Time Domain Simulation of Optical Anlplifiers Incorporating ASE Noise

Effect in WDM Photonic Systems

By

CHEUK CHI (ANTONY) LIU, B. ENG

A Thesis

Submitted to the School of Graduate Studies

in Partial Fulfillment of the Requirements

for the Degree

Master of Applied Science

McMaster University

© Copyright by Cheuk Chi Liu, November 2004

MASTER OF APPLIED SCIENCE (2004)

(Electrical and Computer Engineering)

McMaster University

Hamilton, Ontario

TITLE: Time-Domain Simulation of Optical Amplifiers incorporating ASE

Noise Effect in WDM Photonic Systems

AUTHOR: Cheuk Chi (Antony) Liu,

B.ENG (McMaster University)

SUPERVISOR: Dr. Xun Li

NUMBER OF PAGES: vii, 120

11

Abstract

To overcome optical signal attenuation m fiber-optic transmission system,

amplifiers must be used in the optical link. However, the accompanying amplified

spontaneous emission (ASE) noise in optical amplifiers becomes the major factor that

impairs the amplified optical signal, thereby degrade the system performance

especially in a cascaded amplifier system. This thesis aims at providing a numerical

tool that simulates the noise effects when applying optical amplifiers in high-speed

long haul transmission systems. A time domain model for Erbium-doped fiber

amplifier (EDFA) and semiconductor optical amplifier (SOA), which is capable of

handling the locally generated broadband ASE noise and multichannel signals, is

developed with affordable computational complexity. Not only the averaged ASE

noise contribution to gain saturation has been included in this model, but also the

random nature of the ASE noise in optical amplifiers is incorporated through

appropriate statistics. Other effects such as the nonuniform spatial distribution of

carriers and frequency chirping are also considered in this model. This model is

implemented numerically in order to examine the static and dynamic behaviors of the

optical amplifiers. Various effects arising from the ASE noise are shown in signal

waveforms picked up at any point along the optical link. Furthermore, the newly

developed optical amplifier simulator is integrated with an existing time-domain

simulation platform that has many other optical components assembled and is capable

of handling point-to-point multichannel fiber-optic transmission system in arbitrary

configuration. Consequently, the influence of the ASE noise on power booster, in-line

111

amplifier, preamplifier, and the combination of them has been studied thoroughly in

both single-channel and WDM fiber-optic transmission systems.

iv

Acknowledgements

I would like to gratefully acknowledge the enthusiastic supervIsIon of my

supervisor, Professor Xun Li, during the whole process of this work.

I would specially like to thank my girlfriend Janette Wong for her willingness

and assistance to discuss ideas and her constant support throughout my study period. I

am grateful to all members from the Photonics Research Group. McMaster University.

for being the surrogate family during the years I stayed there and for their continued

moral support there after.

Finally, I am forever indebted to my family for their unconditional love, endless

patience and encouragelnent when it was most required.

v

Contents

Abstract

Acknowledgements

1 Introduction

iii

v

1

1.1 Background 1

1.2 Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... 3

1.3 Thesis Organization 3

2 Principles of Optical Amplifiers 5

2.1 Basic Usage of Optical Amplifier 5

2.2 Principles of Operation 6

2.3 Characteristics of Different Types of Optical Amplifier 7

2.4 System Applications 8

3 Optical Amplifier Modeling 10

3.1 Semiconductor Optical Amplifier '" 11

3.2 Erbium-Doped Fiber Amplifier 16

3.3 Frequency Chirp Computation 21

3.4 Noise Characteristics 22

4 Model Inlplementation 25

4.1 Steady State Model 25

4.2 Block Diagram for Steady State Implementation 28

4.3 Large Signal Dynamics Model 29

4.4 Block Diagram for Large Signal Dynamics Model 31

5 Simulation Results 33

5.1 Steady State Simulation Results 33

5.2 Large Signal Dynamics Simulation Results 47

5.3 WDM Channels Dynamics Results 58

5.4 Noise Power Spectrum 63

VI

6 Transmission Link Simulations 65

6.1 Single Channel System Simulations .. '" ., " . " " '" 67

6.1.1 Case 1: Power Boost Amplifier " " '" , 67

6.1.2 Case 2: In-line Amplifier 72

6.1.3 Case 3: Preamplifier 78

6.1.4 Case 4: Combination of Power Booster, In-line Amplifier, and

Preamplifier 82

6.2 WDM System Simulations '" , " 86

6.2.1 Case 1: DWDM 4 channels with MQW SOAs in the 1550nm

window 86

6.2.2 Case 2: DWDM 4 channels with EDFAs in the 1550nm window 99

7 Conclusion

Appendix

Bibliography

vii

108

109

113

\L\!. :

Chapter 1

Introduction

1.1 Background

The field of optical fiber communications, which makes use of the low-loss,

broadband characteristics of optical fibers and the advantages of having light as the

carrier, is progressing at a tremendous speed [1]. Invention of the optical amplifiers

and wavelength-division multiplexing (WDM) technology enabled very high capacity

fiber-optic transmission links that run for thousands of kilometers without any

electronic repeaters, but many design challenges were brought at the same time. As

electronic amplifiers do, optical amplifiers add noise to the signal they amplify.

Therefore, in the design of a fiber-optic communication link, it is essential to be able

to predict the deterioration that the information signals experience due to the gain

saturation caused by amplified spontaneous emission (ASE) noise in the optical

amplifiers.

,r~~'ir,:::

Laser Diode ;,':~;,,'1>.'

;1ft (

MedUlate,~; • Op~~~:.~;e, ~c -#- {,-__O_P_ti_ca_l_fi_be_r_~0m:

Lt •NOise :~J,- -----,~ Optical in-line

t;, V amplifierSJJ:S i"

Opticalreceiver

Optical pre­amplifier

-7'7'-0 Optical fiber r--J

Figure 1.1: Major elelllents of a fiber-optic translllission link. The basic cOlllponents are the

laser diode. the optical lIIodulator. the optical fiber. the optical amplUlel; and the

photodetecting receivCl:

Generally, a basic fiber-optic transmission system comprises the elements shown

in Figure 1.1. In WDM transmission systems, information bits are used to modulate

the carriers from the laser diode at a number of wavelengths, which are then

transmitted through the optical fiber. The attenuation of optical signal level due to the

loss from the fiber needs to be restored by the optical amplifiers. In the meantime, the

optical amplifiers add noise to the signal and thus hamper the performance of data

recovery at the recei vel'.

The main source of noise in an optical amplifier is the spontaneous emission of

photons. In the spontaneous emission process, there is non-zero probability per unit

time that a conduction band (CB) electron (excited ion) will spontaneously recombine

with a valence band (VB) hole (ground ion) to emit a photon with random phase and

direction. These spontaneously emitted photons cover a wide range of frequencies,

and also take part in reducing the population available for optical gain [2]. The

photons generated at the front section of the active medium travel along with the

signals and get amplified accordingly; it is so-called the amplified spontaneous

emission (ASE) noise. On the basis of the optical signal is not converted back to the

electrical domain until the end of the chain, the ASE noise continues to grow and

accumulates over many amplifiers in a cascade amplifiers system. As a result, the

signal level drops and the ASE level increases along the transmission line. and thereby

degrade the signal-to-noise ratio (SNR) considerably at the receiver. Hence,

depending on the amount of accumulation, ASE at the output of one amplifier stage

could influence the operation conditions of the next stage and result in severe system

performance degradation [3].

2

1.2 Motivation

The goal of this project is to develop a numerical tool that simulates the noise

effects when applying optical amplifiers in high-speed long haul transmission systems.

The model of both semiconductor optical amplifier (SOA) and Erbium-doped fiber

amplifier (EDFA) is implemented. Making use of the time domain simulation, the

noise behavior of optical amplifiers can be predicted and evaluated. Other than that,

special attention should be paid to the noise effects when the amplifiers are cascaded

in an optical link, so that this numerical solver will be integrated with our existing

system platfonn to fonn a whole fiber-optic communication system in order to study

this circumstance. In fact, with the increased complexity of optical links and networks

nowadays, computer-based simulation and modeling tools can make the design

process more efficient, cheaper, and faster.

1.3 Thesis Organization

The following six chapters describe the thesis work carried out, and their

contents are briefly outlined here. In chapter 2, we describe the basic principles of

operation and the characteristics of two different types of optical amplifier. In addition,

their applications are discussed and compared with respect to each other. In chapter 3,

a detailed model for both SOA and EDFA based on sets of rate equations is

established. As well as, the noise characteristics are described with appropriate

statistical properties. In chapter 4, we explain how to implement our model based on

numerical methods in detail. All of the time domain simulation results are shown and

analyzed and the noise and cross gain saturation effect during multichannel signal

amplification are also examined in chapter 5. In chapter 6, the amplifier module is

incorporated into our system platform to form a fiber-optic transmission system, so

the ASE noise effect in single channel and WDM fiber-optic transmission system for

3

Vb~ll~r Tl1c::,j ~ - /\ mOl, '. !.I U McMaster Univ(;r"il\ -. L.kL'lricd 8.:. Compul.er [~11~jl1(>uili.~c

different applications can be studied. Finally, we summarize the main results of the

preceding chapters in chapter 7.

4

Chapter 2

Principles of Optical Amplifiers

In this chapter, first looks at the basic usage of optical amplifiers and classifies

the two fundamental amplifier types: semiconductor optical amplifiers (SOAs) and

Erbium-doped fiber amplifiers (EDFAs). Secondly, the operational principles of

optical amplifiers are explained, and their basic properties, such as gain and saturation

will be discussed. We then turn to noise characteristics, which are of great

significance when amplifiers are applied to transmission systems.

2.1 Basic Usage of Optical amplifier

Optical amplifiers are used in the optical transmission link, in order to

compensate for signal attenuation during transmission due to fiber loss. They operate

solely in the optical domain with no inter-conversion of photons to electrons.

Therefore, instead of using regenerative repeaters, which require optoelectronic

devices for source and detector, together with electronic circuitry for reamplifying,

retiming and reshaping, optical amplifiers can be placed at intervals along a fiber link

to provide linear amplification of the transmitted optical signal. The optical amplifier,

in principle, provides a much simpler solution in that it is a single in-line component

which can be used for any kind of modulation at any transmission rate. Moreover, if

such device is sufficiently linear it may allow multiplex operation of several signals at

different optical wavelengths (i.e. wavelength division multiplexing - WDM).

5

2.2 Principles of Operation

The two main optical amplifier types can be classified as semiconductor optical

amplifiers (SOAs) and doped-fiber amplifiers (DFAs). Optical amplification is

produced by the process of stimulated emission induced by a population inversion in a

lasing medium. It applies to semiconductor optical amplifiers or erbium doped fiber

amplifiers. All optical amplifiers increase the power level of incident light through a

stimulated emission process. The mechanism to create the population inversion that is

needed for stimulated emission to occur is the same as is used in laser diodes [4].

Although the structure of an optical amplifier is similar to that of a laser, it does not

have the optical feedback mechanism that is necessary for lasing to take place. Thus,

an optical amplifier can boost incoming signal levels, but it cannot generate a

coherent optical output by itself. The basic operation is shown in Fig.2.1. Here, the

device absorbs energy supplied from an external source called the pmTIp. The pump

supplies energy to electrons in an active medium, which raises them to higher energy

levels to produce a population inversion. An incoming signal photon will trigger these

excited electrons to drop to lower levels through a stimulated emission process,

thereby producing an amplified signal [4]. Beside, an incoming photon can stimulate

an electron from lower to upper level. This is a stimulated absorption process as the

incoming photon is extinguished.

In general, the optical gain depends not only on the wavelength of the incident

signal, but also on the local power at any point in the amplifier [5]. As the signal

power increases, the population inversion in the active region is greatly depleted

leading to a decrease in the amplifier gain. Signal distortion can be caused by such

gain saturation. Moreover, it can also further limit the gain achievable when optical

amplifiers are used as multichannel amplifiers.

6

Stimulated absorption

eo.Spontaneous emi"S10!1

!V+- IE,~!V+- ~

~ ~Energy bandgap

!V+-

0.0 E,OJfOHole

eoStimulated emission

Figure 2.1: Schematic diagram of two-level system with spontaneous and stimulated

processes.

On the other hand, optical output from optical amplifiers is composed of an

amplified optical signal and an amplified spontaneous emission (ASE) of a broad

spectral width [1]. The spontaneous emission noise is the dominate source of noise in

optical amplifiers and it is a random process, which is statistically stationary and will

cause fluctuations in both amplitude and phase of optical signal. In addition, photons

of the spontaneous emission can interact directly with the signal. Moreover,

interference is created between ASE components and the light signal. So, several

types of noises (the shot noise of the signal and spontaneous emissions, beat noise

between signal and spontaneous emissions, and beat noise between spontaneous

emission components) can be observed, when the output photons are detected by a

photodetector.

2.3 Characteristics of Different Types of Optical Amplifier

The two major types of SOAs are the resonant. Fabry-Perot amplifier (FPA) and

the non-resonant, traveling-wave amplifier (TWA). In an FPA, the two cleaved facets

of a semiconductor crystal act as partially reflective end minors that form a

Fabry-Perot cavity. When an optical signal enters the FPA, it gets amplified as it

7

reflects back and forth between the mirrors until it is emitted at a higher intensity. The

structure of a traveling-wave amplifier is the same as that of an FPA except that the

end facets are antireflection-coated, so that internal rellection does not take place.

Thus, the input light gets amplified only once during a single pass through the TWA.

These devices have been used more widely than FPAs because they have a large

optical bandwidth, high saturation power, and low polarization sensitivity. For most

cases, recent literature on optical fiber systems uses the term "SOA" without

qualification, for traveling-wave semiconductor optical amplifiers [4]. In this thesis,

we will concentrate on TWAs only.

