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APPLIED DIGITALOPTICSFROM MICRO-OPTICSTO NANOPHOTONICS
Bernard C. Kress
Photonics Systems Laboratory, Universit�e de Strasbourg, France
Patrick Meyrueis
Photonics Systems Laboratory, Universit�e de Strasbourg, France
APPLIED DIGITALOPTICS
APPLIED DIGITALOPTICSFROM MICRO-OPTICSTO NANOPHOTONICS
Bernard C. Kress
Photonics Systems Laboratory, Universit�e de Strasbourg, France
Patrick Meyrueis
Photonics Systems Laboratory, Universit�e de Strasbourg, France
This edition first published 2009
� 2009 John Wiley & Sons, Ltd
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Library of Congress Cataloguing-in-Publication Data
Kress, B.
Applied digital optics : from micro-optics to nanophotonics / Bernard C. Kress, Patrick Meyrueis.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-02263-4 (cloth)
1. Optical MEMS. 2. Nanophotonics. 3. Integrated optics. 4. Signal processing–Digital techniques.
5. Diffraction gratings. I. Meyrueis, Patrick. II. Title.
TK8360.O68.K74 2009
621.36–dc22
2009004108
A catalogue record for this book is available from the British Library.
ISBN: 978-0-470-02263-4
Set in 9/11pt, Times by Thomson Digital, Noida, India.
Printed in Great Britain by CPI Antony Rowe, Chippenham, Wiltshire.
To my lovely wife Mei-Mei, whose unconditional love and support
made this book possible. I even learned to appreciate her constant nagging,
which drove me up the wall but helped me finish this project.
Bernard
I would like to dedicate this book to all my university colleagues, students,
Photonics Systems Laboratory staff, my assistant Anne and members of institutions
and companies all over the world that allowed us, by contributing to or supporting
our microphotonics and nanophotonics activities in research and education,
to gather the information that made this book possible.
Patrick
Contents
About the Authors xi
Foreword by Professor Joseph Goodman xiii
Foreword by Professor Trevor Hall xv
Acknowledgments xvii
Acronyms xix
Introduction 1
Why a Book on Digital Optics? 1
Digital versus Analog 2
What are Digital Optics? 2
The Realm of Digital Optics 3
Supplementary Material 4
1 From Refraction to Diffraction 5
1.1 Refraction and Diffraction Phenomena 5
1.2 Understanding the Diffraction Phenomenon 5
1.3 No More Parasitic Effects 8
1.4 From Refractive Optics to Diffractive Optics 9
1.5 From Diffractive Optics to Digital Optics 11
1.6 Are Diffractives and Refractives Interchangeable Elements? 13
2 Classification of Digital Optics 15
2.1 Early Digital Optics 15
2.2 Guided-wave Digital Optics 16
2.3 Free-space Digital Optics 17
2.4 Hybrid Digital Optics 19
3 Guided-wave Digital Optics 21
3.1 From Optical Fibers to Planar Lightwave Circuits (PLCs) 21
3.2 Light Propagation in Waveguides 22
3.3 The Optical Fiber 25
3.4 The Dielectric Slab Waveguide 27
3.5 Channel Waveguides 28
3.6 PLC In- and Out-coupling 30
3.7 Functionality Integration 36
4 Refractive Micro-optics 47
4.1 Micro-optics in Nature 47
4.2 GRIN Lenses 49
4.3 Surface-relief Micro-optics 55
4.4 Micro-optics Arrays 58
5 Digital Diffractive Optics: Analytic Type 71
5.1 Analytic and Numeric Digital Diffractives 73
5.2 The Notion of Diffraction Orders 73
5.3 Diffraction Gratings 76
5.4 Diffractive Optical Elements 90
5.5 Diffractive Interferogram Lenses 106
6 Digital Diffractive Optics: Numeric Type 111
6.1 Computer-generated Holograms 111
6.2 Designing CGHs 115
6.3 Multiplexing CGHs 149
6.4 Various CGH Functionality Implementations 151
7 Hybrid Digital Optics 157
7.1 Why Combine Different Optical Elements? 157
7.2 Analysis of Lens Aberrations 157
7.3 Improvement of Optical Functionality 163
7.4 The Generation of Novel Optical Functionality 166
7.5 Waveguide-based Hybrid Optics 169
7.6 Reducing Weight, Size and Cost 171
7.7 Specifying Hybrid Optics in Optical CAD/CAM 173
7.8 A Parametric Design Example of Hybrid Optics via Ray-tracing Techniques 175
8 Digital Holographic Optics 181
8.1 Conventional Holography 181
8.2 Different Types of Holograms 185
8.3 Unique Features of Holograms 188
8.4 Modeling the Behavior of Volume Holograms 192
8.5 HOE Lenses 199
8.6 HOE Design Tools 203
8.7 Holographic Origination Techniques 203
8.8 Holographic Materials for HOEs 207
8.9 Other Holographic Techniques 212
9 Dynamic Digital Optics 217
9.1 An Introduction to Dynamic Digital Optics 217
9.2 Switchable Digital Optics 223
9.3 Tunable Digital Optics 235
9.4 Reconfigurable Digital Optics 244
9.5 Digital Software Lenses: Wavefront Coding 250
10 Digital Nano-optics 253
10.1 The Concept of ‘Nano’ in Optics 253
10.2 Sub-wavelength Gratings 253
viii Contents
10.3 Modeling Sub-wavelength Gratings 255
10.4 Engineering Effective Medium Optical Elements 267
10.5 Form Birefringence Materials 272
10.6 Guided Mode Resonance Gratings 275
10.7 Surface Plasmonics 277
