada, 2013.[Online]. Available: http://www.optiwave.com

147

http://www.optiwave.com

Bibliography

[133] Photonic Design Automation. PDAFlow Foundation. [Online]. Available:http://www.pdaflow.org/

[134] C. Gibson, Elementary Geometry of Differentiable Curves. CambridgeUniversity Press, 2001.

[135] PhotonDesign, PICWAVE, Oxford, United Kingdom, 2014. [Online].Available: http://www.photond.com

[136] Filarete s.r.l., Aspic Design, Milano, Italy, 2014. [Online]. Available:http://www.aspicdesign.com/

[137] A. Milton and W. Burns, “Mode coupling in optical waveguide horns,”Journal of Quantum Electronics, IEEE, vol. 13, no. 10, pp. 828–835, Oc-tober 1977.

[138] J. Leuthold, M. Mayer, J. Eckner, G. Guekos, H. Melchior, and C. Zell-weger, “Material gain of bulk 1.55 µm InGaAsP/InP semiconductor opti-cal amplifiers approximated by a polynomial model,” Journal of AppliedPhysics, vol. 87, no. 1, pp. 618–620, 2000.

[139] OpenAccess Database. Silicon Integration Initiative, Inc (Si2). [Online].Available: http://www.si2.org/

[140] M. Smit et al., “An introduction to InP-based generic integration technol-ogy,” Semiconductor Science and Technology, vol. 29, no. 8, p. 083001,2014.

[141] T. Benson, R. Bozeat, and P. Kendall, “Rigorous effective index method forsemiconductor rib waveguides,” Optoelectronics, IEE Proceedings J, vol.139, no. 1, pp. 67–70, Feb 1992.

[142] J.-S. Lee and S.-Y. Shin, “On the validity of the effective-index methodfor rectangular dielectric waveguides,” Journal of Lightwave Technology,vol. 11, no. 8, pp. 1320–1324, Aug 1993.

[143] D. Marcuse, Theory of dielectric optical waveguides, 2nd ed. AcademicPress, 1991.

[144] W. Bogaerts, R. Baets, P. Dumon, V. Wiaux, S. Beckx, D. Taillaert,B. Luyssaert, J. Van Campenhout, P. Bienstman, and D. Van Thourhout,“Nanophotonic waveguides in silicon-on-insulator fabricated with CMOStechnology,” Journal of Lightwave Technology, vol. 23, no. 1, pp. 401–412,Jan 2005.

148

http://www.pdaflow.org/

http://www.photond.com

http://www.aspicdesign.com/

http://www.si2.org/

Summary

For a long time the photonics industry has been dominated by vertically inte-grated companies. These companies control the entire manufacturing chain fromresearch and chip design to fabrication and marketing. Maintaining the necessaryinfrastructure is very costly. Very large volumes to reach high utilization levelsare therefore required to be profitable. The need for high volumes excludes manysmall market applications from benefiting from photonic integration technology.In electronics a similar issue was overcome in the seventies through the introduc-tion of generic integration technologies. Such a technology is not optimized fora single application, but instead forms a platform that can be used for many dif-ferent applications. This allows companies owning fabrication facilities to alsoproduce for other players. This idea forms the heart of the foundry model andwas only introduced relatively recently to the integrated photonics community. Inelectronics the foundry model was introduced in the eighties and has been a hugesuccess.

A second idea originating in electronics is the use of basic building blocks.The idea is that a broad range of functionality can be realized from a rather smallset of basic building blocks. In electronics these are the transistor, resistor, ca-pacitor, etc. In photonics these could be optical amplifiers, modulators, detectorsand various passive components. When optimizing the basic building blocks, anycircuit constructed from them also benefits from improved performance. Thisjustifies investments in development at the basic building block level. Adoptingthe building block based approach gives rise to hierarchical design methods be-cause a collection of basic building blocks (BBBs) can be combined to form aComposite Building Block (CBBs). The time needed to design a circuit designcan be reduced by reusing existing CBBs. A PIC designer no longer needs to beaware of the layer stack and process details. Instead, a circuit can be designed bycombining different BBs. The circuit performance can be verified using circuitsimulation. When fast circuit simulation methods are available, designers can usesimulation at every step in the design process. Large collections of BBs can beefficiently shared by storing them in software component libraries. These librariescontain information on the geometry, on the symbolic representation, and on thebehavior of the components. By agreeing on a common library format, many dif-

