Transcript chapter 05 -- Optical Amplifiers

Chapter 5: Optical Amplifiers
5.1 Basic Concepts
5.1.1. Introduction
5.1.2. Gain Spectrum and Bandwidth
5.1.3. Gain Saturation
5.1.4. Amplifier Noise
5.1.5. Amplifier Applications
5.2 Semiconductor Optical Amplifiers
5.2.1. Amplifier Design
5.2.2. Amplifiers Characteristics
5.2.3. Pulse Amplification
5.2.4. System Application
5.3 Raman Amplifier
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5.3.1. Introduction
5.3.2. Raman Gain and Bandwidth
5.3.3. Amplifier Characteristics
5.3.4. Raman Amplifier Performance
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Chapter 5: Optical Amplifiers
5.4 Erbium-Doped Fiber Amplifiers
5.4.1. Introduction
5.4.2. Pumping Requirement
5.4.3. Gain Spectrum
5.4.4. Simple Theory of EDFAs
5.4.5. Amplifier Noise
5.4.6. Multi-channel Amplification
5.4.7. Distributed-Gain Amplifiers
5.5 System Applications
5.5.1. Optical Pre-amplification
5.5.2. Noise Accumulation in Long-Haul System
5.5.3. ASE-Induced Timing Jitter
5.5.4. Accumulated Dispersive and Nonlinear Effects
5.5.5. WDM-Related Impairments
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5.1: Basic Concepts
5.1.1. Introduction
 Electric regenerators become quite complex and
expensive for WDM lightwave systems.
 A homogeneously broadening two-level system with
gain coefficient
g(w) = go/[1+(w-wo)2T22 + P/Ps]
where go is the peak value of the gain
w is the optical frequency
wo is the atomic transition frequency
P is the signal power
T2 is the dipole relaxation time < 1ps
Ps is the saturation power dependent on
T1 and cross section
T1 is the population relaxation time:
100ps ~ 1ms.
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5.1: Basic Concepts
5.1.2. Gain Spectrum and Bandwidth
 The unsaturated region, P/Ps << 1, the gain spectrum
g(w) and the gain bandwidth Dng (FWHM) are
g(w) = go/[1+(w-wo)2T22]
Dng = Dwg/2p = 1/(pT2) ~ 5 THz for SOA.
 The amplifier bandwidth at FWHM of G(w,z)
DnA = Dng.[ln2/ln(Go/2)]1/2 < Dng
where
G(w,z) = Pout/Pin = exp[g(w)z]
Go = exp(goL)
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5.1: Basic Concepts
5.1.3. Gain Saturation
 For large signal,
dP(z)/dz = goP/(1+P/Ps)
with b.c. P(0) = Pin,
P(L) = Pout = GPin
 The large-signal amplifier gain
G = P/Pin= Goexp[-(G-1)Pout/GPs]
 The output saturation power:
the output power for which G = Go/2
Psout = PsGoln2/(Go-2) ~ 0.69Ps for Go > 20dB
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5.1: Basic Concepts
5.1.4. Amplifier Noise
 Resulted from the beating of spontaneous emission
with the signal.
 Amplifier noise figure
Fn = (SNR)in/(SNR)out
 The SNR of the input signal
(SNR)in = <I>2/ss2
= (RPin)2/2q(RPin)Df
= Pin/2hnDf
where <I> is the average photocurrent
ss2 is the shot noise by setting the dark current zero,
and Df is the detector bandwidth.
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5.1.4. Amplifier Noise
 The spectral density of spontaneous-emission-induced
noise Ssp(n) = (G-1)nsphn is nearly constant
 The spontaneous-emission factor (the population inversion
factor) nsp= N2/(N2-N1), N1, N2 being populations for the
ground and the excited states.
 The mixed photocurrent
I = R |√G Ein + Esp|2
 The beat noise current and its variance
DI = 2R(GPin)1/2|Esp|2 ,
s2 ~ 4(RGPin)(RSsp)Df
 The SNR of the amplified signal
(SNR)out = <I>2/s2 ~ GPin/4SspDf
 Noise figure : Fn=2nsp(G-1)/G ~ 2nsp ~ 5.8 dB
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5.1.5. Amplifier Applications
 Power amplifier/booster to boost the power
transmitted
 In-line amplifiers to replace electronic
regenerator,
but limited by the cumulative effects of fiber
dispersion, fiber nonlinearity and amplifier noise.