10.8 Photonic Crystals 279
10.9 Optical Metamaterials 288
11 Digital Optics Modeling Techniques 295
11.1 Tools Based on Ray Tracing 295
11.2 Scalar Diffraction Based Propagators 298
11.3 Beam Propagation Modeling (BPM) Methods 321
11.4 Nonparaxial Diffraction Regime Issues 323
11.5 Rigorous Electromagnetic Modeling Techniques 326
11.6 Digital Optics Design and Modeling Tools Available Today 327
11.7 Practical Paraxial Numeric Modeling Examples 330
12 Digital Optics Fabrication Techniques 339
12.1 Holographic Origination 340
12.2 Diamond Tool Machining 342
12.3 Photo-reduction 346
12.4 Microlithographic Fabrication of Digital Optics 347
12.5 Micro-refractive Element Fabrication Techniques 385
12.6 Direct Writing Techniques 388
12.7 Gray-scale Optical Lithography 394
12.8 Front/Back Side Wafer Alignments and Wafer Stacks 406
12.9 A Summary of Fabrication Techniques 408
13 Design for Manufacturing 413
13.1 The Lithographic Challenge 413
13.2 Software Solutions: Reticle Enhancement Techniques 418
13.3 Hardware Solutions 445
13.4 Process Solutions 449
14 Replication Techniques for Digital Optics 453
14.1 The LIGA Process 453
14.2 Mold Generation Techniques 455
14.3 Embossing Techniques 459
14.4 The UV Casting Process 464
14.5 Injection Molding Techniques 464
14.6 The Sol-Gel Process 471
14.7 The Nano-replication Process 472
14.8 A Summary of Replication Technologies 475
15 Specifying and Testing Digital Optics 479
15.1 Fabless Lithographic Fabrication Management 479
15.2 Specifying the Fabrication Process 480
15.3 Fabrication Evaluation 494
15.4 Optical Functionality Evaluation 510
Contents ix
16 Digital Optics Application Pools 521
16.1 Heavy Industry 522
16.2 Defense, Security and Space 532
16.3 Clean Energy 539
16.4 Factory Automation 541
16.5 Optical Telecoms 544
16.6 Biomedical Applications 548
16.7 Entertainment and Marketing 553
16.8 Consumer Electronics 554
16.9 Summary 574
16.10 The Future of Digital Optics 574
Conclusion 581
Appendix A: Rigorous Theory of Diffraction 583
A.1 Maxwell’s Equations 583
A.2 Wave Propagation and the Wave Equation 583
A.3 Towards a Scalar Field Representation 584
Appendix B: The Scalar Theory of Diffraction 587
B.1 Full Scalar Theory 587
B.2 Scalar Diffraction Models for Digital Optics 594
B.3 Extended Scalar Models 595
Appendix C: FFTs and DFTs in Optics 597
C.1 The Fourier Transform in Optics Today 597
C.2 Conditions for the Existence of the Fourier Transform 600
C.3 The Complex Fourier Transform 600
C.4 The Discrete Fourier Transform 601
C.5 The Properties of the Fourier Transform and Examples in Optics 604
C.6 Other Transforms 606
Index 611
x Contents
About the Authors
Bernard Kress has been involved in the field of digital optics since the late 1980s. He is an associate
professor at theUniversity of Strasbourg, France, teaching digital optics. For the last 15 yearsDrKress has
been developing technologies and products related to digital optics. He has beenworkingwith established
industries around the world and with start-ups in the Silicon Valley, California, with applications ranging
from optical data storage, optical telecom, military and homeland security applications, LED and laser
displays, industrial and medical sensors, biotechnology systems, optical security devices, high power
laser material processing, to consumer electronics. He is on the advisory boards of various photonics
companies in theUS andhas also been advising venture capital firms in the SiliconValley fordue diligence
reviews in photonics, especially in micro- and nano-optics.
He holds more than 25 patents based on digital optics technology and applications, and is the author of
more than 100 papers on this subject. He has taught several short courses given at SPIE conferences. His
first book on digital optics, Digital Diffractive Optics (2000), was published by John Wiley & Sons, Ltd
and has been translated into Japanese in 2005 (published by Wiley-Maruzen). He is also the author of
a chapter in the best seller Optical System Design (2007), edited by R. Fisher and published by
McGraw-Hill. Bernard Kress can be contacted at [email protected].
Patrick Meyrueis is full professor at the University of Strasbourg since 1986 (formerly Louis Pasteur
University). He is the founder of the Photonics Systems Laboratory which is now one of the most
advanced labs in the field of planar digital optics. He is the author of more than 200 publications and was
the chairman of more than 20 international conferences in photonics. He was the representative of the
Rhenaphotonics cluster and one of the founders of theCNOP in 2001 (national French committee of optics
and photonics). He is nowacting as the scientific director of the Photonics SystemsLab and the head of the
PhD and undergraduate program in the ENSPS National School of Physics in Strasbourg.