The active medium in an Erbium-doped fiber amplifier consists of a nominally

10 to 100-m length of optical fiber that has been lightly doped with rare-earth

element - erbium (Er). Whereas semiconductor optical amplifiers use external current

injection to excite electrons to higher energy levels, optical fiber amplifiers use

optical pumping. In this process, one uses photons to directly raise electrons into

excited states. The optical pumping process requires the use of three energy levels.

The top energy level to which the electron is elevated must lie energetically above the

desired lasing level. After reaching its excited state, the electron must release some of

its energy and drop to the desired lasing level. From this level, a signal photon can

then trigger it into stimulated emission, whereby it releases its remaining energy in the

form of a new photon with a wavelength identical to that of the signal photon. Since

the pump photon must have a higher energy than the signal photon, the pump

wavelength is shorter than the signal wavelength [4].

2.4 System Applications

Three main applications of optical amplifiers in optical transmission system are

power booster to increase transmitter laser power and compensate for the splitting

8

,:

losses in optical distribution network; in-line amplifier to compensate the fiber loss;

and preamplifier to improve receiver sensitivity. The optical fiber amplifier has tended

to be dominating conventional system applications as it possesses higher gain, low

noise figure, and negligible nonlinearities. However, the SOA can still be used as

basic amplifiers because of its compact size and low cost, and it is easily integrated

with other optical devices and circuits. In addition, the SOA is showing a great

promise using in many functional applications, such as optical switch, wavelength

converter, and other optical signal processing device, all of those cannot be performed

by fiber amplifiers [21.

9

Chapter 3

Optical Amplifier Modeling

Models of optical amplifier steady-state and dynamic behavior are important

tools that allow optical amplifier designer to develop optimized devices. They also

allow us to predict how an SOA and EDFA or cascade of them respectively behaves in

a particular application. In this chapter we concentrate on specific models and use

them to focus on the main characteristics of SOAs and EDFAs.

Different from the laser diodes (LDs) which operate in a narrow spectral range,

the optical mnplifiers have to be described in a broad wavelength spectrum as the

multichannel signals may spread over the entire gain spectrum whe~e spontaneous

emission noise is also emitted and coupled into the signal wavelength [6]. In our

model, the spontaneous emission noise is generated by randOIll nmnber sources over

the entire wavelength spectrum and is coupled to the signal channels in a

self-consistent manner.

Firstly, the time-domain traveling wave model developed on the photon number

(photon power) rate equations and the phase rate equations will be established for the

simulation of both SOAs and EDFAs, where the optical power and phase driven by

the locally generated noise source is described. In the spatial domain, such devices

exhibit non-uniform population and photon distributions along the propagation

direction. Therefore, the governing equations have to be discretized along the active

medium to treat these variations. As stated before, it is necessary that the governing

10

I :' ' ;" ,\ nt( Ifl \ ! ,IiI

equations are also solved in a broad spectral range, so the broad-band spontaneous

emission noise and the multichannel optical signals can be considered. Last of all, the

photon number (or photon power) rate equation and the phase rate equation are

coupled to the carrier density (or population density) rate equation for the variation of

gain and spontaneous emission noise.

3.1 Semiconductor Optical Amplifier

At present, there are numerous techniques for simulating semiconductor optical

amplifier numerically. However, we use a more detailed model to take into account

the longitudinal spatial nonuniformity of the carrier density and the locally generated

broadband ASE noise. In opposite to [7], our aim is to provide the models of both

SOA and EDFA to be adaptable with various bit rates of input signals for flexibility

when they are assembled in the communication system platform. Therefore, we

provide a set of coupled rate equations including t and z dependence to describe the

ampllfication process in SOA, and in EDFA later. Originally, the time-dependent

coupled wave equations for simulating the active devices can be derived from

Maxwell's equations as follows:

(3.1.1)

where E k + (t, z) and E k _ (t, z) are the slowly varying forward and backward complex

optical field respectively, k represents the corresponding wavelength located at the

center of the segments that cover the entire spontaneous emission spectrum with N k

indicating the total number of the wavelength segments. On the other hand, v g (m/s)

is the group velocity, a (m- I) is the material loss coefficient, and r is the confinement

11

factor. gm (m- I) is the material gain that depends on the position in the cavity and the

carrier density N(t, z) (m-3) , which turns to depend on the spatial position and time.

Finally, EN (t, z) represents the spontaneous emission noise, which operates as the

driving sources for oscillation.

It is convenient to introduce normalized complex field amplitude E(t, z.), so that

the absolute square of this field amplitude corresponds to the photon number rate

S(t,;,) (lis) inside the amplifier cavity

where ¢ (t, z) represents the phase of the optical field.

We can obtain the photon number rate equations from (3.1.1) as follows:

1 dSk±(t,Z) dSk±(t,Z) ( )

I± d = rgm(vk,N(t,z»-a(N(t,z» Sk±(f,z)+R.lp(vk,N(t,z»+Fs(t,z)

v~ (t Z

(3.1.2)

where Sk+(t,Z) and Sk_(t,Z) represent the forward and backward signal or

amplified spontaneous emission noise (ASE) photon rates at the k-th wavelength

segment (N k is total number of wavelength segments), respectively.

RIp (vI.' N(t, z)) is the mean value of the spontaneous emission rate.

The material loss coefficient and the spontaneous emission rate are defined as (3.1.3)

and (3.1.4) respectively:

(3.1.3)

(3.1.4)

12

\llll111y I III

Here K o is the carrier-independent loss coefficient; K) IS the carrier-dependent

loss coefficient, and nIp is the population inversion factor.

For the SOA gain model, a good approximation given by equation (3.1.5)

presented in [8],[9] was used. There are two gain expressions since we considered two

commonly used SOA materials, which are the Bulk and Multi-Quantum Well (MQW).

When a phenomenological gain model is used, the optical gain is given by

where

(Bulk)

(MQW)

(3.1.5)

I v-vp"lD(l') = ll- (-v-)-J

\\'1

I v-vp "lD(v)=ll-(~)-J

v>v p

Here, g N is the differential gain, the unit of it is (m2) for bulk and (m'l) for MQW,

Nfr

is the transparent carrier density, E is the gain saturation factor, and D(v) is

the detuning factor at the corresponding frequency. The detuning factor is used to

adjust the gain profile of SOA, where v p is the frequency of the peak of gain, v wl

and v".,. are the left and right position on the gain spectrum at FWHM frequency

width respectively.

In our model, the SOA is divided into M longitudinal sections of equal length,

and a uniform carrier and averaged photon rates are used for each section. Fig. 3.1

illustrates the SOA sectioning. The i th section has a uniform carrier density N1

' an

averaged signal photon rate S.I/g,/, and an averaged ASE spectral photon rate SASE,1 •

The total cun-eot injected into the active region I is supposed to be equally

13

distributed among the sections, hence II = I / M . On the other hand, the photon

number rate equations at different wavelengths in (3.1.2) are coupled through the

carrier population sharing, governed by the carrier rate equation

(3.1.6)

where II is the aInplifier bias current. In (3.1.6) all of the bias current is assumed to

pass through the active region only, no current leakage is considered. The first term on

the right hand side (RHS) of (3.1.6) represents the addition of carriers to the active

region from the bias cunent. These injected carriers are then depleted by various

mechanisms occurring within the amplifier. The second term represents radiative

recombination of carriers due to the amplified signal and amplified spontaneous

emission (ASE). The last term represents the radiative and nonradiative

recombination mechanisms given by

- - '} -,RR(N

l)= AllflulN' +BnuIN' - +CaugN " (3.1.7)

where AI/rtul is a linear nonradiative recombination coefficient, Bmd is bimolecular

radiative coefficient, and Caug is the Auger recombination coefficient.

....---~P ASE,- (A )

N1 N2 N3 N NMJ

SSI9,1 SSI9,2 SSI9,3... . . . . . .

SSI9,)......

SSIQ,M

Sase,1 Sase.2 Sase.3 Sase.! Sase,M

PQut, sI9-~

--~

PASE,+(A )

Figure 3.1: The SOA is divided into M sections of equal length.

In the model N.I. signals are injected into the amplifier with optical frequencies

V J (j =: l. ...NJ and power ~1l,llg _ J before coupling loss, The signals travel through

the amplifier cavity, and exit at the opposite facet. The SOA model is based on a set of

14

coupled differential equations that describe the interaction between the internal

variables of the amplifier. i.e. the photon rate and carrier density. The solution of these

equations enables external parameters such as signal fiber-to-fiber gain to be predicted.

In the following analysis it is assumed that traverse variations (i.e. normal to the

propagation direction) in the photon rates and carrier density are negligible. This is

valid assumption because most SOAs have a narrow active region [101. In the model,

the left (input) and right (output) facets have power reflectivity Rj and R'2'

respectively. (3.1.8) is subjected to boundary conditions for the traveling signal

photon rates and spontaneous emission photon rates

} Left facet

} Right facet

(3.1.8)

The input signal photon rate from the optical fiber is given as

O_ rJi/l ~'l,\ig _.I (t)

Sill\i" ,(t, ) - I' ,'- J lV .

.I

(3.1.9)

where 7l ill is the input coupling efficiency from the fiber to the device waveguide,

and ~/l.S(Lj is the input power at the j th channel. The output power of the j th

channel from the SOA can be expressed as

~Jltl.Slg _ J (t) = hv j7]ow (1- R'2)S.I+ (t, L) (3.1.10)

where 77,,111 is the output coupling efficiency from the device waveguide to the fiber.

15

3.2 Erbium-Doped Fiber Amplifier

A method for describing the model of EDFA is similar with that we did for SOA

before. The EDFA can be modeled by a two-level and homogeneously broadened

atomic model [12].[13]. This is true for 1480-nm pump wavelength, where only upper

level 113 / 2 and bottom level 115 / 2 are involved, as shown in Fig. 3.2. For 980-nm

pumps, erbium ions are more accurately described by a three level model [14]-[ 16].

However a two-level model is still a good approximation since the number of atoms

on the pump level 111 / 2 is small due to its short lifetime. We choose the model used

in [17]-[ 19], and start with a set of coupled rate equations to describe the steady state

and transient dynamic of EDFA with random mnplified spontaneous emission CASE)

noise incorporated.

TO =: 10 ms

980 nm 1480 nm 1520 ­1570 om

Figure 3.2: Energy level structure of Erbium ions il1 glass fiber host. EDFA can be

pumped either at 980nl11 or 1480m1l.

The photon power rate equations describing the propagation 111 forward and

backward directions of the signals and ASE noise over the entire wavelength spectrum

is as follows:

16

I dPa (t, z) dPa (t, ::) ( )-;- dt ± d- :::: r, 0",,\ (~)N '2 (t, z) - am' (~)Nj (t,::) PH (t, Z) + R,p (Vk , N'2 (t, ::»

,~ ..... ,

+ F j (t,::)

(3.2.1)

As well as, the evolution of the pump light power through the longitudinal coordinate

z can be described by the pump power propagation equation

(3.2.2)

Here Pk+ (t, z) and Pk - (t, z) are the forward and backward signal or amplified

spontaneous emission noise photon powers at kth wavelength segment, whereas

Pp+ (t, z) and Pp_(t, z) represent the forward and backward propagation of the pump

powers. v.li is group velocity of light in the fiber, and is assumed identical for signal

and pump. ~,. and r p correspond to overlap factors between the pump and signal

modes and the doped fiber core. The absorption (a) and emission (e) cross sections

of the pump (p) and signal (s) are CFp,.,;a.f!' The total population is given by

NT = N) + N'2' where N) and N'2 are the population densities of the ground level

and metastable level respectively. The mean value of the spontaneous emission noise

spontaneous emission noise power is given in term of a Langevin force function

FN (t, z), which will be discussed in detail later in this chapter.

For the sake of simplicity, the optical gam of EDFA is represented by a set of

analytical data, which is curve-fitted by a well-known Levenberg Marquardt method.

17

The analytical gain expression of EDFA can be written in the form of rational function

which depends on the carrier density and the wavelength, is given as follows [7]

ao + a1A+ a 2 /l? + a:)? + .g(A, N) :::: 2 '\ (3.2.3)

1+ b1A+ b2 A +b3A +.........

where each coefficient is a jUllction (?f N,

After testing by trial and etTor procedure, a combination of 20 and 30 coefficients on

the numerator and denominator respectively was chosen with a great balance between

the efficiency and accuracy.

18

\ 1" ,:

020

0.18

0.16

0.14

:[.-- 0.12

~ 0.10'u~ 0,08o~ 0.06.iii0> 0.04

0.02

000

population density (1 023/m3)-'-8.871-'-8.000- -7.000-'-6.765

1.50 152 154

Wavelength (urn)

(a)

1,56 158

0,18

016

0.14

:€ 0.12

C 0.10<l>

'(3:E 008<l>ou 0.06c'(ijOJ 0.04

002

0.00

population density (1 023/m3)-. - 8.871

80007.000

-. - 6.765

1.50 1.52 1.54

Wavelength (urn)

1.56 1.58

(b)

Figure 3.3: Analytical gain spectrum for EDFA a) without curve-fitting b) lvitlz

Level1bel~p' Marquardt curve-fitting.

19

': , : '! : Ik' j-, - .\l1lnll\ LIIl

Originally, the rate equation which governs the population density on the

metastable level is

(3.2.4)

where A is the unifonnly doped fiber core area, and t is the spontaneous emission

lifetime of the metastable level. Further reduction in (3.2.1) and (3.2,2), it gives

aN 2 (z,t) ~ Pk11: [ ] Pplp r ]a =-L.,;-hA CYI',\N:;(Z,t)-a;I,\NI(z,t) --,AlCYl'pN2(z.,t)-aapNj(z.,t)

t k vA: l Vp

N 2 (z,t)

z

(3.2.5)

From (3.2.1), we note that (3.2.5) can be expressed as

dN:;(z,t) =-2: 1 apl:(t,z)

at I: h vI: A dz

app Ct, z)

hVpA dz(3.2.6)

Then, we define the average population density over each subsection as

. 1IIN~(t)=- N,,(t,z)dz which is kept as constant at i-th section and can vary in

- I 0 -

different subsections. I is the length of one subsection.