149

Summary

ferent software packages can make use of the same libraries. The goal of thisthesis is to develop such libraries for the COBRA generic integration technology.The main focus lies on developing component models that are fast enough to beused in circuit simulation, while retaining sufficient accuracy to provide meaning-ful results. This thesis presents novel models to describe the behavior of severalcomponents. It also introduces new components, and improved components. Themain results presented in this thesis are:

• a novel approach to describe layer stack properties. In this approach, ac-curate numerical results are fitted to a model. This results in an enormousincrease in speed and improved reliability while retaining full accuracy.

• a new approximate simulation method to model reflections at MMI junc-tions. Compared to rigorous methods, this model has reduced accuracy butoffers four orders of magnitude increase in speed. Its use has led to insightinto the effects of small reflections on circuit performance.

• a new geometry for MMIs that strongly suppresses parasitic reflections. Animprovement of 7.3 dB was achieved with respect to the state-of-the-art.

• a new kind of reflective component, so called Multimode Interference Re-flectors. This component functions as a broadband mirror and can be freelyplaced anywhere on-chip, while being relatively easy to fabricate. Thisfunctionality was difficult to obtain before the introduction of MIRs.

• an extremely fast, novel analytical method for simulating AWGs that offerssimilar accuracy as computationally intensive numerical methods.

• a software library that contains the above mentioned models and compo-nents, which is used to support designs in COBRA MPW runs.

150

Acknowledgments

Looking back on four years of doing a PhD I have to say it all went very smoothly.I guess I have to thank the excellent people at the Photonic Integration group formaking my PhD period so nice.

First of all I want to thank Meint for his relentless effort of making genericintegration a success. Xaveer, I feel very lucky to have had you as a supervisor.We share many interests, and also a sense of humor. You were always availablefor a discussion on any subject. You taught me many things, not the least of whichis Linux’ superiority as an OS. I also wish to thank Mike. My internship at Oclarowas my first real experience with Photonic Integration and it has held my interestever since. I also wish to thank the rest of my PhD committee for their constructivecomments on my thesis.

I want to thank Domenico for our nice afternoon sessions, which coveredthose slow minutes from 16.45 to 17.00 on Fridays. Tjibbe, thanks for introducingme to the clean-room, and for organizing the monthly drinks. For learning howto stir properly I have to thank Barry. Huub, Erik-Jan, Robert and Jeroen, thankyou for making sure things run smoothly in the clean-room and for processing theMPW runs. Jos, thanks for always making sure we know after any presentationwhether there are polarization issues. I also wish to thank Nando for providingthe cover photograph.

Now, my fellow X-men PhD’s! Jing, we shared so much in our aquariumoffice. Thanks for the wonderful noises and gestures, introducing me to jujube,crazy Jing stories, and many more things. Staszek, playing tennis again withyou was very nice. You have a dangerous service and forehand! Dima, thanks formaking me addicted to bouldering. I really enjoyed our weekly climbs and swims,and the diving course. Deepak, with your radio-active samples you are probablythe closest to the X-men from the movies. Thanks for the friendly good morningsand nice chats on Monday mornings. Rui, you were always good for a nice jokeand laugh. Also thanks for your help in some of the measurements. To all of you:good luck with your further research and careers.

During processing in the clean room, Daniele you were there with me whilewe waited for the machines to finish. I enjoyed working together very much in thesix months you spent in Eindhoven, and also during the week I was in Milan.

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Acknowledgments

Giovanni, thanks for the limoncello and the wine. With such rewards it was atrue pleasure assembling masks for you. Then the travel companions for Paradigmmeetings: Elton, Valentina, Dima, and from time to time Luc and Erwin. Thankyou for making time fly by while waiting at the airport. IMOS people, Josselin,Ray, Yuqing, Srivathsa, Victor, Aura, Longfei, Dominik, good luck in makingthings ever smaller. Sylwester, Hadi, Saeed, Josselin, and the rest of the OLAcommittee, together with Erwin you made sure that OLA was a workable place.Antonio, Alonso and Weiming, good luck with your research and your thesis.