Foreword by ProfessorJoseph Goodman
The field of digital optics is relatively new, especially when compared with the centuries-long life of the
more general field of optics. While it would perhaps have been possible to imagine this field a century or
more ago, the concept would not have been of great interest, due to the lack of suitable sources, computing
power and fabrication tools. But digital optics has now come of age, aided by the extraordinary advances
in lasers, processor speed and the remarkable development of tools for fabricating such optics, driven in
part by the tools of the semiconductor industry.
It was perhaps in the seminal work of Lohmann on computer-generated holograms that interest in the
field of digital optics was launched. Lohmann based his experimental work on the use of binary plotters
and photo-reduction, but today the plotting tools have reached a level of sophistication not even imagined
at the time of Lohmann’s invention, allowing elements with even sub-wavelength structure to be directly
fabricated on a broad range of materials.
Applied Digital Optics is a remarkable compendium of concepts, techniques and applications of digital
optics. The book includes in-depth discussions of guided-wave optics, refractive optics, diffractive optics
and hybrid (diffractive/refractive) optics. Also included is the important area of ‘dynamic optics’, which
covers devices with diffractive properties that can be changed at will. The optics of sub-wavelength
structures is also covered, adding an especially timely subject to the book.
Most interesting to me is the extremely detailed discussion of fabrication and replication techniques,
which are of great importance in bringing diffractive optics to the commercial marketplace. Finally, the
wide-ranging discussion of applications of digital optics is almost breathtaking in its range and coverage.
Professors Kress and Meyrueis provide therefore a comprehensive overview of the current state of
research in the field of digital optics, as well as an excellent analysis of how this technology is
implemented today in industry, and how it might evolve in the next decade, especially in consumer
electronics applications.
In summary, this book will surely set the standard for a complete treatment of the subject of digital
optics, and will hopefully inspire even more innovation and progress in this important field.
Professor Joseph W. Goodman
William Ayer Professor, Emeritus
Department of Electrical Engineering, Stanford University
Stanford, CA, USA
Foreword by Professor Trevor Hall
It was my privilege to host Bernard Kress at an early stage in his career. I was very impressed by his
creativity, determination and tireless energy. I knew then that he would become a champion in his field of
diffractive optics.
Applied Digital Optics is the second book written by Bernard and Professor PatrickMeyrueis from the
Photonics Systems Laboratory (LSP) at Universit�e de Strasbourg (UdS) in France. While their first book,
Digital Diffractive Optics, was solely dedicated to diffractive optics, this one covers a much wider range
of fields associated with digital optics, namely: waveguide optics, refractive micro-optics, hybrid optics,
optical MEMS and switchable optics, holographic and diffractive optics, photonic crystals, plasmonics
and metamaterials. Thus, the book’s subtitle, From Micro-optics to Nanophotonics, is indeed a faithful
description of its broad contents. After reviewing these optical elements throughout the first chapters,
emphasis is set on the numerical modeling techniques used in industry and research to design and model
such elements. The last chapters describe in detail the state of the art in micro-fabrication techniques and
technologies, and review an impressive list of applications using such optics in industry today.
Professors Kress and Meyrueis have been investigating the field of digital optics at LSP since the late
1980s, when photonics was still struggling to become a fully recognized field, like electronics or
mechanics. The LSP has been very active since its creation, not only by promoting education in photonics
but also by promoting national and international university/industry relations, which has yielded a number
of impressive results: publications, patents, books, industrial applications and products as well as
university spin-offs both in Europe and the USA. This experience fueled also several European projects,
such as the Eureka FOTA project (Flat Optical Technologies and Applications), which coordinated 27
industrial and academic partners, or more recently the European NEMOnetwork (Network in Excellence
in Micro-Optics).
The LSP has thus become today one of the premier laboratories in photonics and digital optics, through
education, research and product development, and this book serves as a testimonial to this continuous
endeavor.