Finally, (3.2.6) can be rewritten including backward photon powers as follows:

(3.2.7)

where G1:+ i is the forward and backward sectional optical gain for pump and signal

at the corresponding section of the doped fiber, and V is uniformly doped fiber core

volume.

In the EDFA model, there arc no reflectivities at both ends as it uses an optical

fiber as gain medium. (3.2.8) is subjected to boundary conditions for the traveling

20

\ 1 I" : \ 111, lfl\ Lill ',. i II 'II,\TIIL:

signal photon powers, spontaneous emission photon powers, and pump photon power

where k = 1,... ,NI; and j = 1,.... N,

(3.2.8)

The output power of the j th channel from the EDFA can be expressed as

(3.2.9)

3.3 Frequency Chirp Computation

Frequency chirping is an important phenomenon that is known to limit the

performance of lightwave systems. Optical pulses with time-dependent phase shift are

called chirped. In consequence of the frequency chirp imposed on an optical pulse, its

spectrum is considerably broadened. Such spectral broadening affects the pulse shape

at the fiber output because of fiber dispersion and degrades system performance [5].

The optical gain in the active region will change due to the carrier fluctuation

when the signal propagating through the amplifier. In the meanwhile, the material

refractive index change is induced from the gain change. It is normally computed by

the Kramers-Kronig transform as long as the optical gain profile is obtained [21].

(3.3.1)

Performing the Kramers-Kronig transformation to obtain the refractive index change

at each section once the change of gain has been computed. Finally, the phase change

can be computed straightforwardly by adding up each refractive index change of

21

section.

The total phase change is given by:

Consequently, the frequency chirping 4f of the output signal IS

differentiating its phase ¢ with respect to time:

1 !1¢(t) v.t; (1 ~ 21l l~f(t) =----=-- - ~(-t1n )t1z + F (t)

21l!1t 21[ L i A, I 1,;,\ .

(3.3.2)

defined by

(3.3.3)

The output field can be determined for both SOA and EDFA after obtaining the output

power and the output phase change:

E (I) =~P (t)e'\¢'" ,({)+MJ(t))out" 11111. /

3.4 Noise Characteristics

(3.3.4)

The spontaneous elnission noise brings in fluctuations on both of the photon

power and the frequency, known as the intensity noise and the phase noise. In order

to include the intensity and phase noise from spontaneous elnission, the photon power

rate equation (3.1.2) & (3.2.1) and the phase equation (3.3.2) have been transformed

into stochastic equations by adding Fs (t, z) and Fo (t) respectively, which are

random Langevin noise sources. For optical amplifiers, the most important signal

degradation in optical communication system comes from the spontaneous emission

noise.

In many cases of interest. it is sufficient to assume that the events of spontaneous

emission at different times and different locations along the amplifier are statistically

independent, and due to large numbers of photons it is possible to treat the noise in an

22

amplifier using Gaussian statistics. The complex amplitude EN (t, z) for the noise is

written as EN(t,Z.)::::~SN(t,z.)ej¢,V(t) , where SN(t,Z) follows an approximately

Gaussian statistic around its mean value (SN)' while the phase ¢N may have any

value O:s; ¢N < 2Jr with equal probability.

The amplified spontaneous emission (ASE) nOIse IS assumed as a stationary,

uncorrelated zero-mean Gaussian white noise with an autocorrelation function

[22],[23].

(3.4.1 )

A stationary random signal is one whose characteristics do not depend upon the time

origin, which implies that the mean values are independent of time whereas the

autocorrelation function are functions of time difference only.

Since the slowly varying complex field E/d (t, z) = ~P/d (t, z) exp(j</J/d (I» can be

separated into the photon power P and the phase ¢ .

So, the Langevin noise power term in (3.1.2) and (3.2.1) can be expressed as

(3.4.2)

The spontaneous emission contribution to the photon power is generated from a

Gaussian distributed random number generator that satisfies the mean and

autocorrelation:

(SOA)

(EDFA)

23

(3.4.3 )

Likewise, the Langevin noise phase term in (3.3.2) can be expressed as

(3.4.4)

The spontaneous emission contribution to the phase is generated from a Gaussian

distributed random number generator that satisfies the mean and autocorrelation:

(SOA)

(EDFA) (3.4.5)

It can be noted that the autoconelation of both noise sources are photon power

dependent.

24

Chapter 4

Model Implementation

In order to obtain the optical amplifier performance, the set of coupled

differential equations must be solved. Since the optical amplifiers model equations

cannot be solved analytically, a numerical solution must be required. The methods for

solving the SOA and EDFA model are based on the similar manner, except we used

photon power in EDFA model instead of photon number rate used in SOA's. So, both

of photon power and photon number rate are used interchangeably throughout this

thesis. As well as, we only need to input and select a different set of parameters and

constants for corresponding type of amplifiers. Moreover, the models of both SOA

and EDFA we used are adaptable with various bit rates of input signals for

generalization and flexibility when they are assembled in the communication system

platform.

4.1 Steady-state Model

In this section, we use a steady state model to explore the main characteristics of

various types of optical amplifiers. Firstly, in steady state conditions, the time

derivative tenns in all of the coupled differential equations stated in Chapter 3 are set

ato zero ( at = 0), since all parameters are independent with respect to time by now.

We then apply a shooting method to solve the following set of equations for the

carrier densities according to both signal and noise photon rate at each section

25

interfaces. The following canier rate equation of SOA and population density

equation of EDFA should be satisfied:

(4.1.1a)

and

(4.1.1b)

whereas the photon rate equation of SOA can be written as

(4.1.2a)

and the photon power and pump power equations of EDFA can also be written as

(4.1.2c)

In the numerical simulation, the amplifier is split into a number of sections

labeled i= 1 to M. The signal and spontaneous emission noise photon rates are

computed at the section interfaces. It is assumed that the injection current is uniform

in each section and the ith section has a uniform canier density N'. The ASE

spectrum is divided into a number of intervals labeled k = 1 to N ~ with a uniform

frequency V k in the k - th interval. The first step in the algorithm is to initialize the

signal and spontaneous emission photon rates to zero, in order to obtain the initial

carrier density in the first section from (4.1.1). The iteration then begins. Using

Newton's Method section by section can solve the canier density rate equation. With

the known canier density value, the coefficients of the photon rate equation in the

corresponding section can be calculated, as well as the photon rate of its next section

26

I i 11 l', \ lltnll \ I I Ii

can be computed by using the general solution of differential equation.

pt±l = pi (t)G 1 (N I)p± p± p± 2

(4.1.3)

where Gl± is the sectional gain at conesponding section and wavelength segment.

(SOA)

(EDFA)

for pump power (4.1.4)

and the excited ion density dependent population inversion factor 11 \{J is given as

We deal with both forward and backward computation for the forward and backward

photon rate with obeying the boundary conditions at both facet ends. So, we have to

compare those two carrier density values, which are computed from the forward and

backward computation. If they do not agree with each other in a desired tolerance, the

iteration continues with newly initial values every time until the percentage change is

less than the desired tolerance. This process enables convergence toward the correct

value of carrier density for each section, and its algorithm shows stability over a wide

range of operating conditions.

Below shows the block diagram of implementation of both SOA and EDFA steady

state mode l.

27

\' \lIlilfl\ I.lll

4.2 Block Diagram of Steady State nlodel implementation

I Start Simulation ISOA ~ EDFA

J SOAor EDFA I~ I I ~

I . . J' . A d dN I () SmtJa IzatlOn: t stea y state: -- = . etdl

all photon number rate to zero to compute

the initial carrier density N 1, and RR( N ' ),

Initialization: Assume zero input power

P I pN-,+1 0 'th t de.g. I.+ = I.- = WI S ea y pump

All a/at = 0 and set N ~ = NT /2

I

I Begin IterationL..I

Solve the carrier density or population density equations for N i of

each section by I-D root searching method (Newton Method),

and a(Ni), and spontaneous emission rate R,P (vI.' N

1).

Solve the forward and backward traveling wave equations for each

section using general solution of differential equation with the given

boundary conditions.

Compare the two carrier densities values or population densities N 1

Tolerance

satisfied???

28

Use latest calculated

---...---~~ carrier density as the

initial condition, and

iterates again

1 ,:';-, \1\;(111 \ 1)11

4.3 Large Signal Dynamic Model

As optical amplifiers are used to amplify modulated light, it is of interest to

model the large signal dynamic performance of the amplifiers. Dynamic SOA and

EDFA models can be used to predict pattern effects where ampli fied optical bits affect

the following bits, signal distortion due to the amplified spontaneous emission (ASE)

noise and gain saturation, and channel crosstalk that occurs when multiple signals are

amplified in WDM system [2]. Moreover, the system performance of using SOA and

EDFA can be distinguished due to they possess different properties and

characteristics.

The first step in the algorithm is to initialize the carrier densities, signal photon

and spontaneous emission noise rates, and the coefficients of the photon rate equation

using the steady state algorithm described in previous section at the beginning of time

(t = 0). The time iteration now begins. We then start to switch on the time varying

input signal powers and compute the photon rate at the first section with the boundary

conditions. As well as, we use two independent random number generators to generate

both Langevin noise sources in the photon rate equations and phase equations with

Gaussian distribution and the given variances from (3.4.3) and (3.4.5). The

time-dependent photon rate equations can be transformed into a time-stepped solution

in [9], [25] by dividing the device into a number of subsections with the relation

i1: = v,~i1t utilized, as shown in Fig.4.3.1.

(SOA)

(EDFA)

29

\, , 11, 'i ~ .'. i. I 11

(for signal power)

(for pump power)

(4.3.1 )

(4.3.2)

Iz+11 z

Iz

Figure 4.3.1: Schematic view ofa section with nvo input powers at time t and two

output powers at time t+.Llt are updated.

The next step is to solve the carrier density (population density) rate equation by

using Fourth-order Runge Kutta method [26], which is well-known method to solve

ordinary differential equation, is accurate enough with the principle of simplicity and

efficiency. On the other hand, we need to pelfonn Kramers-Kronig transformation to

evaluate the refractive index change in each subsection for computing the phase

change and frequency chirp using the analytical equations (3.3.1)-(3.3.3).

(SOA)

(4.3.3)

where x ck and x¢ in (4.3.1) and (4.3.3) respectively, are independent Gaussian

random variables with zero mean and with variance equal to 1.

If the simulation time limit is reached the algorithm stops. The output signal

powers with intensity noise and the frequency chirping with phase noise in time

domain can be obtained and the performance of the device can be analyzed. After the

noise has been normalized, the noise power spectrum can also be calculated.

30

\1.('-,j;'j j: \1. '. , '11_:

4.4 Block Diagranl of Large signal dynamics model implementation:

Set all solutions from the steady state as its initial conditions (canier

density or population density, photon number rate or photon power),

Calculate the gain and loss coefficients, and spontaneous emission rate.

IBegin time iteration 11""'lll~1-----------------'

~

Switch on time-varying input signal S+ (t) or p, (t) , and computeJ }

S ~+ (t + ~t) or p)+ (t + ~t) with the boundary conditions.

Use two independent RNGs for both Langevin noise

functions for the power and phase with Gaussian

distributions and given variances.

Solve the forward and backward photon rate

equations by time-stepped solution for photon

number rate or photon power S~± (t + ~t) , Pk/± (t + ~t)

Solve the carrier density or population density equations for N i (t + 6t) by

fourth order Runge-Kutta Method. Then, compute the coefficients

Perform Kramers-Kronig (K-K) relations to evaluate

the refractive index change ~ni for each section.

Sum up the refractive index change from all sections

to compute the phase change ~ ¢ and frequency

chirping ~ f using the analytical solution.

31

I II,,';" ,\lll()l1~ I,ll

Time Limit

Output Results &

End Simulation

32

No

',1, ,i IIL",i~ --\111(111\ l III

Chapter 5

Simulation results

The steady state and large signal dynamics simulation results for both

semiconductor optical amplifier (SOA) and erbium-doped fiber amplifier (EDFA) are

shown and analyzed. The noise and cross gain saturation effects during multichannel

signal amplification in optical amplifier will also be examined. Finally, the frequency

spectra of ASE noise are calculated with help of the fast Fourier transform.

5.1 Steady state simulation results

The longitudinal structure of the SOA is sufficiently divided into M:=20

subsections with a uniform carrier density in each subsection, as we found that further

increases in the subsection number gives a little improvelnent in the accuracy.

Whereas the ASE spectrum is divided into N k := 390 intervals with wavelength

interval ~A = 0.30848 nm [7]. Other material and structure parameters for the device

under consideration are listed in Table 5.1.1.

Symbol Parameter Bulk active region MQW active region

L Acti ve region length 400 ~m 1400 ~m

W Active region width 1.5 ~m 1.5 ~lm

d Active region thickness O.l~m 0.06 ~m

r Optical confinement factor 0.4 0.05

33

11 1 Effective refractive index 3.22 3.22

R1,R2 Input & output facet reflectivity 5 x 10-5 5 X 10-5

17m, 17oU/ Input & output coupling loss 0.5012 0.5012

I Bias current 130 rnA 130 rnA

gill Differential gain 4 x 10-20 m:2 2 x 105 m- I

N tr Transparency carrier density 5 x 1023 m-3 5 x 1013 m-3

E Nonlinear gain saturation 3.0 x 10-:23 m3 3.0 x 10-23 m3

coefficient

AI/tlld Linear nonradiative coefficient 1 x 109 s- 1 0.5 X 109 S-I

Bnlll Bimolecular coefficient 6.8 x 10- 16 S-l m3 6.8 x 10- 16 s- l m3

C augAuger coefficient 3.0 x 10-41 S-l m6 3.0 x 10-41 S-l m6

nIpPopulation inversion factor 1.7 2.0

Table 5.1.1 Parameters llsed for the simulations o.f both Bulk and MQW SOAs

As for the structure of EDFA, it is divided into M=lO subsections; the ASE

spectrum is divided into N~ = 400 intervals with wavelength interval ~A= 0.2 nm

[7]. Other pertinent simulation parameters for the EDFA are given in Table 5.1.2.

