A SimullnkTM toolbox for simulation and analysisof optical fiber links

Cláudio F. de Melo JR, César A. Lima, Licinius D. S. de Alcantara, Ronaldo 0. dos Santos andJoão C. W. A. Costa.

Laboratório de Eletromagnetismo Aplicado - Departamento de Engenharia ElétricaCentro Tecnológico - Universidade Federal do Pará

ABSTRACT

This paper presents a complete toolbox to be used together with the MATLAB ISIMULINK software. The versatility ofthis software is used to form analysis blocks in the time and frequency domains, allowing the user to simulate optical fiberlinks of any topology, as long as the analysis of its performance face changes in the values of its parameters. Results forLED (F.D.), Quantum Well (T.D.) and Fabry Perot (F. D.) LASERS are shown.

KeyWords: Optical Links, Simulation of optical links, LED, Fabry-Perot LASER, Quantum Well LASER, Rate Equations,SimulinkTM.

1. INTRODUCTION

The use of educational softwares is widely recommended in present days as a complementary tool in electrical engineeringand associated disciplines. This results primarily from the fact that these softwares offer convenient means for mathematicalmanipulations and for the visualization of the physical phenomena associated with these disciplines. In addition, the highcost of modern laboratories in this area enhances the interest of a more diversified use of these softwares [1].The Matlab, Mathcad, Maple and Mathematica softwares, for example, are widely used in engineering, not only as ateaching but also as a professional tool. Besides, these softwares provide a friendly computational environment in which thefacilities of numerical and/or classical algebraic equations solutions combine with the facilities of visualization anddocument integration. As a result, the difficulty, quite often encountered by undergraduate and graduate students, is partiallyovercome from the moment that these students are faced with a didactic computational tool and of easy comprehension,implemented in an environment familiar to the students.The analysis need of the performance of each component individually or in group in a optical fiber telecommunication linkhas given reason for the creation of a toolbox, which should be used along with the Matlab/Simulink software, allowing theprogrammer to concentrate only in the validity ofthe model being used.The toolbox may be understood as a group of blocks which represent the various components of a optical link, such as lightsources (LEDs and lasers), optical fibers (multimode and monomode), photodetectors (PIN or APD) and allow thesimulation of its dynamic behavior individually or in group. Its main characteristic is therefore its flexibility, for there is notopology defmed, and the user is the one who decides the way the system is built up.

2. DEVICE MODELS

In this section is shown how to construct Simulink blocks using the mathematical (physical) model. The devices can beanalyzed using T.D. or F.D. model. For illustrating proposals, the source models for LED, Fabry-Perot Laser and MQWlaser will be described. In the F.D. the Fourier Transform (F.T.) ofthe optical power, Pe(f) (watts) can be expressed as:

e (f)= HT (f).Id (f)' ( 1)Where H(f) is the transfer function of the source and 'd (f) is the F. T. of the injected current (A). The transferfunction can be decomposed in two parts:

HT(f)=HT(O).H(f) (2)

Correspondence: e-mail: jweyl@ufpa.br; P.O Box: 8619, ZIP 66075-900, Belém-Pa-BrazilSimulinkTu is a trademark of The Mathworks Inc.

In Sixth International Conference on Education and Training in Optics and Photonics,240 J. Javier Sánchez-MondragOn, Editor, SPIE Vol. 3831 (2000) • 0277-786X1001$15.O0

1H; (f) = _______

1+jf/f'1

fc=27lTr

The meaning of parameters in (3)-(7) are given at TABLE I.

2.2. Multimode Fabry-Perot:

['d—'thHT(0) = I Thntext2.q)

TABLE IPARAMETERS OF (3),(7)L External Quantum efficiency Q Electron charge (1 .60218 iø' c)

Internal Quantum efficiency Nonradiative recombination lifetimer______7hnj

h

Injection current efficiency

Planck's constant (6.62 x iøTr

Radiative recombination lifetime

Semiconductor refraction index

C Light velocity in the vacuum (2.99793 x 108 mIs) , Refraction index (air =1)

2 Emission wavelength (m) 7 Optical cutoff frequency (3 dB)

241

In the previous equation, HT(O) is the quantum efficiency of the light source (W/A), H(f) is the normalized frequencyresponse of the light source.