 Optical preamplifier to improve the receiver
sensitivity
 Distribution amplifier to compensate distribution
loss in LAN
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5.1: Basic Concepts
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5.2 Semiconductor Optical Amplifiers
5.2.1. Amplifier Design
 Fabry-Perot amplifier: gain spectrum and its
amplifier bandwidth
 The condition of TW-type SOA
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5.2 Semiconductor Optical Amplifiers
5.2.2. Amplifiers Characteristics
 Peak gain increases linearly with the carrier
population N:
g(N) = (Gsg/V)(N-No)
where, G: the confinement factor,
sg: the differential gain
V: the active volume,
No: the value of N required at
transparency
 Carrier population/photon number
dN/dt = I/q – N/tc – Psg(N-No)/smhn
= 0 for steady state
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5.2.2. Amplifiers Characteristics
 The saturated gain
g = go/(1 + P/Ps)
where, small signal gain go = (Gsg/V)(Itc/q - No)
saturation power Ps = hnsm/(sgtc)
 Noise figure including internal losses (absorption
& scattering)
Fn = 2[N/(N-No)][g/(g-aint)] ~ 5-7dB
 The polarization sensitivity from the different
gain between TE and TM modes. (Dg ~ 5-8dB)
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5.2 Semiconductor Optical Amplifiers
5.2.3. Pulse Amplification
 The amplification factor is shape dependent,
implying distortion
 Saturation-induced SPM and the associated
frequency chirp
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5.2.3. Pulse Amplification
 The frequency chirp is opposite compared with that
imposed by directly modulated semiconductor lasers.
 The amplified pulse would pass through an initial
compression stage when it propagates in the
anomalous-dispersion region of optical fiber
 The compression mechanism can be used to design
fiber-optic communication systems in which in-line
SOAs are used to compensate simultaneously for
both fiber loss and dispersion by operating SOAs in
the saturation region
 The gain of each bit in an SOA depends on the bit
pattern. This phenomenon be quite problematic for
WDM systems in which several pulse trains pass
through the amplifier simultaneously.
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5.2 Semiconductor Optical Amplifiers
5.2.4. System Application
 Preamplifier-- degrading the SNR through
spontaneous-emission noise. Fn = 5-7 dB
 Power amplifier-- too low saturation power ~ 5mW
 In-line amplifier-- polarization sensitive, interchannel crosstalk, large coupling losses
 Possible applications
(1) wavelength conversion
(2) fast switch for wavelength routing in WDM
networking
(3) low-cost fiber amplifier for metropolitan-area
network
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5.3 Raman Amplifier
5.3.1. Introduction
 Stimulated Raman scattering(SRS)
 The incident pump photon gives up its energy to create
another photon of reduced energy at a lower frequency
(inelastic scattering); the remaining energy is absorbed
by the medium in the form of molecular vibration
(optical phonons)
 The pump and signal beams counter-propagate in the
backward-pumping configuration commonly used in
practice.
 The gain peaks at a Stoke shift of about 13.2 THz.
 The gain bandwidth Dng is about 6 THz by FWHM
 The large BW makes fiber Raman amplifier attractive
 Large pump power:
Pp = 5W for 1-km-long fiber, when gR = 6 x 10-14 m/W,
λ=1.55 mm, ap= 50 mm
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5.3 Raman Amplifier
5.3.2. Raman Gain and Bandwidth
 gR/ap, a measure of Raman-gain efficiency
 Raman Spectrum from SiO2 fiber
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5.3.3 Raman Amplifier Characteristics
 Small-signal amplification factor GA & smallsignal gain go, When apL>>1
go = gR(Po/ap)(Leff/L) ~ gRPo/apapL
GA = Ps(L)/[Ps(0)exp(-asL)]
= exp(goL) = exp(gogRPo/apap)
where Po = Pp(0)
ap is the loss coefficient of pump
L is the amplifier length.
 Noise from spontaneous Raman scattering, but is
neglected because of the distributed nature of the
amplification
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5.3.3 Raman Amplifier Characteristics
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5.3.4. Raman Amplifier Performance
 Raman amplifier can provide 20-dB gain at a
pump power of ~1 W.
 The broad width of Raman amplifiers is useful for
amplifying several channels simultaneously (dense
WDM)
 Lumped Raman amplifier:
a discrete device is made by spooling 1-2 km of an
especially prepared fiber that has been doped with
Ge or P for enhancing the Raman gain.
 Distributed Raman amplifier:
the same fiber that is used for signal transmission
is also used for signal amplification.
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5.3.4. Raman Amplifier Performance
 Compact high-power semiconductor and fiber lasers
make Raman amplifiers competitive to EDFA.
 Rayleigh scattering limits the performance of
distributed Raman amplifiers.
 The crosstalk accumulates over multiple amplifiers,
it can lead to large power penalties for undersea
lightwave system with long lengths.
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5.3.4 Raman Amplifier Performance
 With multiple pump lasers at different wavelengths,
the gain spectrum of Raman amplifier is flattened
to suit for WDM system.