Symbol Parameter Value

L EDFA length 100 m

['~ Overlap factor (signal or noise) : 0.505

f pOverlap factor (pump) 0.505

A Effecti ve cross-section 3.456 x 10-12 m2

Ap.Pump wavelength 1480 nm

34

'1 i i:.' I" ,\111,)11\ I III

Z 113 /'2- ion lifetime 12 ms

PpPump power (forward) 36mW

NT Total erbium-Ion concentration 9.28 x 1023 m· 3

Table 5.1.2 Parameters used for the simulation ofEDFA

4.2

40

"1_ 3.8

..E'b 3.6

:::.~ 34'(jjcCll 3.2

"'0

(j)3.0'C

ro0

2.8

2.6

2.4

-50 o 50 100 150 200 250 300 350 400

Longitudinal position (pm)

(a)

I-.- MOW SOA I5.18

",- 516

~E'b

~ 5.14"inc(I)"0

(j)"C 512~o

5.10

•••••••••• ••.- ..• •/". --..,• •I \• •/ \• •/ \• •/ \• •/ \• •

/ \• •/ \i \• •

o 100 200 300 400

Longitudinal position (pm)

(b)

Figure 5.1.1 Lonf{itlldinal carrier density profiles in a SOA with an absence of input

signal (0 W). (a) Bulk material (b) MQW material.

35

\k\!:l"1n l 11'\ I'·

140

120

100

~80

2,60Qi

~0

0... 40

20

0

-20

IBulk SOAI

-. - forward propagating ASEl>. u backward propagating ASE

o 100 200 300 400

5

4

o

Longitudinal poSItion (jim)

(a)

IMQW SOAI

-.- forward propagating ASE00.- backward propagating ASE

o 100 200 300

Longitudinal position (jim)

400

(b)

Figure 5.1.2 SOAjorl'i'ard and bacJ...vvard propagating ASE photon powers spatial

distribution with zero input power. (a) Bulk SOA (b) Multi quantum-well SOA.

36

40

c! 3.5

"ENO

20

.~.-.-.~. with input power~ ' ..!' \. -.-10pW

I \/ \. .\

/ .. \•\ •

'".,....' .

....................

-50 o 50 100 150 200 250 300 350 400

Longitudinal position (jim)

(a)

10

8

~..s 6a;5:oCL 4

<0c01

U5 2

o

o 100 200 300

Longitudinal position (jim)

400

(b)

Figure 5.1.3 Bulk SOA (a) carrier density, (b) forward propagating signal photon

power spatial distributions Yt'ith the input signal power is lOp \V (-20 dBm). Signal

wavelength is 1550.12 n11l.

37

\1 \ Ilt( >II" I ;II

520

5.15

5.10

'"~E 5.05NO

.::. 5.00

~.~ 495Q)

"0

Q) 4.90'':

mo 4.85

4.80

with input power---10j.JW

100 150 200 250 300 350 400

Longitudinal position (,urn)

50a4 75 +---r----.---r---.,-.--.-.----.--.--,---r--,r-....--,----.----.-~_,.--,

-50

(a)

2.0

1.5

~g~ 1.0oc..Ctil

~ 0.5

0.0

~.~ fmwa,d propagating signal iI­

I--I

/_/...................

------------------------o 100 200 300

Longitudinal position (,urn)

400

(b)

Figure 5.1.4 MQW SOA (a) carrier density, (b) forward propagating signal photon

power spatial distributions with the input signal power is 10 IlW (-20 dBm). Signal

H'avelength is 1550.12 11111.

38

40

~ 30-incQ)

TI

.~ 25crio

2.0

18

-50 o

with input power-.-1mW

50 100 150 200 250 300 350 400

Longitudinal position (,urn)

(a)

-. - forward propagating signal I

16

14

12

~.s 10

ill~ 80-

ro 6cOJ

i:f.i 4

2

o

o 100 200 300

Longitudinal position (,urn)

400

(b)

Figure 5.1.5 Bulk SOA (a) carrier density, (b) forward propagating signal photon

power spatial distributions with the input signal power is 1l1lW (0 dBl1l). Signal

wavelength is 1550.12 nm.

39

5.5

5.0

",- 4.5

~EN~ 40

~'inc 3.5Q)"0

iii'C 3.0~()

2.5

50 100 150 200 250 300 350 400

Longitudinal position (j.im)

o2.0 --t--,----r-----.-----.-.--..---,--_._--,----r~____.,r_..--.,.__.___,__---r___.---.

-50

(a)

25

-.- forward propagating signal

20

~ 15

-Siii~ 10a.(ticOJ

U5 5

o

.?

-----/•./..--,........-.-.-.-.-o 100 ~o 300

Longitudinal position (j.im)

400

(b)

Figure 5.1.6 MQW SOA (a) carrier density, (b) forward propagating signal photon

power spatial distributions with the input signal power is 1 111 W (0 dBm). Signal

wavelength is 1550.12 /1111.

40

, ; .11

45

40

35

ill~ 30c.~ 25

mn-= 20

$m 15nu::

10

5

bias current-.-130mA

• 150mA~. -200mA

·40 -30 -20 -10 o 10

30

25

10

Input power (dBm)

(a)

-40 -30 -20 -10 o 10

Input power (dBm)

(b)

Figure 5.1.7 SOAfiber-to-fiber gain as afzU1ction of input signal power under (l

bias current of 130 mA. (a) Bulk SOA (b) MQW SOA.

In Fig.S.1.1 to S.1.6, simulations are presented for the SOA under a variety of

operating conditions. Three significant cases are perfoflned to understand the

properties of the amplifier, namely: (a) absence of input signal; b) regime of weak

saturation (P'Il,sig =10 JlW); (c) regime of strong saturation (P'Il.Slg =1 mW). They show

41

the carrier density, ASE and signal photon power spatial distributions in the amplifier

at these three input powers. At zero input powers, the carrier density profile has a

symmetrical spatial distribution with the peak located at the center of device, and it is

determined by the ASE photons that deplete the carriers at the input and output ends

of the active waveguide. At low input power, the peak is tending to shift towards the

input end, due to both signal and ASE photons can influence the carrier profile while

they deplete the carriers increasingly in a way of proceeding to the amplifier end. At

high input power, a strong saturation effect occurs. The carrier density spatial

distribution becomes more asymmetrical, as shown in Fig.5.1.5a and Fig.5.l.6a, with

the peak locating at the input facet. This is caused by the input signal power

dominating over ASE power. Moreover, it can be observed that the Bulk SOA is more

readily saturated than the MQW SOA, so it indicates that the later one has a higher

saturation output power than the former. Fig. 5.1.7 compares the signal gain against

input power at a signal wavelength 1550.12 nm for both bulk and MQW SOA at

I =130 rnA. When the input signal power exceeds a critical leveL the output signal

power becomes saturated and the fiber-to-fiber gain drops rapidly as the input power

further increases.

42

888

-.- EDFA with forward pumping

886

",EN~ 884

~.~ 8.82CD

"'0Co 880~-S0-8.. 878

"'02.~ 876W

.---.-.-.-.- ...........~/ ."'.

• 'I./ \/ .. \/ .. \/ .

. \•

8 74 -+--...,.---,--r-----.----.----r------r--..........-...,.....--....---,..----,

30

2.5

2.0

§' 15.3a>3:

1000...

05

00

o 20 40 60 80

Longitudinal position (m)

(a)

-.- forward ASE propagation.' 4- backward ASE propagation

100

o 20 40 60 80 100

Longitudinal position (m)

(b)

Figure 5.1.8 EDFA (aJ poplIllation density, (b) fonvard and backward propagating

ASE photon power spatial distributions with zero input power.

43

885

E~o 880

~·Ui 875cQ)

"0

25 870.§:::l

g- 865Q.

"0$·0 860xw

855

o 20 40 60 80 100

Longitudinal position (m)

(a)

I -.- forward propagating signal I40

3.5

3.0

~ 2.5

-SUi 2.030Q. 15~cOJ 10

(J5

05

0.0

-0.5o 20 40 60 80 100

Longitudinal position (m)

(b)

Figure 5.1.9 EDFA (a) population density, (b) for..vard propagating signal photon

power spatial distributions with the input signal power is 10 flW (-20 dBm). Signal

wavelength is 1550.12 mn.

44

9

~'iiia5 7-0co:;u 6""50..o0..

~ 5'0xW

with input power-·-trnW

o 20 40 60 80 100

l35

30

25

~.s 20iii$:8.. 15

CiicOJ 10en

5

o

Longitudinal position (m)

(a)

-. - Forward propagating signal power I

o 20 40 60 80

Longitudinal position (m)

100

(b)

Figure 5.1.10 EDFA (a) population density, (b) forward propagating signal photon

power spatial distributions with the input signal pOl""er is 1 11l W (0 dBm). Signal

wavelength is 1550.12 11111.

45

\ Ili, '11'. 1,111

30

25

EO::s 20c'co0)

~ 15

~<u.0 10u::

5

I - -- wi pump power 36mA I.-.--------.~.

\.\

\\

-40 -30 -20 -10 o 10

Input power (dBm)

Figure 5.1.11 EDFA fiber-to-fiber gain versus input signal power under a fonvard

pump power of36 111 W

In Fig.S.1.S to S.1.11, the simulation results for the EDFA are shown as same as

for the SOA in previous section. At zero input power, the population density profile

has just a quite symmetrical spatial distribution due to the model utilizes a forward

pumping scheme. An even symmetrical profile can be surely obtained by using dual

pumping. Besides, the other results of EDFA with non-zero input power are also

similar to that of SOA as well.

As far as this, a broadband SOA and EDFA steady state model and numerical

solution has been described. The characteristics of optical amplifiers are investigated

under a various operating conditions. In addition, steady-state simulations obtained

the device Inaterial parameters used in the dynamic model.

46

: :., iri, ,tI,\: ('onl[1111." 1 II

5.2 Large signal dynamics results:

After having obtained the crucial parameters and results from the steady state

model, we are able to simulate the dynamic model of optical amplifiers. In this section

we consider a simple dynamic model for the optical amplifiers with digitally

modulated inputs. A rectangular-wave input signal at wavelength 1550.12nm IS

adopted for a single channel simulation, to observe the transient characteristics of

optical amplifiers.

10

o

0,0 0.1 0,2

Time (ns)

03 0,4

Figure 5.2.1 FOllr bits NRZ square-wave signal input at 10 Gbitsls with bit pattern

0101. Signal wavelength is 1550.12 11m. On and off states are 10pW and D.l/lW

The effects of amplification by the SOA on an optical signal are shown in Fig.

5.2.2 and 5.2.3. It can be observed that signal distortion due to the gain saturation

occurs in SOAs, although the multi quantum well SOA has less severely saturation

than the bulk SOA. Generally speaking, gain saturation is induced by the reduction of

carrier concentration from the depletion by signal and ASE noise photons. In

mathematical point of view, equation (3.1.6) becomes negative, which ilnplies that the

carrier density is decreasing with respect to time all the way whenever the amplified

signal and amplified spontaneous emission (ASE) term exists. In Fig. 5.2.2a, at the

47

leading edge of each pulse, caniers are beginning to emit photons correlated to input

signal photons, so the population inversion is beginning to be reduced. As such

leading part has already depleted large amount of carriers. the part followed by it

could not acquire the same high gain. Therefore the pulse would be experienced a

likely exponentially decay in bulk SOA and a slowly decay in MQW SOA as shown

in Fig. 5.2.3. To see the signal outputs with ASE noise, there are random fluctuations

on power caused by the ASE noise, which gives rise to further signal impairment. In

cascaded amplifier system, the ASE accumulates over many amplifiers and makes the

system performance severely degraded. In Fig.5.2.9, it can be observed that the

random fluctuation becomes smaller as the input power increases. The reason is that a

large amount of carriers are depleted by the high input power for amplification, it

leaves only small portion of carriers for spontaneous emission. Therefore, in any

situation the amount of ASE noise can be limited to the minilTIUm when the optical

amplifier operates under saturated condition. Thus the effect of ASE is negligible

when the gain is small enough, or when the input powers are sufficiently high as it is

commonly the case in WDM systelTIS [18].

48

12

(a)10

00 01 02

Time (ns)

03 04

12(b)

10

00 01 02

Time (ns)

0.3 04

25(C)

2.4

E 23

"'0:::::..c- 22<~

Q)"0 2 1Q)0::

rn 200

19

1 800 01 02 03 04

Time (ns)

Figure 5.2.2 Dynamics Olltput from Bulk SOA (a) signal without random ASE noise

(b) signal with ral1dom ASE noise (c) dynamics ofcarriers under amplification

according to (b).

49

\1-.'. ,

12 (a)

~ 10

SQj 083;0a.~ 06cOl·iii

"S 04a."S0

02

00

00 01 02 03 04

Time (ns)

14

(b)1.2

~10 r-1s

Cos: 080a.~c 06

J'OJ'Cij

::;Q. 04::;0

0.2

00

00 0.1 02 03 04

Time (ns)

515

(C)510

ENO 505

:::..C'iii 500c(l)"0

Co.;::4.95ro

U

490

48500 01 0.2 03 04

Time (ns)

Figure 5.2.3 Dynamics output/rom MQW SOA (a) signal without random ASE noise

(h) signal with random ASE noise (c) dynamics ofcarriers under ampl~fication

according (0 (h).