2.1. LED

For the LEDs the transfer function can be expressed as/4J

(h.cHT (0) =

j_J71intT1injTi ext (3)

where:

Vnrhint —rnr+'rr

= 1 ——

J2[_ (5)

lls+flm L

The term H (f) in (2) is expressed by

(6)where:

(7)

(8)

For the Fabry-Perot laser the transfer function can be expressed as [4]

Where:

(iml

lext ( )

ri+mn[__Jand i7 is the same as in (4).

2

H(f)= Jo (10)f —4,r2f2 +j/32tf

where:

f2(101th) (11)r5P rph 'th

I1= ° (12)

rSP.[h

The description of new parameters at (8)-(12) are given in TABLE II.

TABLE IIPARAMETERS OF (8)-(12)

Injected current j Polarization current (A)

7 The threshold current (A). . Carrier recombination lifetime (s)

1? Mirror reflectancy (m) p Dumping frequency (Hz)

7 loss coeficient Resonant frequency (Hz).

1 Cavity longitudinal dimension (m)

Obs : the former expressions are valid only for 'd > 'th i.e., in the stimulated emission region

2.3. Quantum-Well (QW) LASER.

To obtain the response of the quantum-well (QW) LASER was not used a model, but a implementation in the time domainthrough a block diagram using SIMULINK, according to the following rate equations [2]:

dN I NN—= -g0(N—N01—eS)S——+----- (13)dt qV0 -C,, r,4: Fg0 (N -N0Xi - eS)S + F/3N

(14)dt 1,, T1,

S FrA.0—= =v (15)Pf Vactl7hC

The terms of the above equation are described in TABLE Ill

242

TABLE IIIPARAMETERS OF (13)-(15)

7___ Active region carrier density fl Spontaneous emission coupling factor

r— Photon density . Photon lifetime

7___ LASER output power 17 Differential quantum efficiency per facet1 Injection current , Lasing wavelength

v;— Active region volume Q Electron charge

g0Gain coefficient. H Planck's constant

N0 • .

Optical transparency density.C Light velocity (vacuum)

•1 Fenomenological gain-saturation term y Equilibrium carrier density

-•:——Carrier lifthme 1' Optical confinement factor

Accordingly with [1], the standard rate equations that use a linear gain-saturation term of the form (1-c)S canpossess three dc solution regimes for nonnegative values of injection current, which two of them are nonphysical solutions,characterized for negative power and high power solutions. For the parameter values used in this paper, the nonphysicalsolutions would happen above a injection current value between 0.5 and 2A [1J, which is higher than typical values appliedin these simulations

3. TOOLBOX PRESENTATION

The developed blocks are separated in five main groups for the convenience of the user. They are: Signal Origin, LightSources (explained here), Optical Fibers, Photodetectors and Passive Devices. Anytime one of these groups are "double-clicked" with the mouse, the user gets access to the windows containing blocks representing each component of the system.These windows are shown in Figures 1 through 6 Using this blocks, it is possible to assemble a simulation diagram, as willbe demonstrated in the next section.

r;iir

Signal Origin Light Sources Optical Fibers Photodetectors Passive Devices

r + + 1993 CésarAlbuquerque Limaemons ra on Joäo Crisóstomo Weyl A. Costa

Figure 1 - Toolbox Main Window.

file lipboaid dit options imulation 5yle

ToolboxiorSimulation andAnalysis ofOptical Links

243

244

Figure 2 - Signal Origin Group Window.

Figure 3 - Light Sources Group Window.

Figure 4- Optical Fibers Group Window

file Qlipboard edit Qptiorss imuIation S4yleSignal Origin flS E2

Signal Sources:

UDDOI I0 * r [1,51 r sinal.dat

Signal Generator Signal from a Vector Signal from a File

Connections:

I DemuxfMux

Demultiplex Multiplex

[jin4 _Pulse Generator Band-Limited

White Noise

Switch

Gain Sum Product

Display Devices:

1 998 - CésarAlbuquerque LimaJoão Crisóstomo Weyl A. Costa

so easGraph Scope Spectrum Average Spectrum PSD Average PSD Autocorrelation Scope

Analyzer Analyzer

Light Sources fljA

file Qlipboard dit Qptions Sulation S!yle

Light Sources :

I I I I I I 1

LED LASER1 r 1 LASER2 r 1 LASER2 r 3Light Emitbng Diode LASER Multimode LASER Monomode DFB LASER