Professor Trevor Hall
Director, Centre for Research in Photonics
University of Ottawa, School of Information Technology and Engineering
Ottawa, Canada
Acknowledgments
We wish to acknowledge and express many thanks to the following individuals who helped directly or
indirectly in the production of the material presented within this book:
Prof. Pierre Ambs (ESSAIM, Mulhouse, France)
Prof. Stephan Bernet (Innsbruck Medical University, Austria)
Mr Ken Caple (HTA Enterprises Inc., San Jose, USA)
Dr Chris Chang (Arcus Technology Inc., Livermore, USA)
Prof. Pierre Chavel (IOTA, Paris, France)
Mrs Rosie (Conners Photronics Corp., Milpitas, USA)
Mr Tom Credelle (Holox Inc., Belmont, USA)
Dr Walter Daschner (Philips Lumileds, San Jose, USA)
Mr Gilbert Dudkiewicz (Telmat Industrie S.A., Soultz, France)
Mrs Judy Erkanat (Tessera Corp. San Jose, USA)
Dr Robert Fisher (Optics 1 Corp., Los Angeles, USA)
Prof. Jo€el Fontaine (INSA, Strasbourg, France)Prof. Joseph Ford (UCSD, San Jose, USA)
Dr Keiji Fuse (SEI Ltd, Osaka, Japan)
Prof. Joseph Goodman (Stanford University, Stanford, USA)
Prof. Michel Grossman (UdS, Strasbourg, France)
Prof. Trevor J. Hall (University of Ottawa, Canada)
Mrs Kiomi Hamada (Photosciences Inc., Torrance, USA)
Dr Phil Harvey (Wavefront Technologies Inc., Long Beach, USA)
Mr Vic Hejmadi (USI Inc., San Jose, USA)
Dr Martin Hermatschweiler (Nanoscribe GmbH, Germany)
Dr Alex Kazemi (Boeing Corp., Pasadena, USA)
Prof. Ernst-Bernhart Kley (FSU, Jena, Germany)
Prof. Sing H. Lee (UCSD, San Diego, USA)
Mr Ken Mahdi (Rokwell Collins Inc., Santa Clara, USA)
Prof. Jan Masajada (Wroclaw Institute of Technology, Wroclaw, Poland)
Dr Nicolas Mauduit (Vision int�egr�ee, Paris, France)Prof. Juergen Mohr (Forschungszentrum Karlsruhe, Germany)
Mr Paul Moran (American Precision Dicing Inc., San Jose, USA)
Prof. Guy Ourisson (ULP, Strasbourg, France)
Prof. Olivier Parriaux (Universit�e St. Etienne, France)Prof. Pierre Pfeiffer (UdS, Strasbourg, France)
Dr Milan Popovitch (SBG Labs Inc., Sunnyvale, USA)
Dr Steve Sagan (BAE Corp., Boston, USA)
Prof. Pierre Saint-Hilaire (Optical Science Center, University of Arizona, USA)
Dr Edouard Schmidtlin (JPL/NASA, Pasadena, USA)
Mr Michael Sears (Flextronics Inc., San Jose, USA)
Prof. Bruno Serio (UdS, Strasbourg, France)
Dr Michel Sirieix (Sagem SA, Paris, France)
Dr Ron Smith (Digilens Inc., Sunnyvale, USA)
Dr Suning Tang (Crystal Research Inc., Fremont, USA)
Dr Tony Telesca (New York, USA)
Prof. Hugo Thiepont (Vrije Universiteit Brussel, Belgium)
Dr Jim Thomas (UCSD, San Diego, USA)
Prof. Patrice Twardowsky (UdS, Strasbourg, France)
Dr Jonathan Waldern (SBG Labs Inc., Sunnyvale, USA)
Dr Paul Wehrenberg (Apple Corp., Cupertino, USA)
Prof. Ming Wu (UCLA, Los Angeles, USA)
Prof. Frank Wyrowsky (LightTrans GmbH, Jena, Germany)
Dr Zhou Zhou (UCSD, San Diego, USA)
Wealsowish to express our gratitude to all our friends and family,who contributed to the completion of the
book (Janelle, Sandy, Erik, Kevin, Dan, H�el�ene, Sabine, Christine, Claire, etc.), and a special thank you toGeoff Palmer, who did a terrific job in copy editing this book.
xviii Acknowledgments
Acronyms
Optical Design Acronyms
BPM Beam Propagation Method
CGH Computer-Generated Hologram
DBS Direct Binary Search
DFT Discrete Fourier Transform
DOE Diffractive Optical Element
DOF Depth Of Focus
EMT Effective Medium Theory
FDTD Finite Difference Time Domain
FFT Fast Fourier Transform
FZP Fresnel Zone Plate
HOE Holographic Optical Element
IFTA Iterative Fourier Transform Algorithm
M-DOE Moir�e DOE
MTF Modulation Transfer Function
NA Numeric Aperture
PSF Point Spread Function
RCWA Rigorous Coupled Wave Analysis
SBWP Space Bandwidth Product
Computer Design Acronyms
CAD/CAM Computer-Aided Design/Computer-Aided Manufacturing
CIF Caltech Intermediate Format
DFM Design For Manufacturing
DRC Design Rule Check
EDA Electronic Design Automation
EPE E-beam Proximity Effect
GDSII Graphical Data Structure Interface
OPC Optical Proximity Correction
OPE Optical Proximity Effect
RET Reticle Enhancement Techniques
Fabrication-related Acronyms
AFM Atomic Force Microscope
AOM Acousto-Optical Modulator
ARS Anti-Reflection Surface
CAIBE Chemically Aided Ion-Beam Etching
DCG DiChromated Gelatin
GRIN GRaded INdex
HEBS High-Energy Beam-Sensitive Glass
H-PDLC Holographic-Polymer Dispersed Liquid Crystal
HTPS High-Temperature PolySilicon
IC Integrated Circuit
LBW Laser Beam Writer
LC Liquid Crystal
LCD Liquid Crystal Display
LCoS Liquid Crystal on Silicon
LIGA LIthography/GAlvanoforming
MEMS Micro-Electro-Mechanical System
MOEMS Micro-Opto-Electro-Mechanical System
OCT Optical Coherence Tomography
OE Opto-Electronic
PLC Planar Lightwave Circuit
PSM Phase Shift Mask
RIBE Reactive Ion-Beam Etching
SLM Spatial Light Modulator
VLSI Very Large Scale Integration
Application-related Acronyms
BD Blu-ray Disk
CATV CAble TV
CD Compact Disk
CWDM Coarse Wavelength Division Multiplexing
DVD Digital Versatile Disk
DWDM Dense Wavelength Division Multiplexing
HMD Helmet-Mounted Display
HUD Head-Up Display
LED Light-Emitting Diode
MCM Multi-Chip Module
OPU Optical Pick-up Unit
OVID Optically Variable Imaging Device
VCSEL Vertical Cavity Surface-Emitting Laser
VIPA Virtual Image Plane Array (grating)
VOA Variable Optical Attenuator
xx Acronyms
Introduction
Why a Book on Digital Optics?
