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 :
Bibliography
[1] S. Shimada, H. Ishio, ed., Optical Ampl{fiers and their Application. John Wiley &
Sons, 1994. ISBN 0-471-94005-4.
[2] MJ. Connelly, Semiconductor Optical Ampl~fiers. Kluwer Academic Publishers,
2002. ISBN 0-7923-7657-9.
[3] J.G.L.Jennen, Noise and Saturation effects in High-speed Transmission Systems
with Semiconductor Optical Amplifiers. Technische Universiteit Eindhoven, 2000.
ISBN 90-386-1760-7.
[4] G. Keiser, Optical Fiber Communications (3 rd Edition). McGraw-Hill International
Ed., 2000.
[5] G.P. Agrawal, Fiber-Optical Communication Systems (2 nd Edition). John Wiley &
Sons, 1997. ISBN 0-471-17540-4.
[6] Jongwoon Park, Xun Li, Wei-Ping Huang, "Performance simulation and design
optimization of gain-clamped semiconductor optical amplifiers based on distributed
bragg reflectors", IEEE Journal of Quantum Electronics, vol. 39, pp. 1415-1423,
November 2003.
[7] C.Y. To, Xun Li, Time-Domain Simulation of Optical Amplifiers in Wavelength
Division Multiplexed (WDM) Photonics Systems and Networks. Master thesis,
McMaster University, Canada, November 2003.
[8] Xun Li, Wei-Ping Huang, "Simulation of DFB semiconductor lasers incorporating
thermal effects", IEEE Journal of Quantlll71 Electronics, vol. 31, pp. 1848-1855,
October 1995.
[9] W. Li, W.P. Huang, X. Li, J. Hong, "Multiwavelength gain-coupled DFB Laser
Cascade: Design modeling and simulation", IEEE Journal of Quantum Electronics,
113
• I j '(I \1.- .; r 1,'.·!I:t.,: x (1::1'.'.1':'
vol. 36, pp. 1110-1116, October 2000.
[10J M.J. Connelly, "Wideband semiconductor optical amplifier steady-state
numerical model", IEEE Journal of QuantulIl Electronics, vol. 37, pp. 439-447,
March 2001.
[11] M.J. Connelly, "Wideband dynamic numerical model of a tapered buried stripe
semiconductor optical amplifier gate", lEE Proc.-Circuits Devices Syst., vol. 149, pp.
173-178, June 2002.
[12] A.A.M. Saleh et aI., "Modeling of gain in erbium-doped fiber amplifiers", IEEE
Photonics Technolog',' Letters, vol. 2, pp. 714-717, October 1990.
[13] Y. Sun et al.. "Model for gain dynamics in erbium-doped fibre amplifiers",
Electronics Lettr!rs, vol. 32, pp. 1490-1491, August 1996.
[14] C.R. Giles, E. Desurvire, J.R. Simpson, "Transient gain and crosstalk in
erbium-doped fiber amplifiers", Optics Letter, vol. 14, pp. 880-882, August 1989.
[15] E. Desurvire, Erbium Doped Fiber Amp/~fiers: Design and System Applications.
Artech House, Boston, 1993.
[16] E. Desurvire, "Analysis of transient gain saturation and recovery in
erbium-doped fiber amplifiers", IEEE Photonics Technology Letters, vol. 1, pp.
196-199, August 1989.
[17] K.Y. Ko et aI., "Transient analysis of erbium-doped fiber mnplifiers", IEEE
Photonics Technology Letters, vol. 6, pp. 1436-1438, December 1994.
[18] Y. Sun et aL "Average inversion level, modeling, and physics of erbium-doped
fiber amplifiers", IEEE Journal of Selected Topics in Quantum Electronics, vol. 3, pp.
991-1007, August 1997.
[19] S.R. Chinn, "Simplified modeling of transients in gain-clamped erbium-doped
fiber amplifiers", IEEE Journal ofLightH'ave Technology, vol. 16, pp. 1095-1100,
June 1998.
[20] E. Desurvire et aI., "Gain saturation effects in high-speed, multichannel
114
erbium-doped fiber amplifiers at A= 1.53 !Jm", IEEE Journal (~r Lightwave Technology,
vol. 7, pp. 2095-2104, December 1989.