(First Module) (Second Module) (Second Module) <x

1998- CésarAlbuquerque LimaJoo Crisóstomo WeylA. Costa %

file clipboard fdit Qptions simulation Sflple

Fibras Opticas:

Optical Fibers

L FIBER1F

FIBER2F

FIBER2 FOptical Fiber Monomode Fiber Plastic Multimode Fiber

Coupling Efficiency Frequency Response Frequency Response

FIBER3 F FIBER3F )[

FIBER3 JSimplified Atennuation Detailed Atennuation Atennuation due to

Rayleigh Scattering only

1 998 - CésarAlbuquerque LimaJoâo Crisóstomo Weyl A. Costa

;jFIBER2

FStep Index Glass Multimode Fiber

Frequency Response

1FIBER2

FGraded Index Glass Multimode Fiber

Frequency Response

IZr

Figure 5 - Photodetectors Group Window

Figure 6- Passive Devices Group Window

3.1. LED

En fig.7 can be seen the LED block, with other blocks like signal generator and scope. The user can quickly change thparameters of a LED block, as shown in fig.8.

Fig. 7- Structure used to simulate the behavior of a LED

Values used in the simulations of this work are also shown in figs. 8, 11 and 14. Using this structure to simulate thebehavior of a LED, and plotting the optical power emitted when the input is a test square wave, can be seen in the fig. 9.

245

Photodetectors

Elle clipboard kdit Qptions imuIation Sjylera

Photodetectors and Receptors:

PIN Photodetector F APD Photodetector F Receptorwith PIN ReceptorwithAPD

Fotodetector PIN FotodetectorAPD Receptor using Receptor usingPIN Photodetector APD Photodetector

1998 CesarAlbuquerque LimaJoâocrisOstomoWeylA Costa. ,.

4

Passive Devices Elfile Qlipboard fdi( Qptions simulation Style

Passive Devices Used in Optical Links:

IN Coupler OUT IN Coupler OUT

Non-Ideal 9 dB CouplerNon-Ideal 6 dB Coupler

IN Coupler OUT

IN Coupler OUT

Non-Ideal 3 dB Coupler

)J IN Connector OUTFConnector

Ideal 9dB Coupler

IN Coupler OUT

>

>

Ideal 6 dB Coupler

IN Coupler OUT

Ideal 3 dB Coupler

1998- CésarAlbuquerque LimaJoâo Crisóstomo Weyl A. Costa

9tZ

.TT

oq in uaas snpuwnd aq snfp o nsn aip 2rnMOJIE 'uodo hiM xoq 2OJt([ &iiMOJjOJ O ')jOOjq >gyq aqi &IT3EAT3OV

apoip iasv'i ajniuis o pasn airpanus -OI8!d

"aasv'i on-AiqJ aporuqjnw jo ppoiu si smj ojaq uhtoqs 5! apO!p iasvi aip jo uoiwnuijs aip o UJEJ2EIP aojq Otij

(apowpjnui) �1218V7 ;oaj-C'qvj .r cia'i 34204 S3JflS3)J U09EIfl1U!S — 68!d

Sla4OWEJtd uai 344 03 xoq 8°W!G —

. : : ' ' ' ' . . N?Z 'au

e Mt H

1e*uo '¼ S$ s•3

% DLCL:

- .. '

L17Z

r •uopjnius I'fl!!P JO A4qIqS am aautnn o 'ntgap aq urn.j JOAtOJ dais atm I '(poaui tnnj-a2un>j) xj o 'xoq 2OjEip siaowrnd SUOI4EjUURS,, in ddJs owq oq isnfpt o Anssooou SEAt 'UOISSOS

[rnMOjJOJ aq U! pOSSUOSIp aq 04 'flELSV1 MO aq S IIOM S 'IdSV1 joiaj-Aiqj am jo uoqjnurrs aip 4iuuad oj :a2oM

apoi flsyi aq o sjnsau uoiwjnuug Z12!d

ig!S 1ndrn jo uanno OAEM 1j) uojrnuis jo sjnsai auj sn2awarcd apoip }J3SV1 4W" xoq SOIE!U -II!d

N

& ' - 1000 ;rtr ' "

)f '

' % , ' '%' " .'

' ' ' . :\ . ;%

tt S

' 3C0.

ffa fl%a% .. ' "

fl : .

t fr-a \ ? flth1*9WiflQthf3fltU4Afl,

.\\%' ' , F t*Ud3WaMoP

" ' $' '.% '.