I also wish to thank all the PhDs that finished while I was in the group and laidthe ground work: Boudewijn, Milan, Bauke, Ray, Josselin, Manuela, and Dima.The efforts of the secretaries did not go unnoticed and I wish to thank Jolanda andAudrey for them.

Most of my work was carried out within the Paradigm project. I want to thankthe partners from Oclaro, HHI, CIP, Willow Photonics, Fraunhofer, Chalmers, Fi-larete, Phoenix, Gooch & Housego, Alcatel-Thales, Photon Design, CambridgeUniversity, Linkra, Warsaw University, Bright Photonics, and Politecnico di Mi-lano for their efforts in making PARADIGM a success.

I wish to acknowledge the authors of the many free software packages I used:KLayout, Inkscape, MikTeX, GCC, Eclipse, Gimp, Python, SciPy, NumPy, Mat-plotlib, Mercurial, SVN. All their efforts have made my life a lot easier.

Ik wil ook graag al mijn vrienden van Elektro bedanken. De afgelopen 10 jaarwaren fantastisch. Dankjewel Barend, Bas, Cedric, Evert, JWN, Koen, Marijn,Michiel, Niels, Rob en Sven. Natuurlijk ook mijn vrienden uit Nieuwegein, DeJin, Niels, Belén, Chuck, Mol en Mike. Het was altijd een plezier om weer terugnaar Utrecht te gaan.

Pap en mam, wie had gedacht dat ik het nog tot doctor zou schoppen. Weliswaarde eerste in de familie, maar niet voor lang. Over twee jaar ben jij immers ookklaar Suus. Bedankt alle drie dat jullie er altijd voor me zijn.

Anneke, dushi, ik ben ontzettend blij dat ik jou heb mogen ontmoeten. Wehebben het zo fijn samen en ik hoop dat dat voor altijd zo blijft. Ik kijk heel erguit naar onze reis. Ik houd van je lieverd.

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Curriculum vitae

Emil Kleijn was born in Nieuwegein, the Netherlands, on July 6 1986. After fin-ishing gymnasium in 2004 at the Cals College in Nieuwegein, the Netherlands,he moved to Eindhoven. There he received the bachelor’s degree in electrical en-gineering from Eindhoven University of Technology in 2007. Also at EindhovenUniversity of Technology he followed the Broadband Telecommunication Tech-nologies master track. After an internship at Oclaro dealing with Photonic Inte-gration, he decided to graduate within the Photonic Integration group. In 2010 hehanded in his master thesis on Multimode Interference Reflectors and obtained themaster’s degree in electrical engineering. While studying for his master’s degreehe became involved with Formula Student, a design competition for students. Heparticipated in the competition as a member of a team of 40 students from 2008until 2010. Determined to provide other students with a similar wonderful experi-ence, he joined the organization of Formula Student Germany as an official from2010 to 2014. Also in 2010 he started his Ph.D. research within the PhotonicIntegration Group in the COBRA Research Institute at Eindhoven University ofTechnology. The results of this research are presented in this thesis.

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List of publications

Journal publications

• E. Kleijn, P. Williams, N. Whitbread, M. Wale, M. Smit, and X. Leijtens,“Sidelobes in the response of arrayed waveguide gratings caused by pola-rization rotation,” Optics Express, vol. 20, no. 20, pp. 22 660–22 668, 2012.

• E. Kleijn, M. Smit, and X. Leijtens, “Multimode interference reflectors: anew class of components for photonic integrated circuits,” Lightwave Tech-nology, Journal of, vol. 31, no. 18, pp. 3055–3063, 2013.

• E. Kleijn, M. Smit, and X. Leijtens, “New analytical arrayed waveguidegrating model,” Lightwave Technology, Journal of, vol. 31, no. 20, pp.3309–3314, 2013.

• S. Stopinski, M. Malinowski, R. Piramidowicz, E. Kleijn, M. Smit, andX. Leijtens, “Integrated optical delay lines for time-division multiplexers,”IEEE Photonics Journal, vol. 5, no. 5, pp. 7 902 109–1/9, 2013.