121] C.H. Henry et aI., "Spectral dependence of the change in refractive index due to
canier injection in GaAs lasers", Journal ofApplied Physics, vol. 52, pp. 4457-4461,
July 1981.
[22] N. Schunk, K. Petermann, "Noise analysis of injection-locked semiconductor
injection lasers", IEEE Journal of Quantum Electronics, vol. QE-22, pp. 642-650,
May 1986.
[23] K. Petermann, Laser Diode Modulation And Noise. Kluwer Academic Publishers,
1991.
[24] M. Shtaif, G. Eisenstein, "Noise characteristics of nonlinear semiconductor
optical amplifiers in the Gaussian limit", IEEE Journal of Quantum Electronics, vol.
32, pp. 1801-1809, October 1996.
[25] B.S. Kim, Y. Chung, lS. Lee, "An efficient split-step time-domain dynamic
modeling of DFBIDBR laser diodes", IEEE Journal of Quantum Electronics, vol. 36,
pp. 787-794, July 2000.
[261 W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in
C - The Art ofScientzjic Computing (2/ld Edition). Cambridge University Press, 1992.
ISBN 0-521-43108-5.
[27J T. Watanabe et aI., "Transmission performance of chirp-controlled signal by
using semiconductor optical mnplifier", IEEE Journal ofLightwave Technology, vol.
18, pp. 1069-1077, August 2000.
[28] A. Bononi, L.A. Rusch, "Doped-fiber amplifier dynamics: A system perspective",
IEEE Journal o.f Lightwave Technology, vol. 16, pp. 945-956, May 1998.
[29) I.P. Kaminow, T.L. Koch, ed., Optical Fiber Telecommunications fllB. Academic
Press, 1997. ISBN 0-12-395171-2.
[30J Y. Yamamoto, K. Inoue, "Noise in amplifiers", IEEE Journal of Lighl1vavc
115
\ I i1 "11:- rill i J l i \ ( • r...., I j', ,[ - f l.' t...' t l : I ,i' l~.... I •
Technology, vol. 21, pp. 2895-2915, November 2003.
[311 N.A. Olsson, "Lightwave systems with optical amplifiers", IEEE Journal of
LightH'([ve Technology, vol. 7, pp. 1071-1082. July 1989.
[32] G.. Giuliani, D. D' Alessandro. "Noise analysis of conventional and gain-clamped
semiconductor optical amplifiers", IEEE Journal ofLightwave Technology. vol. 18,
pp. 1256-1263. September 2000.
[331 J. Jennen, H. de Waardt. G. Acket, "Modeling and performance analysis ofWDM
transmission links employing semiconductor optical amplifiers", IEEE Journal of
Lightwave Technology, vol. 19, pp. 1116-1124. August 2001.
[34] E. Tangdiongga et aI., "Performance analysis of linear optical amplifiers in
dynamic WDM systems", IEEE Photonics Technology Letters, vol. 14, pp. 1196-1198,
August 2002.
[35] D. Marcuse, "Computer model of an injection laser amplifiers", IEEE Journal of
Quantum Electronics, vol. QE-19, pp. 63-73, January 1983.
[36] D. Marcuse, "Computer simulation of laser photon fluctuations: Theory of
single-cavity laser", IEEE Journal of Quantum Electronics, vol. QE-20, pp.
1139-1148, October 1984.
[37] C. Y. Jin et aI., "Photon iterative numerical technique for steady-state simulation
of gain-clamped semiconductor optical amplifiers", lEE Proc. -Optoelectronics, vol.
150, pp. 503-507, Decemeber 2003.
[38] C.Y. Jin et aL, "Detailed model and investigation of gain saturation and carrier
spatial hole burning for a semiconductor optical amplifier with gain clamping by a
vertical laser field", IEEE Journal of Quantum Electronics, vol. 40, pp. 513-518, May
2004.
[39] T. Yamatoya, F. Koyama, "Optical preamplifier using optical modulation of
amplified spontaneous emission in saturated semiconductor optical amplifier", IEEE
Journal ofLightwave Technology, vol. 22, pp. 1290-1295, May 2004.