50

\1,· 1 1 '11\ ! ! \1 \1, .. '!',II\ .! k'CHk;li ,\: ( ,111'1"'1 ;111:":

12 l (b)10

8NI 6Q.Q)

4OJCell.c 2()

>-() 0cQ):::J

-20-OJ

u:-4

-6

-8I j I , ,

00 0.1 0.2 03 0.4

Time (ns)

Figure 5.2.4 Frequency chirping from Bulk SOA (a) without random phase noise

and (b) with random phase noise.

51

"

(a)

NIS2-Q)

OJc<1l..cu 0 ~-~~

_uu u 1>,ucQ)::::J0-Q) -1

u::

-2

0.0 01 0.2 03 0.4

Time (ns)

Figure 5.2.5 Frequency chirping from MQW SOA (a) without random phase noise

and (b) with random phase noise.

Fig.5.2A and 5.2.5 show the frequency chirp imposed on the output signal pulse

for Bulk SOA and MQW SOA. The chirp will become larger as the input power

increases, while the signal is largely distorted due to gain saturation [27]. Without

considering the phase fluctuation induced by ASE. the output pulse undergoes

positive chirp during the rising edge and negative chirp during the falling edge. Then,

the signals have positive chirping which cause pulse broadening when it is transmitted

52

through the fiber. But when the ASE noise induces the random fluctuation on the

frequency, it is not obviously to see the chirps: we only can distinguish the portion

contaminated with more noise as OFF state, likewise with less noise as ON state. It is

because the phase fluctuation is inversely proportional to the photon power.

There is no doubt that gain saturation would be more severe as the signal power

increasing. In addition, the modulation frequency is another factor to influence the

gain saturation effect. At the signal bit rate 10 Gbs/s, the modulation period is at least

0.1 ns, which is smaller than the carrier lifetime of SOAs [2]. In this case the can"ier

density has not enough time to be fully recovered by the continuous bias current

between signal transitions (in Fig.5.2.2c), so giving rise to pattern effects by gain

saturation. As shown in Fig.S.2.2b, the following pulse has a smaller initial gain than

the previous one. This is in contrast to EDFA, since an erbium ions has a extremely

long lifetime (of the order of illS), so the gain dynamics are a slow process which

prohibit the excited population density keeping pace with changes in the signal as

shown in Fig.5.2.6. Thus there is negligible gain saturation or patten1 effects III

EDFAs for modulation frequency well above the population density response. Most

importantly, this slow response reduces the effects of saturation-induced crosstalk and

intermodulation distortion associated with multichannel signal amplification in

high-speed WDM systems.

Moreover, in Fig. 5.2.8, the eye diagrams of the output after single amplifier are

shown. Though all of the three cases are showing clear open eyes in a single mnplifier

stage, we can still observe that EDFA can provide a better noise performance than

SOAs as its eye is a little bit wider.

53

, ~i 'I' I k ',i~, \111(111\ I IIJ

(a)

o ---

00 01 02

Time (ns)

03 04

(b)

~£Gi:i:0a.((lc:OJ'iii::;a.::;0

0

00 01 02 03 04

Time (ns)

87468000(C)

E

'b87467995

Ciiic::Q)

"0c:: 87467990,2co'3a.0 87467985a.

"02l'13xw 8 7467980

00 01 02 03 04

Time (ns)

Figure 5.2.6 Dynamics outputfrom EDFA (a) signal without random ASE noise (b)

signal with random ASE noise (c) dynamics ofpopulation under amplification

according to (b).

54

\1 . i· \111(\])\ l.lll

2.0 (a)

N 18

E.(!)0> 1.6cco.ct:)

>. 1.4t:)c(!)~

0-(!) 12Li::

1,0

0.800 01 02 03 0.4

Time (ns)

4

(b)3

N 2IS2-(I)

0>Cctl

0.ct:)

>.t:)c -1(!):J0-(!) -2Li::

-3

-4

0,0 01 0,2 0.3 0.4

Time (ns)

Figure 5.2.7 Frequency chirping from EDFA (a) without random phase noise and (b)

with random phase noise.

55

12(a)

10

8

6

4

2

0

0.00 0.02 0.04 0.06 0.08 0.10Time (ns)

1.4 (b)

1.2

1.0

0.8

0.6

0.4

0.2

0.0

0.00 0.02 0.04 0.06 0.08 0.10Time (ns)

6 (c)

5

4

3

2

a

0.00 0.02 0.04 0.06 0.08 0.10Time (ns)

Figure 5.2.8 The one-bit eye diagrams at the output of the single optical amplljier

a) Bulk SOA b) MQW SOA c) EDFA.

56

1.0 Input power-. - 5fJW

ill0.8

10fJWS 0.1mW0Q. 1mW-S 0.6Q.

"S0-0

0.4(1)

.!::::!<tlE

0.20z

0.0

0.0 0.1 0.2Time (ns)

0.3 0.4

Figure 5.2.9 Gain saturation and ASE noise effects depend on various input signal

powers in Bulk SOA . The randomfiuctuation ofamplitude becomes smaller as the

input power increases.

57

5.3 WDM channels dynamics results:

An advantage of optical amplifiers is that they can be used to amplify several

communication channels simultaneously as long as the bandwidth of the multichannel

signal is smaller than the amplifier bandwidth [5]. The bandwidths of both SOAs and

EDFAs are broad enough to be used for multichannel amplification. MUltiple channels

sharing the limited pool of photons for amplification in an optical mnplifier leads to

gain saturation. As the input power increases, the carriers or ions are depleted from

the active region, resulting in a reduction of the gain. Therefore, the actual gain seen

by a particular channel depends on the power level as well as total number of other

coexisting channels at the amplifier. In this section, the cross gain saturation effect

can be studied through the transient power variation results in a case of two-channel

amplification.

In Fig. 5.3.1, one laser, operating continuous wave at '\1= 1555.12 nm, is used as

a surviving channel, and the other laser, emitting at "2= 1550.12 nm, is used as an

added input channel. As can be seen for Bulk and MQW SOAs from Fig. 5.3.2-5.3.3,

the surviving channel experiences an output power excursion once the added channel

is switched on. The gain of the surviving channel decreases with the characteristic

time equal to that of the saturating signal overshoot in the added channel. It is because

the gain of the surviving channel is saturated not only by its power but also by the

total input power from all channels to the amplifier. As well as, the output power of

surviving channel also need some more time to reach back its initial value after the

added channel is switched off. However, the same phenomenon cannot be seen from

the results of EDFA, it is due to its very slow gain response time. The dynamics of

EDFA is generally considered to be slow as a result of the long spontaneous lifetime

of around lOms, which is much longer compared to that of SOA. For transmission of

58

,, I

high-speed data, the gain of EDFA is undisturbed by the signal modulation, and EDFA

does not introduce saturation induced crosstalk among channels in WDM systems.

~ 1.0 (a)E- 0.8

(j) 0.6cc

0.4ttl..c()

'0 0.2Q; 0.0s0

-0.20-

roc -0.4en'w

-0.6"50-

-0.8E

0.0 0.1 0.2 0.3 0.4 0.5Time (ns)

~ 0.10 (b)E-N(j) 0.08ccttl..c() 0.06'0ID~ 0.0400-

Ci3c 0.02OJ'w"5c- 0.00E

0.0 0.1 0.2 0.3 0.4 0.5Time (ns)

Figure 5.3.1 The input signals of two channels a) a constant input pO'tt'er (0. 1mW)

ofchannel 1. b) suddenly switched Oll power ofchannel 2.

Therefore, this property makes EDFAs suitable for WDM lightwave systems [5J. In

contrary, the noise behavior, cross gain modulation and cross gain saturation restrain

the use of SOAs in WDM systems.

59

\1.

~ 7.5 (a)5

7.0Q)c 6.5cca.c0 6.0'0Q5 5.5~0 5.00-

mc 4.5OJ'w:5 4.00-:5 3.50

0.0 0.1 0.2 0.3 0.4 0.5

Time (ns)

~ 8 (b)-S 7N

Q) 6ccca 5.c0

'0 4

JQ5~ 300-

(ij 2cOJ'w:5 00-"':50 -1

0.0 0.1 0.2 0.3 0.4 0.5Time (ns)

2.10 (C)

'" 2.05E

'"'b::::.. 2.00?:-'iiicCD 1.95"'0

(u't::

~ 1.900

1.850.0 0.1 0.2 0.3 0.4 0.5

Time (nsl

Figure 5.3.2 Transient output power variations in a two-channel Bulk SOA

a) & b) output signal powers ofchannel I and 2. c) carrier dynamics changes with

input signals.

60

~5.4

(a)-S 52

ill 5.0cca:l

L 4,8u

'0Q) 4.6~0

4.40-

a:lc

4.2OJ(/)

"S 400-

"S0 38

0.0 0.1 0.2 0.3 04 0.5Time (ns)

~ 6 (b).sC\I

5aJcc(I)

4..cu"0

Q:j 3:;;0Q.

eil 2cOl

'Uj

:5Q.

:5 a0

0.0 0.1 0.2 0.3 0.4 0.5Time (ns)

3.6(C)

E 3.4

"a:::. 3.2.c'Ujc(l) 3.0"0

Q:j'C

~ 2.8u

2.6

0.0 0.1 0.2 0.3 0.4 0.5

Time (ns)

Figure 5.3.3 Transient output power variations in a n'Vo-chawzel MQW SOA

a) & b) output signal powers ofchannell and 2. c) carrier dynamics changes 'rvith

input signals.

61

{ Ij

?28

(a)E-Q)cc

27ttlLU

'0Q)~0Q.

26ttlc01(fj

::;Q.

::;0 25

0.0 0.1 0.2 0.3 0,4 0.5Time (ns)

~ 35 (b)E-N

30Q)cc

25ttlLU

'0 20(jj

I~ 150Q.

qj 10c

l__01'(fj

::; 5.9-::J 00

0.0 0.1 0.2 0.3 0.4 0.5Time (ns)

6.496372 (C)

("'J 6.496370E

6.496368("'J

'b:::::.. 6.496366~ 6.496364.iiicill 6.496362"Dc0 6.496360~ ~~~:J 6.4963580.0 6.4963560...

6.4963540.0 0.1 0.2 0.3 0.4 0.5

Time (ns)

Figure 5.3.4 Transient output power variations in a f1vo-channel EDFA

a) & b) output signal powers ofchannel 1 and 2. c) excited population dynamics

changes with input signals.

62

\1., ,; . ',,, " ! III \1,

5.4 Noise Power Spectrum

The expreSSIon of the slowly varymg output complex field IS

Emil (t) =~ ~'III (t)e Jt1!/J,ml(t). After performing the Fourier transform on the time domain

output signal by using fast Fourier transform (FFT) function, the noise characteristics

in frequency domain can be obtained. The results for both of SOAs and EDFA are

shown below.

o

OJ~ 30

E2U 20Q)0..(j)

.gs 10

.~0..Eeel-0Q)

.~ -10~Eoz

-1 000 -500 0 500 1000Relative frequency deviation (GHz)

Figure 5.4.1: The normalized amplitude spectrum of the ASE noise in Bulk SOA.

en~ 30E2U 20Q)0..(j)

.gs 10

.~0..E 0<U-0Q)

.~ -10~Eoz -20 +---~--""----r----r--,-----'-----.-~---r----'

-1 000 -500 0 500 1000Relative frequency deviation (GHz)

Figure 5.4.2: The normaliz.ed amplitude spectrum of the ASE noise in MQW SOA.

63

200 400 600 800o

10

30

-15 +--..--~---.----.----.-----.-.---,....-...,..---r--,---r---.---..-----.-----.

-800 -600 -400 -200

co2- 25E2 20t5~ 15(JJ

Q)"'0

.~0.. 5E<U 0

"'0

.~ -5~

~ -10oz

Relative frequency deviation (GHz)

Figure 5.4.3: The normalized amplitude spectrum of rhe ASE noise ill EDFA.

64

Chapter 6

Transmission Link Simulations

Our major task is to set up a simulation platform for investigating the

performance of a typical single and multichannel fiber-optic transmission system. As

all of the other individual optical component solvers are connected together, we are

able to demonstrate the performance simulation of the entire fiber-optic transmission

link. By making use of this, we are also able to examine the characteristics of

different applications of optical amplifiers and the ASE noise effects in a cascaded

amplifier system. As a representative simulation model for long-haul transmission

links, we used the flow diagram depicted in Fig. 6.1 to illustrate the system simulation

scheme. The system configuration can be adjusted freely as desired for flexibility.

The ReG was modeled as M independent signal generators that were

multiplexed before launching into the link. We adopted a 32 pseudorandom bit

sequence modulation format to limit the simulation time and memory requirements.

An external or internal modulation scheme can be chosen to use at the transmitter.

For external modulation, the continuous lightwave with constant intensity from a laser

is modulated by an Electroabsorption (EA) or Mach-Zehnder (MZ) modulator. After

that we can select from which configuration composing of fiber, EDFA, or SOA, in

order to exmnine the performance of different system schemes. After the lightwave

signal is amplified by a power booster to boost the transmitted optical power, the

optical pulses are transmitted through standard single mode fiber. The attenuation of

65

'",'\'11, I :Ii "1,,'1"11'-':

optical signal level due to the fiber loss could be restored by a number of in-line

amplifiers. At the receiver, a preamplifier amplifies the received optical signal and a

pin photodiode is used for optical signal detection and convert the signal back to an

electrical pulse. The electrical signal resulting from the photodetector is amplified,

and then sampled and compared with a threshold using a decision circuit to recover

the transmitted digital signaL Finally, an eye-diagram can be used to evaluate the

performance of the communication channel.