• E. Kleijn, D. Melati, A. Melloni, T. de Vries, M. Smit, and X. Leijtens,“Multimode interference couplers with reduced parasitic reflections,” IEEEPhotonics Technology Letters, vol. 26, no. 4, pp. 408–410, 2014.

• M. Smit, X. Leijtens, H. Ambrosius, E. Bente, J. van der Tol, B. Smal-brugge, T. de Vries, E.-J. Geluk, J. Bolk, R. van Veldhoven, L. Augustin,P. Thijs, D. D’Agostino, H. Rabbani, K. Lawniczuk, S. Stopinski, S. Tahvili,A. Corradi, E. Kleijn, D. Dzibrou, M. Felicetti, E. Bitincka, V. Moskalenko,J. Zhao, R. Santos, G. Gilardi, W. Yao, K. Williams, P. Stabile, P. Kuinder-sma, J. Pello, S. Bhat, Y. Jiao, D. Heiss, G. Roelkens, M. Wale, P. Firth,F. Soares, N. Grote, M. Schell, H. Debregeas, M. Achouche, J.-L. Gentner,A. Bakker, T. Korthorst, D. Gallagher, A. Dabbs, A. Melloni, F. Morichetti,D. Melati, A. Wonfor, R. Penty, R. Broeke, B. Musk, and D. Robbins, “Anintroduction to InP-based generic integration technology,” SemiconductorScience and Technology, vol. 29, no. 8, p. 083001, 2014.

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International conference publications

• J. Zhao, E. Kleijn, P. Williams, M. Smit, and X. Leijtens, “On-chip laserwith multimode interference reflectors realized in a generic integration plat-form,” in Proceedings of the 23rd International Conference on Indium Phos-phide and Related Materials (IPRM 2011). Berlin: IEEE Service Center,22-26 May 2011, pp. 1–4.

• J. Zhao, E. Kleijn, M. Smit, P. Williams, I. Knight, M. Wale, and X. Leij-tens, “Novel lasers using multimode interference reflector,” in Proceedingsof the 2011 ICO International Conference on Information Photonics (IP2011). Ottawa: IEEE Service Center, 18-20 May 2011, pp. 1–2.

• E. Kleijn, P. Williams, N. Whitbread, M. Wale, M. Smit, and X. Leijtens,“Sidelobes caused by polarization rotation in arrayed waveguide gratings,”in Proceedings of the International Conference on Information Photonics(IP 2011). Ottawa: IEEE, 18-20 May 2011, pp. 1–2.

• E. Kleijn, M. Smit, M. Wale, and X. Leijtens, “New two-port multimodeinterference reflectors,” in Proceedings of the 16th European Conferenceon Integrated Optics (ECIO 2012), Sitges, 18-20 April 2012.

• E. Kleijn, M. Smit, and X. Leijtens, “Analysis of parasitic effects in PICsusing circuit simulation,” in Integrated Optics: Physics and Simulations,P. Cheben, J. Ctyroky;, and I. Molina-Fernandez, Eds., vol. 8781. Prague:SPIE, 15 April 2013 2013.

• D. D’Agostino, E. Kleijn, R. Lemos Alvares Dos Santos, H. Ambrosius,and M. Smit, “A dense spot size converter array fabricated in a genericprocess on InP,” in Integrated Optics Materials Devices, and Applications,F. Ramiro-Manzano, N. Prtljaga, L. Pavesi, G. Pucker, and M. Ghulinyan,Eds., vol. 8767. Grenoble: SPIE, 24-28 April 2013.

• E. Bitincka, E. Kleijn, and M. Smit, “Accuracy analysis of the Fabry-Perotmeasurement method,” in Proceedings Integrated Photonics Research, Sili-con and Nano-Photonics, H. Chang, V. Tolstikhin, T. Krauss, and M. Watts,Eds., Rio Grande, Puerto Rico, 14-17 July 2013.

• E. Kleijn, M. Smit, and X. Leijtens, “Monolithically integrated digitallytunable laser using a reflective arrayed waveguide grating with multimodeinterference reflectors,” in Proceedings Integrated Photonics Research, Sili-con and Nano-Photonics, H. Chang, V. Tolstikhin, T. Krauss, and M. Watts,Eds., Rio Grande, Puerto Rico, 14-17 July 2013.