When a new technology is integrated into consumer electronic devices and sold worldwide in super-
markets and consumer electronic stores, it is usually understood that this technology has then entered the
realm of mainstream technology.
However, such progress does not come cheaply, and has a double-edge sword effect: first, it becomes
widely available and thus massively developed in various applications, but then it also becomes a
commodity, and thus there is tremendous pressure to minimize the production and integration costs while
not sacrificing any aspects of performance.
The field of digital optics is about to enter such a stage, which is why this book provides a timely insight
into this technology, for the following prospective groups of readers:
. for the research world (academia, government agencies and R&D centers) to have a broad but
condensed overview of the state of the art;. for foundries (optical design houses, optical foundries and final product integrators) to have a broad
knowledge of the various design and production tools used today;. for prospective industries – ‘How can I use digital optics in my products to make them smaller, better
and cheaper?’; and. for the mainstream public – ‘Where are they used, and how do they work?’
This book is articulated around four main topics:
1. The state of the art and a classification of the different physical implementations of digital optics
(ranging from waveguide optics to diffractive optics, holographics, switchable optics, photonic
crystals and metamaterials).
2. The modeling tools used to design digital optics.
3. The fabrication and replication tools used to produce digital optics.
4. A review of the main applications, including digital optics in industry today.
This introductory chapter will define what the term digital opticsmeans today in industry, before we start
to review the various digital optics implementation schemes in the early chapters.
Applied Digital Optics: From Micro-optics to Nanophotonics Bernard C. Kress and Patrick Meyrueis
� 2009 John Wiley & Sons, Ltd
Digital versus Analog
In attempting to define the term ‘digital’ as introduced in the title of this book, one has to consider its
counterpart term ‘analog’. The ‘digital’ versus ‘analog’ concept can also be understood when considering
the term ‘continuous’ versus ‘discrete’ (see Figure 1).
History has proved that the move from analog systems to digital systems in technology (especially in
electronics) has brought about a large number of improvements, for example:
. added flexibility (easy to program) and faster, more precise, computers;
. new functionalities (built-in error detection and correction algorithms etc.);
. ease of miniaturization (very large scale integration, VLSI); and
. ease of mass replication (microlithographic fabrication techniques).
What are Digital Optics?
As far as optics are concerned, the move from analog (conventional lenses, mirrors and fiber optics) to
digital (planar optical elements composed of microscopic structures) has been mainly focused on the last
two points: miniaturization and mass replication. This said, new or improved optical functionalities have
also been discovered and investigated, especially through the introduction of digital diffractive optics and
digital waveguide optics, and their hybrid combination, as will be discussed in detail in the chapters to
come.
Miniaturization and mass-production have begun to lead the optical industry toward the same trend as
in themicro-electronics industry in the 1970s, namely to the integration of densely packed planar systems
in various fields of application (optical telecoms, optical data storage, optical information processing,
sensors, biophotonics, displays and consumer electronics).
At first sight, the term ‘digital optics’ could lead one to think that such elements might be either digital
in their functionality (in much the same way that digital electronics provide digital signal processing) or
digital in their form (much like digital – or binary – microscopic shapes rather than smooth shapes).Well,
it actually takes none of these forms.
The adjective ‘digital’ in ‘digital optics’ refers much more simply to the way they are designed and
fabricated (both in a digital – or binary – way). The design tool is usually a digital computer and the
fabrication tool is usually a digital (or binary) technology (e.g. by using binary microlithographic
fabrication techniques borrowed from the Integrated Circuit, or IC, manufacturing industry).
Figure 2 details the similarities between the electronic and optic realms, in both analog and digital
versions. In the 1970s, digital fabrication technology (binary microlithography) helped electronics move
from single-element fabrication to mass production in a planar way through very large scale integration
(VLSI). Similarly, identical microlithographic techniques would prove effective in helping the optics
industry to move from single-element fabrication (standard lenses or mirrors) down to planar integration
0000000000000000011111110000011110001000111110001011011010001011
(a) Analog form (b) Sampled analog form (c) Digital form
Figure 1 Analog systems versus digital systems
2 Applied Digital Optics
with similar VSLI features. The door to planar optics mass production has thus been opened, exactly as it
was for the IC industry 30 years earlier, with the noticeable difference that there was no need to invent a
new fabrication technology, since this had already been developed for digital electronics.