User Interface

System parameter initialization

Internal Modulation External Modulation

Figure 6.1 Flow diagram of the system simulation scheme

66

\k\Ll r,.· :

6.1 Single-channel system simulation

In this section. all types of the previous mentioned amplifier applications were

discussed based on single channel transmission systems.

6.1.1 Case 1: Power Boost amplifier

Laser

NRZ, Pseudo ~Random BitGenerator

~ 6

-S.8 5<Il

"-0

~ 4

Qi;t::<Il

(ij;-::ol:l.. 2rocOJiii 1~

~o 0'----------' \

-05 00 05 10 1 5

Time (ns)

20 25 30 35

Figure 6.1.1 Input signal power of the power booster from modulat01:

A power boost amplifier is used to launch high power signals, to extend the

transmission distance, or to increase the link power budget. Because there is little or

no loss between the transmitter and the power amplifier, the amplifier usually operates

in deep saturation as shown in Fig. 6.l.2a and 6.1.3a. As can be seen from Fig.

6.l.2a, it is important to note that the signal transmitted after the bulk SOA is severely

distorted and it even misread the original bit "0" as bit "1". Therefore in our case.

the bulk SOA is not suitable to be used as power booster in our transmission system.

Typical gain compression for power amplifiers is between 20 and 40dB [29]. At these

levels of saturation, the ASE noise output is reduced and the optical SNR at the output

67

of the amplifier is extremely high. Thus, the noise figure is not an important design

parameter for power amplifiers. On the other hand, the most important parameter for

power amplifiers is maximum saturated output power. If this is high enough, the

pattern effects due to gain saturation can be reduced. Fig.6.1.3 and 6.1.5 show the

vertical closure of the eye is mainly due to the signal distortion by gain saturation

when using SOA. In contrast to the case of using SOA, the eye pattenl for using

EDFA in Fig. 6.1.7 shows a clear open eye, as the gain does not respond to the signal

modulation in EDFA due to its slow gain response time.

353025201.5

Time (ns)

100500

(a)

4

6

2+--r----r----.----,---,.----,-...--'r--r--,--.-----,----r---,----,,...----,

-05

10 15 20 25 30 35

Time (ns)

154780 (b)

154775

E 154770

.s

..c154765g,

QlQ.i

154760>C<l~

154755

154750

154745

-05 00 05

Figure 6.1.2 Output results after the Bulk SOA poyver booster a) output signal

power, b) dynamic wavelength changes due to chirp.

68

\ 1 "-," . " IIIL:

12 (a)

11

10

9

8

7

6

5

0.00 0,05 0.10 0.15 0.20Time (ns)

0.028 (b)0.026

0.024

0.022

0.020

0.018

0.016

0.014

0.012

0.010

0,008

0.006

0.004

0,002 -+--..,---....--,..--~-r---.------,r--------r---r-----,

0.00 0.05 0.10Time (ns)

0,15 0.20

Figure 6.1.3 Eye diagrams a/the output aJ right after the Bulk SOA power

booster amplifier, bJat the receiver after low pass filter.

69

~ 20 (a)S

* 18

i\ I00.D 16m~

14 1\00-

m12 ; I;t::

rnf IQ)

~ 10

~00-

~OJiii:50-:50

-05 00 05 10 15 20 25 30 35

Time (ns)

154780 (b)

154775

f 1547 70

..c1547650,

~~rc:~<lJ

Qi154760>

n:ls:154755

154750

154745

-05 00 05 10 1 5

Time (ns)

20 25 30 35

Figure 6.1.4 Output results after the MQW SOA power booster aJ output signal

power, b) dynamic wavelength changes due to chirp.

(a) 0.045 (b)18

0.040

16 0.035

0.03014

0025

120020

10 0015

00108

00056

000 005 010 0.15 0.20 0.00 0.05 010 0.15 020Time (ns) Time (ns)

Figure 6_1.5 Eye diagrams of the output aJ right qfier the MQW SOA power

booster ampl(jiel; bJ at the receiver after la-w passfiltel:

70

, I: 'i' !:tI I I ! 1~:

~ 30(a)

*--I

0250

.Da;~

200a.a;.t=

15<Il

a;:s:0 10a."iiic:Ol

\jiii 05

'5a.'5 000

-05 00 05 1 0 1 5 20 25 30 35

Time (ns)

1547.80 (b)

154775

E 154770

.sJ::

154765~~~0,

c:Q)

Q)154760>

<IlS

154755

154750

154745

-05 00 05 10 15

Time (ns)

20 2.5 3.0 35

Figure 6.1.6 Output results after the EDFA power booster a) output signal pm,ver,

b) dynamic wavelength changes due to chirp.

3500 (a) 8 (b)

73000

62500

5

20004

1500 3

1000 2

500

00

0,00 005 010 015 020 000 005 010 015 020Time (ns) Time (ns)

Figure 6.1.7 E.ve diagrams of the output a) right after the EDFA power booster

amplijict; b) at the receiver after low pass filtet:

71

6.1.2 Case 2: In-line Anlplifiers

Photodetecloc I

Optical FiberOptical FiberOptical Fiber

f-----------"'~~-'--"-~I ~{>-: (J'-----~~--' SOAI

EDFA

Laser

NRZ, PseudoRandom BitGenerator

0018

~ 0016

1~-s ,. ,---.~

0014

CD 0012..0:;:;:

q;0010::

<1l

CD 0008~0a. 0006

~a> 0004(i)

S 0002a.S

"'"'"~

0 0000

-0002-05 00 05 10 15 20 25 30 35

Time (ns)

Figure 6.1.8 Input signal power oj the inline ampl(fierjronz the first optical fiber.

Secondly, we consider two cascaded in-line amplifiers used as repeaters to boost

the signal power. Because in-line amplifiers are used to extend the transmission

distance, high output power is required. However, the signals entering in-line

amplifiers are weak, so that noise added by each in-line amplifier is important. Fig.

6.1.9, 6.1.11 and 6.1.13 show clearly that the transmitted signal is contaminated by

the accumulated ASE noise in a cascaded in-line amplifiers system for both SOAs and

EDFAs. Therefore, a low noise figure and high gain both are also required. At this

time, the degraded eye diagrams in Fig. 6.1.10, 6.1.12 and 6.1.14 show that the partial

closing of eye is caused by both of the accumulated ASE noise and gain saturation

effect. However, the EDFA not only have a higher gain and is iITImUne to gain

saturation, but also it does give a better noise performance compared to the SOA.

Since in-line amplifiers must be designed with high gain, high output power, and a

low noise figure, all realized for a wide dynamic range of input signals. However, it is

72

difficult to optimize all these three parameters simultaneously. For example, high gain

is reached by using a long device length. In contrast, the best noise figure is obtained

by maintaining a high inversion at the input and is usually achieved with short device

length [29]. One of the solutions is to use multistage designs in which the first stage is

designed to function as an efficient preamplifier and the succeeding stages as a power

booster.

~ 10(a)-S

Qi~

Q. 8E<U(l,)

,!:~ 6

enQi~ 4

Qi:;:00- 2rocOl

'00

"S 0B-:.10

-05 00 05 10 15 20 25 30 35

Time (ns)

~ 12S (b)~Ci 10E<U(\)

oS 8:£'0c::N

Qi 6

~Qi~00-

roc::Ol

'u)

"S0-'S 00

-05 00 05 10 15 20 25 30 35

Time (ns)

73

1547.80 (C)1547.75

E 1547.70

S.J::.

1547.65OJcQ)

Qi 1547.60>~

~1547.55

1547.50

1547.45

-05 00 0.5 1.0 1.5

Time (ns)

20 2.5 30 35

Figure 6.1.9 Output results for the in-line Bulk SOAs a) output signal power after

the r t in-line, b) output signal power after the 2nd in-line, c) dynamic wavelength

changes due to chirp.

9 (a)0.020

8 0.018

0.0167

0.014

6 0.012

5 0.010

0.008

40.006

3 0.004

0.0022

0.00 0.05 0.10 0.15 0.20 0.00 0.05 0.10 0.15 0.20Time (ns) Time (ns)

Figure 6.1.10 Eye diagrams of the output a) right after the Bulk SOA 2/1d in-line

amplifier, b) at the receiver after low pass filter.

74

~ (a)s I 6

~ 140-Ero I 2

S~ 1 0

(j)

~08

~ro 06~;;

0400-

ro02c

OJen::J 00.9-0 -02

-05 00 05 10 15 20 25

Time (ns)

30 35

~.s (b)Qj 06

:-E0..E 05(1J

<I!

~.~ 04"0c

N

a; 03~(1J

Qj 02;;00..

m 01cOl'Vi"5 000.."50

-05 00 05 10 1 5

Time (ns)

20 25 30 35

1547 80 (C)

'54775

I 154770

r.'54765e;,

c:OJ

~ 154760ellS

154755

'547 50

'54745

-05 00 05 1 0 1 5

Time (ns)

2 11 25 30 35

Figure 6.1.11 Output results for the ill-line MQW SOAs a) output signal pmver

after the t l in-line, b) output signal power ({fter the 2/1d in-line, c) dynamic

'vvavelength changes due to chirp.

75

.: r" I' ,II :"111-'('1'11 l:.:

(a) 00012 (b)0.5

0.0010

0.4

0.C008

030,CXXJ6

020.0004

0'1oCXXl2

0.00000.0

i I0.00 0.05 0.10 0.15 0.20 0.00 0.05 010 015 0.20

Tirre (ns) Tirre (ns)

Figure 6.1.12 Eye diagrams of the output a) right after the MQW SOA 2nd ill-line

amplifier, b) at the receiver after low pass filter.

(a)

§'s~o0-

rocOJ'iii

-S0--So

-05 00 05 10 1 5

Time (ns)

20 25 30 35

12 (b)10

Qj:=o0-

rocOJ'iii

-S0--So

-05 00 05 1 0 1 5

Time (ns)

20 25 30 35

76

154780 (C)

154775

E 1547.70S..c

154765OJcQ.l

Qi154760>

ctl?;

154755

154750

154745

-05 00 05 10 15

Time (ns)

20 25 30 35

Figure 6.1.13 Output results for the ill-line EDFAs a) output signal pOHier after

the t l in-line, b) output signal power after the 2nd in-line, c) dynamic wavelength

changes due to chirp.

12 (a) 0.025 (b)

100.020

80.015

6

00104

0.0052

0 0.000

000 0.05 010 0.15 0.20 000 0.05 010 0.15 0.20Time (ns) Time (ns)

Figure 6.1.14 Eye diagrams ofthe output a) right after the EDFA 2/1d in-line

amplifier, b) at the receiver after low pass filter.

77

, I; I," i'.. \ 111011 \ I .111 ~ \1 \, i ~ l ~ 1\.' r l nI \ l ~ r~"" i I \ ~. [ It.' I. t I . l.

6.1.3 Case 3) Preamplifier

1

- NN~~;~ PseudoRandom BitGenerator

Laser Optical Fiber

0,018

~0016

.s- 0014 II(v

~ 0012I

~(v

0010

I'l:'ell

(v 0008:;:,8.

0006

~01 0,004'iii:J

0002S-O 0,000

-0002

-05 00 05 1 0 15 20 25 30 35

Time (ns)

Figure 6.1.15 Input signal pOH'er of the preamplifier from the fibn:

10 (a)

-05 00 05 1 0 1 5 20 2 5 30 3 5

Time (ns)

1547 80 (b)

1547 75

I '547 70

L: '547 65Cas'~ 1547 60

~1547 55

1547 50

1547 45

,05 o 0 05 1 0 1 5

Time (ns)

20 25 30 35

Figure 6.1.16 Output results after the Bulk SOA preamplifier a) output signal

power. b) dynamic wavelength changes due to chirp.

78

\ 'i· ,It, [ .111 \L \1 'lfl.

(a) 8 (b)8

7

76

65

54

43

3 2

2

a0.00 005 0.10 0.15 020 000 0.05 0.10 015 020

Time (ns) Time (ns)

Figure 6.1.17

preamplifier,

Eye diagrams of the output a) right after the Bulk SOA

b) at the receiver after low pass jiltel:

3' 1 6 (a).s~

14

0- 1 2E""III 1 0a.:v:l= 0.8

""Qj063

00-

~04

'iii 02~

f}-0.0

8-02

-05 00 05 1 0 1 5 20 25 30

Time (ns)

35

1547 80(b)

1547 75

f 1547 70

t 1547 65

,r- L~

ill 1547 60>

~1547.55

1547 50

1547 45

-05 00 05 1 0 1 5

Time (ns)

20 25 3 0 3 5

Figure 6.1.18 Output results after the MQW SOA preamplifier a) output signal

power , b) d.vna11lic wavelength changes due to chirp.

79

\L \),

1.6 (b)14

1.412

1.210

1.0

080.8

0.6 06

0.4 04

0.2 02

0.0 00

0.00 005 0.10 0.15 0.20 000 0.05 0.10 015 020Tirre (ns) Tirre (ns)

Figure 6.1.19

preamplifier,

Eye diagrams of the output 0) right after the MQW SOA

b) at the receiver after low pass filteJ:

~ (a)E.~QEro

~2(ij

Q;~0a.

~0>Uj

:>.9-d

·0.5 0.0 05 1 0 1 5

Time (ns)

2 a 2 5 3 0 35

1547.80(b)

1547 75

I 1547 70

J:: 1547.65g,(l)

~ 1547 60ell

3:1547 55

1547 50

1547 45

-0 5 a a 05 1 0 1 5

Time (ns)

2 a 2 5 3 0 35

Figure 6.1.20 Output results after the EDFA preamplifier a) output signal power,

b) dynamic wavelength changes due to chirp.