[40] M. Settembre et aI., "Cascaded optical communication systems with in-line
116
\1, \I.:'i.': '
semiconductor optical amplifiers", IEEE Journal (d'Lighnvave Technology, vol. 15,
pp. 962-967, June 1997.
[41] L.B. Spiekman, "8 x 10Gb/s DWDM transmission over 240 km of standard fiber
using cascade of semiconductor optical amplifiers", IEEE Photonics Technology
Letters, vol. 12, pp. 1082-1084, August 2000.
[42] L.M. Zhang, J .E. Carroll, "Semiconductor 1.55 ~m laser source with
gigabit/second integrated electroabsorptive modulator", IEEE Journal of Quantum
Electronics, vol. 30, pp. 2573-2577, November 1994.
[43] G.P Agrawal, N.A Olsson, "Self-phase modulation and spectral broadening of
optical pulses in semiconductor laser amplifiers", IEEE Journal ofQuantum
Electronics, vol. 25, pp. 2297-2306, November 1989.
[44] M. Shtaif, B. Tromborg, G. Eisenstein, "Noise spectra of semiconductor optical
amplifiers: Relation between semiclassical and quantum descriptions", IEEE Journal
ofQuantum Electronics, vol. 34, pp. 869-878, May 1998.
[45] S. Donati, G. Giuliani, "Noise in an optical mnplifier: Formulation of a new
semiclassical model", IEEE Journal ofQuantum Electronics, vol. 33, pp. 1481-1488,
September 1997.
[46] J. Wang, K. Petermann, "Noise analysis of semiconductor lasers within the
coherence collapse regime", IEEE Journal ofQuantum Electronics, vol. 27, pp. 3-9,
January 1991.
[47] M. Ahmed, M. Yamada, M. Saito, "Numerical modeling of intensity and phase
noise in semiconductor lasers", IEEE Journal ofQuantum Electronics, vol. 37, pp.
1600-1610, December 2001.
[48JL.M. Zhang et a!', "Dynamic analysis of radiation and side-mode suppression in
a second-order DFB laser using time-domain large-signal traveling wave model",
IEEE Journal c<lQuantuf1l Electronics, vol. 30, pp. 1389-1395, June 1994.
[49] L.M Zhang et a!., "Large-signal dynamic model of the DFB laser", IEEE Journal
of Quantum Electronics, vol. 28, pp. 604-611, March 1992.
117
[50] A. Mecozzi, J. Mork, "Saturation effects in nondegenerate four-wave mixing
between short optical pulses in semiconductor laser amplifiers", IEEE Journal of
Selected Topics in Quantum Electronics, vol. 3, pp. 1190-1205, October 1997.
(51] B. Thedrez, C.H. Lee, "A reassessment of standard rate equations for low facet
reflectivity semiconductor lasers using traveling wave rate equations", IEEE Journal
of Quantum ElectrO/lies, vol. 28, pp. 2706-2713, December 1992.
[52] P. Vankwikelberge et aI., "CLADISS - A longitudinal multimode model for the
analysis of the static, dynamic, and stochastic behavior of diode lasers with distributed
feedback", IEEE Journal of Quantum Electronics, vol. 26, pp. 1728-1741, October
1990.
[53] D. Cassioli et al., "A time-domain computer simulator of the nonlinear response
of semiconductor optical amplifiers", IEEE Journal of Quantum Electronics, vol. 36,
pp. 1072-1080, September 2000.
[54] A.K. Srivastava et aI., "EDFA transient response to channel loss in WDM
transmission system", IEEE Journal ofQuantum Electronics, vol. 9, pp. 386-388,
March 1997.
[55] Y. Sun et aI., "Fast power transients in WDM optical networks with cascaded
EDFAs", Electronics Letters, vol. 33, pp. 313-314, February 1997.
[56] S. Reichel, R. Zengerle, "Effects of nonlinear dispersion in EDFA's on optical
communiation systems", IEEE Journal ofLightvvave Technology, vol. 17, pp.
1152-1157, July 1999.