However, it is important to understand that although the fabrication technique used may be a binary
microfabrication process, the resulting elements are not necessarily binary in their shape or nature, but can
have quasi-analog surface reliefs, analog index modulations, gray-scale shades or even a combination
thereof.
Also, their final functionality might not be digital – or binary – as a digital IC chip would be, but could
instead have parallel and/or analog processing capabilities (information processing or wavefront
processing). This is especially true for free-space digital optics, and not so much for guided-wave digital
optics.
It is therefore inaccurate to draw a quick comparison between analog electronics versus digital
electronics and analog (refractive) optics versus digital (diffractive or integrated) optics, since both
optical elements (analog or digital) can yield analog or digital physical shapes and/or processing
capabilities.
The Realm of Digital Optics
Now that we have defined the term ‘digital optics’ in the previous section, the various types of digital
optical elements will be described.
The realm of digital optics (also referred to as ‘micro-optics’ or ‘binary optics’) comprises two main
groups, the first relying on free-space wave propagation and the second relying on guided-wave
propagation (see Figure 3).
The various optical elements defining these two groups (free-space and guided-wave digital optics)
are designed by a computer and fabricated by means similar to those found in IC foundries
(microlithography).
Figure 3 shows, on the free-space optics side, threemain subdivisions,which are, in chronological order
of appearance, refractivemicro-optical elements, diffractive and holographic optical elements, and nano-
optics (photonic crystals). On the guided-wave optics side, there are also three main subdivisions, which
are, again in chronological order of appearance, fiber optics, integratedwaveguide optics and nano-optics.
It is worth noting that nano-optics (or photonic crystals) can actually be considered as guided-wave optics
or free-space optics, depending on how they are implemented (as 1D, 2D or 3D structures).
This book focuses on the analysis of free-space digital optics rather than on guided-wave optics.
Guided-wave micro-optics, or integrated optics, are well described in numerous books, published over
Analog electronics
Digital electronics
Analog optics
Digital optics
Optical realmElectronic realm
....
....
Singular, 3D elementsSmall-scale integrationAnalog functionality
MicroscopicPlanar, lithographically printed elements Large-scale integrationDigital/analog functionality
Macroscopic
Figure 2 Analogies between the electronics and optics realms
Introduction 3
more than three decades, and dedicated books on ‘guided-wave’ photonic crystals have been available for
more than five years now.
However, the combination of free-space digital optics and guided-wave digital optics is a very
important and growing field, sometimes also referred to as ‘planar optics’, and that is what will be
described in this book.
Supplementary Material
Supplementary book material is available at www.applieddigitaloptics.com including information about
workshops and short courses provided by the authors. The design andmodeling programs used in the book
can be downloaded from the website.
Digital optics
Free-space digital optics Guided-wave digital optics
Micro-refractives
Diffractive/holographic optics
Nano-optics
Fiber optics
Integrated wave optics(PLCs)
Figure 3 The realm of digital optics
4 Applied Digital Optics
1
From Refraction to Diffraction
1.1 Refraction and Diffraction Phenomena
In order to predict the behavior of light as it is affected when it propagates through digital optics, we have
to consider the various phenomena that can take place (refraction, reflection, diffraction and diffusion).
Thus, we have to introduce the dual nature of light, which can be understood and studied as a corpuscle
and/or an electromagnetic wave [1].
The corpuscular nature of light, materialized by the photon, is the basis of ray tracing and the classical
optical design of lenses and mirrors. The wave nature of light, considered as an electromagnetic wave, is
the basis of physical optics used to model diffractive optics and other micro- or nano-optical elements,
such as integrated waveguides, and photonic crystals (see Chapters 3–10).
In the simple knife-edge example presented in Figure 1.1, the corpuscular nature of light (through ray
tracing) accounts for the geometrical optics, whereas the wave nature of light (physical optics) accounts
not only for the light present in the optical path, but also for the light appearing inside the geometrical
shadow (the Gibbs phenomenon). According to geometrical optics, no light should appear in the
geometrical shadow. However, physical optics can predict accurately where light will appear within
the geometrical shadow region, and how much light will fall in particular locations.
In this case, the laws of reflection and refraction are inadequate to describe the propagation of light;
diffraction theory has to be introduced.
1.2 Understanding the Diffraction Phenomenon
Diffraction comes from the limitation of the lateral extent of awave. Put in simple terms, diffraction arises
when a wave of a certain wavelength collides with obstacles (amplitude or phase obstacles) that are either
singular or abrupt (the knife-edge test, Young’s holes experiment) smooth but repetitive (the sinusoidal
grating), or even abrupt and repetitive (binary gratings). The smaller the obstacles are, the larger the
diffraction effects become (and also the larger the diffraction angles become).
Today, when harnessing diffraction to be used in industrial applications, the obstacles are usually
designed and fabricated as pure phase obstacles, either in reflection or in transmission [2–4]. Fine-tuning
of the obstacle’s parameters through adequate modeling of the diffraction phenomenon can yield very
specific diffraction effects with a maximum intensity (or diffraction efficiency).