80

9 (a)8

7

6

5

4

3

2

0

0.00 005 010Time (ns)

0.15 0.20

8 (b)

7

6

5

4

3

2

o

000 005 0.10 015Time (ns)

020

Figure 6.1.21 Eye diagrams of the output aJ right qfrer the EDFA preamplifier,

b) at the receiver after low pass filte r.

81

6.1.4 Case 4) Combination of Power Booster, In-line amplifier and Preamplifier:

NRZ, PseudoRandom Bit

, Generator

Laser Optical Fiber

-------->-n-"---1[8SOAIEDFA

Finally, we consider the case of the combination of power booster, in-line

amplifier, and preamplifier, which is used to improve the system performance in

long-haul transmission links. An optical preamplifier is used at the end of a

transmission link, just before the photodetecting receiver. The sensitivity of a direct

detection receiver can be improved significantly by using low noise figure (3- to 5~

dB) optical preamplifiers [29]. Fig. 6.1.22 and 6.1.24 give us the output results of

both MQW SOA and EDFA. As usual. the input signal power level of the preamplifier

is extremely low because the signal has lost power in the transmission link. Hence, the

output power of the preamplifier needs to be sufficiently high so that at the

photodetector the noise is dominated not by its receiver noise but by the signal to

spontaneous beat noise of the optical preamplifier [31]. In Fig. 6.1.23a shows us a

completely close eye and indicates that the signal transmitted through the cascaded

'MQW SOAs is severely impaired by the largely accumulated ASE noise in successive

amplifiers. Thus we can conclude that ASE is trivial and does not constitute a serious

problem in a single amplifier stage, but with many stages of amplification ASE can

makes system degradation even worse.

Moreover, we can observe a widely open eye from Fig. 6.1.25 and conclude that

EDFAs are capable of providing high signal gain, high saturation output power and

low noise over a broad optical bandwidth. These nearly ideal characteristics of EDFAs

enable them to be widely used in presently optical transmission system, though

commercial considerations like costs and compactness of these devices can change

the balance in favor of the SOAs.

82

~ 20 (a)E-

*1B

00.c 16W3=

1400-

W12;l::

C<l

W10:;;

00-

~0)

iii:;s-o

-05 00 05

~ (b)~ 4 0

9?

i 35

~ 30

~

2 25'@

Qji: 20~

~1 5OJ

(ji

::>0-

j 00

-0 5 00 05

, 0

, 0

1 5

Tim e (ns)

1 5

Time (ns)

20

20

2.5

2 5

30

30

3 5

3 5

~ 1 2 (C)E-w~ 1 0CiEC<l<l>0- o 8

W;l::C<l

o 6Wi:0c.

~o 4

0)

iii::> o 2S-O

o 0

-0 5 00 o 5 1 0 1 5 20 2 5

Time (ns)

3 0 3 5

Figure 6.1.22 Output resultsjor the combination of MQW SOAs aJ output signal

after the booster, b) output signal (dier the in-line, c) output signal after the

preamp.

83

1,1 (a) 09 (b)1,0 08

0,9 07

08 06

0.7 05

0604

0.503

0.402

0,301

0,20.00 005 010 0.15 0.20 000 0.05 010 015 020

Time (ns) Time (ns)

Figure 6.1.23 Eye diagrams of the output a) right after the MQW SOA

preamplifier of the combination, b) at the receiver after low pass filtel:

~ 3 a (a)

~r--- r

0 250D

GJ~ 200Cl..

Qj;to 1 5<1l

Qj~0 10Cl..

rocOJ 05'w:::J

'--Cl..'5 000

-0 5 00 05 '0 , 5 20 25 30 35

Time (ns)

~ 40 (b)~ 35i5..E

30<1l

~2,5

SGJ 20~

<1l

Qj , 5~0

~Q. , 0

~ 05Ui:::J

E- 00

0-05

-05 00 05 10 1 5 20 25 30 35

Time (ns)

84

III \L' :

~(C)

'"~

I(<0 4il'0-

\1''" 3~

~ I I0 2

\J

0-

<U§,ViJ0-

8 0

-05 00 05 1 0 1 5 20 25 30 35

Time Ins)

154780 (d)

1547 75

I 154770

.c1547 65

~'"g? 154760

~154755

154750

1547 45

-05 00 05 1 0 1 5

Time (ns)

20 25 30 35

Figure 6.1.24 Output results for the combination of EDFAs a) output signal after

the booster, b) output signal after the in-line, c) output signal after the preamp,

d) dynamic wavelength changes due to chirp.

(b)5000

4000

40003000

3000

2000

2000

10001000

0 0

0.00 0.05 0.10 0.15 020 000 005 0.10 015 020Time (ns) Time (ns)

Figure 6.1.25 Eye diagrams of the output a) right after the EDFA preamplifier of

the combination, b) at the receiver after 10HI pass filter.

85

6.2 WDM systenl simulations

WDM transmission can be used to greatly enhance the capacity of optical fiber.

In this section, we focus on WDM in transmission systems that contain all of the

optical amplifiers mentioned before. To determine the influence of ASE noise on

WDM system behaviour, we performed on 4 xl OCbit I s transmission systems

employing different amplifier types [33], [34].

6.2.1 Case 1: DWDM 4 channels with MQW SOAs in the 1550nm window

System Parameters for both case 1 and 2:

System description:

Number of channel:

Bit-rate:

Bit per frame:

Number of frame:

Total fiber length:

Optical bandwidth:

Type of signal:

Channel wavelengths:

External modulation

(With power booster, inline amplifier, and preamplifier)

4

10 Gbls

16

2

2 x 60 km

C-band (l530nm-1563nm)

Gaussian pulse

1550.12, 1549.32, 1548.52, 1551.72 (nm)

Fig. 6.2.2-6.2.8 show the output signal powers and wavelengths of four channels

after modulator, power booster, inline amplifier, and preamplifier. It can be clearly

observed that more noises are accumulated through the cascaded amplifiers. After

passing through the photodetecting receiver, four electrical signals could be recovered

as shown in Fig. 6.2.11. Obviously, there is intersymbol interference effect between

86

the channels caused by the signal dispersion in the transmission system. Moreover,

Fig. 6.2.9 shows all the output eye diagrams after the preamplifier, these severely

degraded eye diagrams are mainly caused by the largely accumulated ASE noise

along the transmission line. Although most of the high frequency noises would be

filtered out by low pass fi Iter at the receiver, there is still a considerable amount of

noise accompanying with the information signal so as to degrade the system

performance. The results for EDFA are shown as same manner as in SOA. The widely

open eyes in Fig. 6.2.20 show us that EDFA not only can be immune to cross-gain

saturation effect in WDM systems, but also it does give a lTIuch better noise

performance compared to SOA in any cases.

1551

1550

1549

Es~ 1548c(l)

"iii>~ 1547

1546

--0-- channel 1---A-- channel 2---0-- channel 3---0-- channel 4

500 1000 1500 2000 2500 3000 3500

Time (ps)

154 5 +-----r-~-..__--r----.--__,-..---_,__--r-___,r__....---__r_---...-,.__.......-___,

-500

Figure 6.2.1: Four different wavelength channels generated/rom the Laser diode.

87

[-~--ChanneI14 0

3 5

3 0

2 5

2 0

15

1 0

a 5

~ 500 500 1000 15 a 0

Tim e Ips)

2 a 0 0 ;:- 5 f) 0 3000 3500

:::>Q.

'5a

3 5

3 0

2 5

2 a

15

1 0

o 5

1--channeI2

~ 500 500 10 a 0 '500

T,me(ps)

2000 ~ 5 0 0 3000 3500

4 a

3 5

3 0

25

2 0

1 5

1 0

o 5

1--channeI3

·500 500 1000 1500

Tlme(ps)

2000 2500 3000 3500

4 0

3 5

3 0

2 5

2 0

, 5

1 0

o 5

I --channel 4

~ 500 500 1000 ,500

Tlme(ps)

2000 2500 3000 3500

Figure 6.2.2 Output signal by external modulation/or 4 different channels.

88

154770

154 I' 68

\ 5 ~ 7 66

1547 6 ~

1 5 ~ 7 62

1 547 6 a

1547 58

1 5 ~ 7 56

I---channell

500 500 1000 150 a

Tim e (ps)

;:000 2500 3000 3500

1548 50

1548 4 B

1548 46

15.4 8 44

1 548 .4 2

154 B 40

1 548 3 B

1548 36

1--channeI2

-500 500 1000 '500

Tim e (p s)

2000 2500 3000 3500

154 e 1 0

1546 08

1546 06

I 546 04

, S 46 02

15.4 6 00

1 545 98

1545 96

1--ChanneI3

-500 500 1000 1500

Tlme(ps)

2000 2500 3000 3500

1 549 3 D

1549 26

1 5.4 9 .2.4

1549 ,2 0

, 549 , 8

15.4 9

1--ChanneI4

500 500 1000

Tlme(pS}

2500

Figure 6.2.3 Output wavelength after the modulator/or 4 different channels.

89

II;

[~-channeI1

500 500 1000 1 500

T,melpsl

?O!JO 2500 3000 3500

I ~-channel 2

-500 500 1000 1500

Tlme(ps)

\

2000 2500 3000 3500

I ~-channeI3

-500 500 '000 , 500

Tim e (ps)

2000 2500 3000 3500

1--channeI4

500 500 1000 15 a 0

Tlme(ps)

2000 2500 3000 3500

Figure 6.2.4.­

channels.

Output signal after the MQW SOA power booster for 4 different

90

---- c han n e 1 1 I

1S476B

154766

1 547 is 2

15.4 7 60

1547 58

'54756

1000 1 5 a aTlme(ps)

~ 500 3 a 0 0 3500

1 5 <18 50

500

Tlme(ps)

1---chan n eI2

1---channeI3

154610

1 546 a B

1546 06

1546 04

154602:

1545 98

1 545 96

5 a a 150 aT,m e (ps)

2000 25 Q 0 3500

1 549 .3 0

1'549 26

1549 2: 2

154920

[--channeI4

500

Tim e (p s)

200 0 2' 500

Figure 6.2.5:

channels.

Output wavelength after the MQW SOA power booster for 4 different

91

.... j" , '" 111 lj I' I III I ' ' " ~'j • '- ' I \

I--Channell I

~.sa;~ 1 2

is.

~coOJ"-

o 0 6

o 4

35uu30002500200010(' n500o 2 +-~-r-~---.--~--r--~---'--'---.-~-r-~---.--~---,

-500

Tlme(ps)

I--channel 2 J, 8

, 6

1 2

1 0

o 8

-500 1 500 2000 3000 3500

Tlme(ps)

I--channel 3 ]

12

'"~is.

~;j) 0 S

OJ"-

oo 4

·s 00 500 1000 1500 2000 2500 3000 3500

Tlme(ps)

1--ChanneI4

o 2 +-~-,---~-....,..-~-.,---~---.-~--,.--~-r-~-.....-~--,10 1)('1 2000 2500 3000 3500

Tlme(ps)

Fig II re 6. 2. 6

channels.

Output signal q{ter the MQW SOA illlille amplifier for 4 dUferent

92

\L \1.1' '_'

!--channeI1

500

Tim e Ips I

2500 3000 3500

1--channeI2

1--channeI3

I1548 46

1546 44

t 1548 42~~

1548 38

1546 36

1:'48 3 ,

1546 12

1546 08

I 1546 06

~ , 5 d 6 02~~ 1546 00

1545 98

1545 96

-500

5 a 0

100 Q

Tim e (p s)

2' 0 a 0

Tim e Ips)

2500

250 a

3000

:3 Q Q 0 3500

J--channeI4

Tim e (~l S I

Figure 6.2.7: Output wavelength after the MQW SOA inline amplifier for 4

different channels.

93

\llli.\li\ Litl,[,.

o 6I--channell I

o 5

o 4

o 3

o 2

o 1

30002S0020001500

Tom e (ps)

1000500

o 0 +-~---,.---~--.--~-----,.---~-.--~-----,.---~--r--~-.---~----,

-500

I-- c han n e 1-2

o 5

o 3

o 2

o I

250020001500

Tlme(ps)

1000500

o 0 -t--~-.,-~-,--.,.'--.,-~-.,--~-.,-~-.---~---,,--~--.-500

I -- Chan n e I_:Uo 5

o 4

o 3

o 2

35003000250020001500

Tim e (ps)

1000500

o 0 +-~---,---,~-,--~-.,-~-.--~-,-~-,--~-----,,--~--,

-500

1--channeI4o 6

o 5

o 4

o 3

o 2

o I

3500JOOO250020001500

Tim e (ps)

1000500

o 0 +-~-----,---,~-.--~---,-~-,--~---,-~-.--~-,--~--,

-500

Figure 6.2.8:

channels.

Output signal after the MQW SOA preamplifier for 4 different

94

o 55

o 50

o 45

o 40

o 35

o 30

o 25

o 20

o 15

o 10

o 05o 00 o 05 o 10 o 15 o 20

Time (ns)

o 55

o 50

o 45

o 40

0.35

0.30

o 25

o 20

o 15

o 10

o 05

o 00 o 05 o 10 o 15 o 20Time (ns)

o 55

o 50

o 45

o 40

o 35

o 30

o 25

o 20

o 15

o 10

o 05

o 00 o 05 0.10 o 15 0.20TIme (ns)

o 60

o 55

o 50

o 45

o 40

o 35

o 30

o 25

o 20

o 1 5

o 10

o 05o 00 o 05 o 10

Tim e (n s)o 1 5 o 20

Figure 6.2.9: Eye diagram output just after the MQW SOA preamplifier for 4

different channels.