• F. Bontempi, N. Andriolli, S. Faralli, J. Klamkin, E. Kleijn, T. de Vries, andG. Contestabile, “An InP monolithically integrated multi-frequency wave-length converter,” in Proceedings of the Optical Fiber Communication Con-ference (OFC 2014), San Francisco, 9-13 March 2014.

• E. Kleijn, M. Smit, and X. Leijtens, “Amplitude and phase error correc-

156

Local conference publications

tion in 3× 3 MMIs,” in Proceedings of the 17th European Conference onIntegrated Optics (ECIO 2014), Nice, 24-27 June 2014.

• D. Pustakhod, E. Kleijn, M. Smit, and X. Leijtens, “AWG-based integratedfiber-Bragg-grating interrogator with improved sensitivity,” in Proceedingsof the 17th European Conference on Integrated Optics (ECIO 2014), Nice,24-27 June 2014.

• N. Calabretta, R. Stabile, E. Kleijn, T. de Vries, K. Williams, and H. Dorren,“Lossless wavelength selector based on monolithically integrated flat-topcyclic AWG and optical switch chain,” in Proceedings of the 40th Euro-pean Conference on Optical Communication (ECOC 2014), Cannes, 21-25September 2014.

Local conference publications

• E. Kleijn, T. de Vries, H. Ambrosius, M. Smit, and X. Leijtens, “MMI re-flectors with free selection of reflection to transmission ratio,” in Proceed-ings of the 15th Annual Symposium of the IEEE Photonics Benelux Chapter,Delft: TNO, 18-19 November 2010, pp. 189–192.

• J. Zhao, E. Kleijn, M. Smit, and X. Leijtens, “Design of multi-wavelengthtransmitters using on-chip MMI reflectors,” in Proceedings of the 15th An-nual Symposium of the IEEE Photonics Benelux Chapter, Delft: TNO, 18-19 November 2010, pp. 233–236.

• E. Kleijn, M. Smit, and X. Leijtens, “Photonic component design librariesand fast circuit simulation,” in Proceedings of the 16th Annual sympo-sium of the IEEE Photonics Benelux Chapter, P. Bienstman, G. Morthier,G. Roelkens, and et al., Eds. Ghent: Unversiteit Gent, 1-2 December 2011,pp. 261–264.

• E. Bitincka, X. Leijtens, J. van der Tol, E. Kleijn, and M. Smit, “Electricalon-wafer testing of photonic integrated circuits (PICs),” in Proceedings ofthe 16th Annual symposium of the IEEE Photonics Benelux Chapter, P. Bi-enstman, G. Morthier, G. Roelkens, and et al., Eds. Ghent: UnversiteitGent, 1-2 December 2011, pp. 145–148.

• E. Kleijn, M. Smit, and X. Leijtens, “Optimized MMI coupler shape forreduced back-reflections,” in Proceedings of the 2012 Annual Symposiumof the IEEE Photonics Benelux Chapter. Mons: IEEE Service Center,29-30 November 2012, pp. 251–254.

• D. D’Agostino, E. Kleijn, R. Lemos Alvares Dos Santos, H. Ambrosius,and M. Smit, “Fabrication and characterization of a dense optical bus at-tached to an AWG,” in Proceedings of the 17th Annual Symposium of theIEEE Photonics Benelux Chapter. Mons: IEEE Service Center, 29-30

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November 2012, pp. 271–274.• E. Kleijn, A. Smit, and X. Leijtens, “Reflective AWG with flattened re-

sponse,” in Proceedings of 2013 Annual Symposium of the IEEE PhotonicsSociety Benelux Chapter, Eindhoven, 25-26 November 2013, pp. 171–174.

• D. D’Agostino, S. Latkowski, H. Rabbani Haghighi, E. Kleijn, E. Bente,H. Ambrosius, and M. Smit, “A InP based generic integration platformfor photonic integrated circuits operating up to 2 µm,” in Proceedings of2013 Annual Symposium of the IEEE Photonics Society Benelux Chapter,X. Leijtens and D. Pustakhod, Eds., Eindhoven, 25-26 November 2013, pp.259–262.

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Documents

Passive components in indium phosphide generic integration