[57] M. Janos, S.C. Guy, "Signal-induced refractive index changes in erbium-doped
fiber amplifiers", IEEE Journal ofLightwave Technology, vol. 16, pp. 542-548, April
1998.
[58] S. Reichel et aL "Simulation of phase modulation in EDFA's using an extended
model", IEEE Photonics Technology Letters, vol. 10, pp. 1724-1726, December 1998.
[59] A.W.T. Wu, A.J. Lowery, "Efficient multiwavelength dynamic model for
erbium-doped fiber amplifier", IEEE Journal of Quantum Electronics, vol. 34, pp.
1325-133 L August 1998.
118
160J C.R. Giles, E. Desurvire, "Modeling erbium-doped fiber amplifiers". IEEE
Journal ofLighnvave Technology, vol. 9. pp. 271-283, February 1991.
[61] C.R. Giles, E. Desurvire, "Propagation of signal and noise concatenated
erbium-doped fiber optical amplifiers". IEEE Journal ofLughtwave Technology, vol.
9, pp. 147-154, February 1991.
[62] Z. Zhang, Xun Li, Simulation (~rErbium-DopedFiber Ampl(fier Based 011 a
Nm'e! Dynamic Model. Master thesis. McMaster University, Canada. 2002.
[63 J Y. Kim et aI., "Analysis of frequency chirping and extinction ratio of optical
phase conjugate signals by four-wave mixing in SOA's", IEEE Journal ofSelected
Topics ill Quantum Electronics, vol. 5, pp. 873-879, May/June 1999.
[64] T. Watanabe et al., "Chirp control of an optical signal using phase modulation in
a semiconductor optical amplifier". IEEE Photonics Technology Letters. vol. 10, pp.
1027-1029, July 1998.
[65] M. Potenza, "Optical fiber amplifiers for telecommunication systems", IEEE
Communications Magazine, pp. 96-102, August 1996.
[66] A. Papoulis, S.U. Pillai, Probabilty, Random Variables and Stoc!zastics Processes
(4 th Edition). McGraw-Hill International Ed., 2002. ISBN 0-07-112256-7.
[671 GP. Agrawal, N.K. Dutta. Semiconductor Lasers (2/ld Edition). Van Nostrand
Reinhold, New York, 1993. ISBN 0-442-01102-4.
[68] Y. Sun et aI., "Error-free transmission of 32 x 2.5Gbit/s DWDM channels over
125km using cascaded in-line semiconductor optical amplifiers", Electronics Letters,
vol. 35, pp. 1863-1865, October 1999.
[69] S. Reichel et aI., "Simulation and experiment verification of a 10-Gb/s NRZ field
trial at 1.3IJm using semiconductor optical amplifiers", IEEE Photonics Technology
Letters, vol. 10, pp. 1498-1500, October 1998.
[70] J. Sun, G. Morthier, R. Baets, "Numerical and theoretical study of the crosstalk in
gain-clamped semiconductor optical amplifiers", IEEE Journal ofSelected Topics in
119
Quantum Electronics, vol. 3, pp. 1162-1167, October 1997.
[71] J. Sun, "Theoretical study on cross-gain modulation wavelength conversion with
converted signal fedback", lEE Proc.-Optoelectrollics, vol. 150, pp. 497-502,
December 2003.
[72] L. Schares et aI., "Phase dynamics of semiconductor optical amplifiers at 10-40
GHz", IEEE Journal of Quantum Electronics, vol. 39, pp. 1394-1408, November
2003.
[73] D.R. Zimmerman, L.H. Spiekman, "Amplifiers for the masses: EDFA, EDWA,
and SOA amplets for metro and access applications", IEEE Journal ofLighnvave
Technology, vol. 22, pp. 63-70, January 2004.
[74] H. Ono, M. Shimizu, "Analysis of gain dynamics of erbium-doped fiber
amplifiers for wavelength-division-multiplexing networks", IEEE Journal of
Quantum Electronics, vol. 39, pp. 541-547, April 2003.
[75] 1. Nusinsky, A.A. Hardy, "Multichannel amplification in strongly pumped
EDFAs", IEEE Journal a/Lightwave Technology, vol. 22, pp. 1946-1952, August
2004.
120
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