95

t iti

1'547 70

\L\1:J

I--channell

:11 , .:

154765

154755

Tlme(ps)

:2 SOD 3000

'54845

1548 40

154835

1--channeI2

-5 a a 500 1000 1 500

Tim e (p s)

2000 250 a 3000 3500

1546 10

1546 08

1546 06

1546 04

1546 02

1546 00

1545 98

1545 96

I --channel 3

-500 500 , a a 0 1500

Tim e (p s)

2000 2500 3000 3500

15.9 3 a

1549 25

1549 2 a

1549 15

1--channeI4

500 500 1000 1500

T,me(ps)

2000 2500 3000 3500

Figure 6.2.10:

channels.

Output wavelength ({fter the transmission link for 4 different

96

'I 11','-1, \ 11::'1)', I !'

o 16C -cha,:;-i1illJ

« o , 2

~.5

i o , 0

c: o 08

'"::J

o 06U

o 04

o 02

-500 500 , 000 '500 2000 250 0 3000 350 0

Tlme(ps)

I channel2o '6

o '4

~« o 12

.5

i o 10

c: o 0 B

'"::JU o 06

o 04

o 02

-500 500 1000 1500 2000 2500 3000 3500

Tlme(ps)

1-- channel 3

«.5 o 10

I o 0 B

cOJ

::J o 0 BU

500 1000 1500

Tim e (ps)

2000 2500 3500

« 0 '2.s"- 0 , 0

::J0

'"0 oB

::J0

I ---- c han n e I 4 I

2000 ;2 SOD

Time (ps)

Figure 6.2.11:

channels.

Output signal after the photo-detector at the end for 4 dUferent

97

0 16

0 14

12

§ o 10

~ o 08.e«

o 06

o 04

o 02

o 00 o 05 o 10

Time (ns)

o 15 o 20

0 16

0 1 4

0 12

g a 10

~ a 08Ei.:.:

a 06

o 04

o 02

o 00 a 05 a 10Tim e (ns)

o 1 5 o 20

0 1 4

0 1 2

g 0 10

~

i a 08

«a 06

0 04

a 02

o 00

0 1 6

0 1 4

0 1 2

§

f0 1 0

.0 0 08~

0 06

0 04

0 02,

0 00

o 05

,o 05

o 10Time (ns)

I

o 10

Tim e (n s)

o 1 5

,o 1 5

a 20

,o 20

Figure 6. 2.12: Eye diagram output af the end of the SOA-based transmission link

for 4 d(fferent channels.

98

·1: .\\,.\1:, .

6.2.2 Case 2: DWDM 4 channels with EDFAs in the 1550nm window

20

I--chan n all

~OJ

& 12 I~

\Jin

"-

"0

5 00 lS0:J 2500 3000 3500

Tim e {p 'I

1--channeI2

2 0

~<lJ

8-~;;;

~ o a

<3

o 2

500 t Q 0 0 :2 Q 0 0 2500 3000 3500

Tim e (p s)

I --channel 3

1 a

~<lJ

8- 1 2

~ 1 0<;;

~

<3 o 6

o 4

02

1000 :2 0 0 0 2500 3000 3500

Tim e (p s)

1---channeI4

~ 1 6

<lJ

8- , 2

t;;;

~(5

Time {ps)

Figure 6.2.13: Output signal after the EDFA power booster for 4 different channels.

99

\ I,'

154766

1547 6:2

1547 60

1547 58

1547 56

,1'1

I

l1--ChanneIIJ

II- ,:1111:":

-500

1548 50

, 500

Tim e Ips)

2000 2500

[--channel:!

154844

154 B 42

-500

154608

1546 06

154602

154598

1545

- 500

500

500

T,me(ps)

1500

TIm e (ps)

2500

2500

1--channeI4

154928

500 1000

Tim e (p s I

Figure 6.2.14:

channels.

Output wavelength q(ter the EDFA power booster for 4 different

100

c==:.:=:i~~

2 0

~

[

~§,iii

1 0

~<5

OS

o 0- SO a 1500 3 sao

Tim e (p s)

2 51---channeI2 I

2 0

~

~8-

~iii:>£l.0

o 5

o 0- 5 a a 1500 2000 2500 3000 3500

Tim e (p s )

2 5

2 0

~Q)

~ 1 5

tiii:::lQ.

:>0

1--- channel3

-500 500 1 000 1500 2000 2500 3500

T,me(ps)

2 5

2 a

~Q)

3:1 58-

~iii

1 0

9-<5

a 5

1--channeI4

500 1000 1500

T,me(ps)

2000 2500 3500

Figure 6.2.15:

clzmlnels.

Output signal ({fter the EDFA illlille amplifier for 4 different

101

'I i" ,,, - \lll('!I\ [ III ,',',,!,,'" [-

1547 70L:O___ ._S:hanneI1

t 547 6 a

~ r

l1547 66

It 547 64.r;

t 'I~

1547 6:2

~ 1547 60

i I , I ~

500 1000 1 500 2000 250 0 3500

Tim e (p s)

t 548 SOI---,:hann~

15 -4 8 .4 6

f1f 1548 .4 4.c

~a;

~ 1548 40

15.4 6 3..4500 1 500 2 Q 00

Tlme(ps)

1--channeI31

I 1546 015

'"c"~ 1546 02

~

-500 500 2000 2500 3500

Tim e (p s I

I--channel.

15.4 9 26

'""~~ 15' 9 20

- 500 1000

Tlme(ps)

2000 3000

Figure 6.2.16:

channels.

Output wavelength after the EDFA inline amplifier for 4 different

102

I --channell

: .;::,

15

, 0

o 5

500 500 1000 1500

Time (psi

2000 2500 3000 3500

1--channeI23 0

25

2 0

15

, 0

o 5 ~\·5 a 0 500 1000 '500

Tlme(ps)

2000 25 a 0 3000 3500

!--channeI3

25

2 a

, 5

1 a

a 5

350030002500200 015001000500a 0 +-..-----,r---....--.--..----,.----.---y--~-~--.--_.__--.--r_---.-_,

- 5 a a

Tlme(ps)

1--channeI43 a

2 5

2 a

15

a 5

500 500 1000 1500 2000 2500 3000 3500

Figure 6.2.17: Output signal after the EDFA preamplifier for 4 d{jferent channels.

103

I I!, Ie- nn \1l1\l1l\ LI Ii

3000

2500

2000

1500

1000

500

o 00 o 05 o 1 0Tlme(ns)

o 1 5 o 20

3000

2500

2000

1 500

1 0 a 0

500

o a a o as 0.1 0 0.15 o 20Tim e (ns)

3000

2500

2000

1500

1000

500

o 00 o 05 o 10 0.15 o 20T,me(ns)

3000

2500

2000

1 500

1000

500

o 00 o 05 o 10Tlme(ns)

o 15 o 20

Figure 6.2.21:

channels.

Eye diagram output after the EDFA preamplifier for 4 different

104

'iI, !II \1

[--channeI1 I

1--channel:I]

1547 70

1547 6 e

1547 66

I , 547 64.r::

~ 1547 62~~

'547 60

1547 5 e

1 547 56

- 5 0 0

'548 50

1548 4 B

'548 46

I 1548 44.r::

~ 154 e 42

~

~ '548 40

154 e 3 e

1 54 B 36

1548 34-500

500

500

1000

1000

, 500

'500

Tlme(ps)

2000

2000

2500

2500

3000

3000

3500

3500

1--channeI3 I

1--channeI4

'546 10

'546 08

I 154606

.r::1546 04

~~ 1546 02

~, 546 00

1545 9 B

'545 96

-500

1549 30

, 549 28

1549 26

I , 549 24.r::

~ 1549 22"iii

~ 1549 20

'549 18

1549 16

'549 14

-5 a 0

500

500

1000

1000

'500

Tim e (ps)

1500

T,me(ps)

2000

2000

2500

2500

3000

3000

3500

3500

Figure 6. 2.19:

channels.

Output wavelength ({fter the EDFA preamplifier for 4 different

105

Ii

800 I--channell

'00

I~~~\~s 50['1

~3

! 3011

U =0 0

500 100 a 2000 2500 3000 3500

Time IPs)

8001--channeI2

700

600

500

400

300

200

100

500 500 1000 1 500

Tim e (P s)

2CJOO 2500 3000 3500

7001--channeI3

600

;;z 50 0

S~ 400

~~ 300

:0U 200

100

·500 500 1000 1500

TlmelPS)

2000 2500 3000 3500

1--channeI4800

700

600

500

10e

500 100('1 20 () 0 2500 3000 3500

T,me(p5)

Figure 6. 2. 20.­

channels.

Output signal after the photo-detector at the end for 4 different

106

<,1

800

700

600

~500

>400

'"D

~ 300

200

100

o 00 o 05 o 10

Tim e {ns)

o 1 5 o 20

BOO

700

600

§ 500

~ 400

D~ 300

200

1 00

o 00 o 05 o 10Tim e (n s )

o 1 5 o 20

700

600

500§> 400'IS

D 300~

200

100

o 00 o 05 o 10 o 15 o 20

Tim e (ns)

800

700

600

§ 500C~ 400is<- 300

200

1 0 a

o 0 a o 05 o 1 0 C 1 5 o 20TIm e t n 5 I

Fig II re 6. 2. 21 : Eye diagram output at the end of the EDFA-based transmission

link for 4 different channels.

107

Chapter 7

Conclusion

The amplified spontaneous emission (ASE) noise constitutes a serious factor in

optical system performance, and thus it plays an important role in designing

fiber-optic transmission links employing optical amplifiers. In this work, a time

domain model including the ASE nOIse effect for both semiconductor optical

amplifier (SOA) and erbium-doped fiber amplifier (EDFA) has been successfully

developed within a reasonable computational complexity. It shows accurate results for

both single channel and WDM transmission. Moreover, this newly optical amplifier

simulator has been integrated with the existing time-domain simulation platform that

has many other optical components assembled, in order to obtain a more realistic

picture to examine the system performance of various transmission links. The system

platform is capable of dealing with point-to-point multichannel optical transmission

links with arbitrary configurations, transmission formats and device parameters. Thus,

we can further study the ASE noise effect during single and multichannel

amplification in different applications through the system simulation. Making use of

this system platform, fiber-optic transmission systems with suitable limitations can be

designed based on the power budget including various sources of power penalties.

108

\1\1< 111 \ I : \l

Appendix

Supplementary device parameters used in the system simulations:

- ReG Parameters

------RCG-pattem-length-

32

__ n __ RCG-power/amplitude-unit-mW1mv­I.

------RCG-bitshape- {rectangle,gpulse,triangle,rcosine}­

gpulse

-u---RCG-variance-unit-(%)-

2.

------RCG-duty-cycle-unit-(%)­

100.

-Laser Parameters

------CHOICE--l >intemal-or--2>external-modulation-

2

------Bias-current-unit-(A)­

0.060

------Modulation-current-uni t-(A)­

0.015

------LD-CHOICE--1>Bulk--2>QW-­

1

------LD-length-unit-(~m)-

300

___ n_LD-width-uni t-(jJm)-

2

109

\!. '

------LD-depth-unit-(~m)-

0.2

------group- index­

3.9

___u_ K-Petermann-factor-

------Population-inversion-factor­

2

------Cavi ty-loss-uni t-(cm-I )­

20

------Li ne wi dth-enhancement-factor-

3

---u-Canier-l ifetime-unit-( le-9s)­

1.0

------Photon-lifetime-unit-(1e- 12s)­

3.0

------Confinement-factor-

0.3

------Gain-coefficient-bulk-unit-( 1e- 16cm2)­

3.0

------Gain-coefficient-QW-unit-(cm-1)­

1000

G . . f . 1 -17)------ am-saturatlon- ·actor-umt-( e -

2

C . d . . (1 18 -3)------ anler- enstty-at-transparency-umt- e m -

1.0

------Gain-width-unit-(nm)­

49.2

------Noise-switch-(1="On", O="OFF")

o

-Modulator Parameters

------CHOICE--l >EA --2>MZ (one-arm)--3>MZ (two-ann)-

1

---u-EA-Modulator-length-unit-(~m)-

195.

110

, < I,

------EA-Modulator-waveguide-confinement-factor­

0.2

------EA-Modulator-modal-refracti ve-i ndex­

3.2

------EA-Modulator-bias-vol tage-uni t-(V)-

O.

------EA-Modulator-modulation-voltage-unit-(V)­

1.5

------MZ-Modul ator-arm-length-unit-(~m)-

620.

------MZ-Modulator-length-difference-between-two-arms-unit-(~m)-

O.

----nMZ-Modulator-input-Y-branch-power-splitting-ratio­

1.4

------MZ-Modul ator-output-Y-branch-power-splitting-ratio­

1.4

------MZ-Modulator-modal-refractive-index-

3.2

------MZ-Modulator (one-arm)-bias-voltage-unit-(V)­

3.

------MZ-Modulator (one-ann)-modulation-voltage-unit-(V)­

2.

--n--MZ-Modulator (two-arm)-bias-voltage-unit-(V)­

3.0

-n-nMZ-Modulator (two-arm)-modulation-voltage-unit-(V)­

1.6

--n--Low Pass Filter -EA-Modulator-rising-time-unit-(ps)­

50.

------Low Pass Filter-MZ-Modulator-rising-time-unit-(ps)­

35.

-Optical Fiber Parameters

----nFiber-length-uni t-(km)-

60.

------Fiber-attenuation-uni t-

0.1

111

____n Fi ber-second-order-dispersion­

o.n-n-Fi ber-th ird-order-dispersion­

-1.117

--nnFiber-nonlinear-gamma-dispersion-

o.n--nFi ber-nuIll ber-of-steps­

20

-Photodetector Parameters

n--nFIB-response time unit-(ps)­

200.

---n-FIB-gain-unit-

1.

nnnFIB-responsivity-unit-(A/W)­

0.8

112

\ L \1;; -:.'1 :

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