Applied Digital Optics: From Micro-optics to Nanophotonics Bernard C. Kress and Patrick Meyrueis
� 2009 John Wiley & Sons, Ltd
1.2.1 Chronological Stages in Understanding Diffraction Phenomena
The diffraction phenomenon was demonstrated for the first time by Leonardo da Vinci (1452–1519) in a
very rudimentary way. The first accurate description of diffraction was introduced by Francesco Maria
Grimaldi (1618–1663) in his book published in 1665, two years after his death. In those times, corpuscular
theory, whichwaswidely believed accurately to describe the propagation of light, had failed to explain the
diffraction phenomenon. In 1678, Christian Huygens (1629–1695) proposed a wave theory for the
propagation of light that described diffraction as a source of secondary spherical disturbance
(see Appendix B). Sir Isaac Newton (1642–1727) had been a strong advocate of the corpuscular theory
since 1704. His strong influence over contemporary scientists had halted progress in understanding
diffraction during the 18th century. In 1804, Thomas Young (1773–1829) introduced the concept of
interference, which directly proceeds from the wave nature of light. Augustin Jean Fresnel (1788–1827)
brought together the ideas of Huygens and Young in his famous memoir. In 1860, James Clerk Maxwell
(1831–1879) identified light as an electromagnetic wave (see Appendix A). Gustav Kirchhoff
(1824–1887) gave a more mathematical form to Fresnel’s expression of diffraction. His work basically
relied on two assumptions concerning the field at the diffraction aperture. Although those assumptions
were quite empirical, his formulation provided a good approximation of the real diffracted field. In 1884,
Arnold J.W. Sommerfeld (1868–1951) refined Kirchhoff’s theory. Thanks to Green’s theorem, he
suppressed one of the two assumptions that Kirchhoff had made earlier, to derive the so-called
Rayleigh–Sommerfeld diffraction theory.
Table 1.1 summarizes, in a chronological way, the understanding of optics as both a corpuscular
phenomenon and an electromagnetic field.
When studying the propagation of light in a homogeneous or nonhomogeneous medium – such as a
lens, a waveguide, a hologram or a diffractive element (through refraction, diffraction or diffusion) – the
refractive index is one of the most important parameters. Light travels through a transparent medium
(transparent to its specific wavelength) of index n at a speed vn that is lower than its speed c in a vacuum.
The index of refraction, n, in a transparent medium is defined as the ratio between the speed of light in a
Spherical wavefront Plane wavefront
Aperture stop (knife edge)
Geometrical shadow
Diffracted field
Isophasewavefront lines
Rays
Rays
Isop
hase
wav
efro
nt li
nes
Figure 1.1 The dual nature of light: geometrical and physical optics
6 Applied Digital Optics
Table
1.1
Chronological
eventsin
theunderstandingofoptics
… 130
Cla
udiu
s Pt
olem
aeus
tabu
late
s an
gles
of
refr
actio
n fo
r se
vera
l med
ia
1305
Die
tric
h vo
n Fr
eibe
rg u
ses
wat
er f
illed
fla
sks
to s
tudy
the
refl
ectio
n/re
frac
tion
in r
aind
rops
that
lead
s to
rai
nbow
s16
04 J
ohan
nes
Kep
ler
desc
ribe
s ho
w th
e ey
e fo
cuse
s lig
ht16
11 M
arko
Dom
inis
dis
cuss
es th
e ra
inbo
w in
De
Rad
iis V
isus
et L
ucis
1611
Joh
anne
s K
eple
r di
scov
ers
tota
l int
erna
l ref
lect
ion,
a s
mal
l-an
gle
refr
acti
on la
w a
nd t
hin
lens
opt
ics
1621
Will
ebro
rd S
nell
stat
es h
is la
w o
f re
frac
tion
Des
cart
es q
uant
itativ
ely
deri
ves
the
angl
es a
t whi
ch r
ainb
ows
are
seen
with
res
pect
to th
e th
e Su
n’s
elev
atio
n16
37 R
ené
1678
Chr
isti
an H
uyge
ns s
tate
s hi
s pr
inci
ple
of w
avef
ront
sou
rces
1704
Isa
ac N
ewto
n pu
blis
hes
Opt
icks
1728
Jam
es B
radl
ey d
isco
vers
the
aber
ratio
n of
sta
rlig
ht a
nd u
ses
it to
det
erm
ine
the
spee
d of
ligh
t 17
52 B
enja
min
Fra
nklin
sho
ws
that
ligh
tnin
g is
ele
ctri
city
1785
Cha
rles
Cou
lom
b in
trod
uces
the
inve
rse-
squa
re la
w o
f el
ectr
osta
tics
1800
Will
iam
Her
sche
l dis
cove
rs in
frar
ed r
adia
tion
from
the
Sun
1801
Joh
ann
Ritt
er d
isco
vers
ultr
avio
let r
adia
tion
from
the
Sun
1801
Tho
mas
You
ng d
emon
stra
tes
the
wav
e na