: 09S1

3.3. Quantum-Well LASER

The block diagram related to the simulation ofthe LASER diode is shown in the fig. 13.Fig. 14 illustrates the dialog box forinput parameters, activated by double clicking the Rate equation block, allowing the simulation of QW LASER fordifferent materials and structures. Accordingly with (13)-(15), the "rate equations" block in fig 13 is composed by thestmcture shown in fig. 15. Fig.16 shows the plot of optical power output corresponding to the values given in fig.15 (defaultvalues), where the injected current varies between 0 and 10 mA with a period of4O nS (25 Mhz). It Can be observed in thisfigure that there is a significant delay in the response, considering that the lower level of the injected current is below thethreshold current to cause lasing. To other experienced simulations, varying the injected current between 8 and 10.5 mA,the output optical power follows the shape of the input signal in a better manner, with less delay, with a consequence that agreater operating frequency could be used. However, the rising of the superior level of the injected current, the overshootbecomes bigger, indicating a reduction in the relative stability of the system. Fig. 17 shows the relation between the photonsdensity S, carrier density N and the optical output power to the same injection current used in fig. 16.

1 502e-1

9e-11

4e-4

S

3e-6 . SSS S

1.2e18ySSS

3000 . umepfS

01..541e10

SS

Fig.14- Dialog box for the QW LASER

248

Fig.13 — Block diagram used to simulate a QW LASER

Out 1- epsS(O Constanti

Fig 15 —Block diagram of "rate equations" module in time domain.

249

Gain (Vact'etattl I (gama'talplambdaOl

Fig 16- Optical Output Power to a input current varying between 0 and 10 mA

time (10' s)Fig. 17— Variation ofthe photons density S, Carriers density N and Optical output Power to an input current varying between 9.5 e 10.5

mA

4. TOOLBOX UTILIZATION EXAMPLE

The blocks shown can be used to simulate a variety of optical links configurations, considering that the blocks dispositiondepends of the user to compose the system. In this example, it will be used a simple point-to-point topology, with purelydidactic objectives. The simulated link can be seen in fig. 18, mounted exclusively with blocks contained in the five groupsmentioned before.

Once the value defmition for the blocks is done, the simulation can be started using the "Start" option in the "Simulation"menu. The result will soon appear on the screen, and is shown in Fig.l9, in the time period of 0 to 10 ns. It mustbe notedthat there are three different points of observation (graph scopes in Fig. 18), all with the same magnitude scale.

250

N(t)>(71O")

. 1(t)1' (1.17

* 10') :

.'__Sn2 10 -?)

r

':

demol SliJ El

Fig. 18 - Simulation diagram for a point to point optical link.

1____5_

0.8

0.6

(2)

0.4

o:

-0.2

0 1 2 3 4 5 6 7 8 9 10Time (nsecs)

Fig. 19 - Simulation results for the diagram shown in Fig. 18.

5. CONCLUSIONS

The SimulinkTM blocks described here have been used as a teaching tool for undergraduating students in basic courses ofoptical fiber communications at UFPa. The facilities ofthe computer simulation allows a better understanding ofthe theory,improving the student's yield, and the flexibility of the software permits the investigation of the influence of variousparameters, proving to be a good didactic complement. Currently, the authors are developing models for filters, optical andsemiconductor amplifiers, non linear fiber optics blocks to analyze high bit rate optical systems.

REFERENCES

1. Delyser, R. R., " UsingMathcad in Eletromagnetic Education", IEEE Trans. on Educ. .,Vol 39, n° 2, pp. 198-209,May 1996.

2. Iskander, M.F., "Computer -basedEletromagnetic education", IEEE Trans. on Microwave Theory Tech., vol 41, n 617,pp. 920-93, June/July 1993.

3. Mathworks, inc. "Simulink: A Programfor Simulating Dynamic Systems- User's Guide." Natick, Massachusetts, 1995.4. Lobäo, P.MS, A Optical Fiber Communication Systems Simulator Software —MsC. Thesis —FEE/UNICAMP, 1992 (in

portuguese).5. Mena, Pablo V., "Rate Equation Based Models with a Single Solution Regime ",J. Ligthwave technol. Vol 15, n 4, p.p.

717-729, April 1997.

251