ture
of
light
and
the
pri
ncip
le o
f in
terf
eren
ce18
09 E
tienn
e M
alus
pub
lishe
s th
e la
w o
f M
alus
, whi
ch p
redi
cts
the
light
inte
nsity
tran
smitt
ed b
y tw
o po
lari
zing
she
ets
elec
tric
vec
tor
of li
ght
1811
Fra
nçoi
s A
rago
dis
cove
rs th
at s
ome
quar
tz c
ryst
als
will
con
tinuo
usly
rot
ate
the
1816
Dav
id B
rew
ster
dis
cove
rs s
tres
s bi
refr
inge
nce
1818
Sim
éon
Pois
son
pred
icts
the
Pois
son
brig
ht s
pot a
t the
cen
ter
of th
e sh
adow
of
a ci
rcul
ar o
paqu
e ob
stac
le18
18 F
ranç
ois
Ara
go v
erif
ies
the
exis
tenc
e of
the
Pois
son
brig
ht s
pot
1825
Aug
ustin
Fre
snel
phe
nom
enol
ogic
ally
exp
lain
s op
tical
act
ivity
by
intr
oduc
ing
circ
ular
bir
efri
ngen
ce18
31 M
icha
el F
arad
ay s
tate
s hi
s la
w o
f in
duct
ion
1845
Mic
hael
Far
aday
dis
cove
rs th
at li
ght p
ropa
gatio
n in
a m
ater
ial c
an b
e in
flue
nced
by
exte
rnal
mag
netic
fie
lds
1849
Arm
and
Fize
au a
nd J
ean-
Ber
nard
Fou
caul
t mea
sure
the
spee
d of
ligh
t to
be a
bout
298
000
km
/s18
52 G
eorg
e St
okes
def
ines
the
Stok
es p
aram
eter
s of
pol
ariz
atio
n18
64 J
ames
Cle
rk M
axw
ell p
ublis
hes
his
pape
rs o
n a
dyna
mic
al th
eory
of
the
elec
trom
agne
tic f
ield
1871
Lor
d R
ayle
igh
disc
usse
s th
e bl
ue s
ky la
w a
nd s
unse
ts18
73 J
ames
Cle
rk M
axw
ell s
tate
s th
at li
ght
is a
n el
ectr
omag
neti
c ph
enom
enon
1875
Joh
n K
err
disc
over
s th
e el
ectr
ical
ly in
duce
d bi
refr
inge
nce
of s
ome
liqui
ds18
95 W
ilhel
m R
öntg
en d
isco
vers
X-r
ays
Arn
old
Som
mer
feld
sol
ves
the
half
-pla
ne d
iffr
actio
n pr
oble
m18
96…
1873
1621
1801
1678
Refraction/reflection Diffraction EM wave
From Refraction to Diffraction 7
vacuum (c) and the speed of light in the medium. This index can also be defined as the square root of the
product of the permittivity and permeability of the material considered for the specific wavelength of
interest (for most media, m¼ 1):
n ¼ c
vn
n ¼ ffiffiffiffiffiffiffie:m
p
8<: ð1:1Þ
At this point, one could ask whether there would be a medium with indices that are positive but lower
than 1 (whichwouldmean that lightwould travel faster than the speed of light in a vacuum). This is largely
improbable: however, there are media in which the phase velocity of light is greater than c, but cannot be
used to send energy or signals at a speed in excess of c.
It is worth noting that the range of refractive indices in nature is much higher than one would imagine
(from air¼ 1.0 to glass¼ 1.5). For example, silicon (Si) has a quite high index of 3.5 for infrared (IR)
wavelengths, which enables the fabrication of photonic crystals in which the index change has to be the
highest possible in order to achieve full photonic band gaps (see Chapter 10). Table 1.2 lists the refractive
indices for some common materials. Interestingly, the range of refractive indices found in nature can be
extrapolated by the fabrication of synthetic materials known as metamaterials (see also Chapter 10), and
even materials with negative indices can be produced.
1.3 No More Parasitic Effects
History shows us that optical engineering has usually considered diffraction effects to be negative and
parasitic. These effects usually manifest when the imaging resolution limit is approached. They are
Table 1.2 Refractive indices for conventional (natural) and nonconventional materials
Media Refractive index Type Examples
Conventional materials
Vacuum 1 exactly Natural —
Air (actual) 1.0003 Natural —
Air (accepted) 1.00 — —
Ice 1.309 Natural —
Water 1.33 Natural Liquid lenses
Oil 1.46 Natural/Synthetic Immersion lithography
Glass (typical) 1.50 Natural BK7 lenses
Polystyrene plastic 1.59 Natural/Synthetic Molded lenses
Diamond 2.42 Natural TIR in jewelry
Silicon 3.50 Natural Photonic crystals
Germanium (IR) 4.10 Natural IR lenses
Media Refractive index Type Examples
Nonconventional materials
Metamaterials Negative indices Synthetic, active
materials (plasmon)
High-resolution lens,
Harry Potter’s
invisibility cloak
Bose–Einstein
condensate
n� 1, validated at
n> 1 000 000 000!
Synthetic, T¼ 0�K(v< 1mph)
Low-consumption chips,
telecom
? 0< n< 1.0 Improbable (v> c) Telecom, time machine,. . .
8 Applied Digital Optics