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5.4 Erbium-Doped Fiber Amplifiers
5.4.1. Introduction
5.4.2. Pumping Requirement
5.4.3. Gain Spectrum
5.4.4. Simple Theory
5.4.5. Amplifier Noise
5.4.6. Multi-channel Amplification
5.4.7. Distributed-Gain Amplifiers
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5.4 Erbium-Doped Fiber Amplifiers
5.4.1. Introduction
 Typical Operating Wavelength Region
 Conventional Band (C band) 1530nm ~ 1560nm
 Long Band (IR or L band) 1575 nm ~ 1605 nm
 OA need one or more pump laser: many pump
wavelengths are available (980 nm and 1480 nm
most commonly used)
 Erbium is the key of optical amplification due to its
unique characteristics (EDFA = Erbium Doped
Fiber Amplifier)
 Amplified Spontaneous Emission (ASE) is broad
band noise
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5.4 Erbium-Doped Fiber Amplifiers
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5.4 Erbium-Doped Fiber Amplifiers
EXCITED
STATE
PUMP PHOTON
980 nm
METASTABLE STATE
SIGNAL PHOTON
1550 nm
FUNDAMENTAL STATE
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STIMULATED
PHOTON
1550 nm
FUNDAMENTAL STATE
5.4 Erbium-Doped Fiber Amplifiers
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5.4 Erbium-Doped Fiber Amplifiers
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5.4 Erbium-Doped Fiber Amplifiers
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5.4.2. Pumping Requirement
 The amorphous nature of silica broadens the
energy levels of Er+ into bands.
 Efficient EDFA pumping is possible using
semiconductor lasers operating near 0.98- and
1.48-mm wavelengths.
 Efficiencies as high as 11 dB/mW were achieved
by 1990 with 0.98-mm pumping.
 Most EDFAs use 980-nm pump lasers as such
lasers are commercially available and can provide
more than 100mW of pump power.
 Pumping at 1480 nm requires longer fibers and
higher powers because it uses the tail of the
absorption band.
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5.4.2. Pumping Requirement
 In the saturation regime, the power-conversion
efficiency is generally better in the backwardpumping configuration, mainly because of the
important role played by the amplified
spontaneous emission (ASE)
 Bidirectional pumping has the advantage that the
population inversion, and hence the small-signal
gain, is relatively uniform along the entire
amplifier length.
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5.4.2. Pumping Requirement
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5.4.3. Gain Spectrum
 The gain spectrum of erbium ions alone is homogeneously
broadened.
 The gain spectrum of EDFA doped with Ge is quite broad
and has a double-peak structure. The addition of Al to the
fiber core broadens the gain spectrum even more.
 The gain spectrum of alumino-silicate glasses has roughly
equal contributions from homogeneous and inhomogeneous
broadening mechanisms, contributing up to 35 nm.
 The gain spectrum of EDFA depends on the amplifier
length because both the absorption and emission cross
sections having different spectral characteristics.
 The local inversion or local gain varies along the fiber
length because of pump power variations.
 The total gain is obtained by integrating over the amplifier
length.
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5.4.3. Gain Spectrum
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5.4.3. Gain Spectrum
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5.4 Erbium-Doped Fiber Amplifiers
5.4.4. Simple Theory of EDFAs
 A three-level rate-equation model commonly used for lasers can be
adapted for EDFAs.
 A simple two-level model is valid when ASE and excited-state
absorption are negligible.
 The pump and signal powers vary along the amplifier length
because of absorption, stimulated emission, and spontaneous
emission. If the contribution of ASE is neglected,
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5.4.4. Simple Theory of EDFAs
 The total amplifier gain G for an EDFA of length L
 A 35-dB gain can be realized at a pump power of 5 mW
for L=30m and 1.48-mm pumping
 The output saturation power is about 10-mW.
 As single-pulse energy are typically much below the
saturation energy (~10mJ), EDFAs respond to the average
power.
 Gain saturation is governed by the average signal power,
and the amplifier gain does not vary from pulse to pulse
even for a WDM signal.
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5.4.5. Amplifier Noise of EDFAs
 For a lumped EDFA, the impact of ASE is quantified
through the noise figure Fn given by Fn= 2nsp > 3dB
 For three-level pumping, N1≠0, so nsp= N2/(N2-N1)>1
 A noise figure of 3.2dB was measured in a 30-m-long EDFA
pumped at 0.98um with 11 mW of power.
 It is difficult to achieve high gain, low noise, and high
pumping efficiency simultaneously. The main limitation is
imposed by the ASE traveling backward toward the pump
and depleting the pump power. An internal isolator can
reduce this problem.
 The measured values of Fn are generally larger for EDFAs
pumped at 1.48-mm. The reason is that the pump level and
the excited level lie within the same band for 1.48-mm
pumping.
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5.4.6. Multi-channel Amplification
 The cross-gain saturation can be avoided by
operation the amplifier in the unsaturated regime.
 Due to 10 ms carrier lifetime, the gain of EDFAs
can not be modulated (carrier-density modulation)
at frequencies much than 10 kHz.
 The main limitation of an EDFA stems from the
spectral nonuniformity of the amplifier gain.
 Even a 0.2-dB gain difference grows to 20 dB over a
chain of 100 in-line amplifiers.
 The entire BW of 35-40 nm can be used if the gain
spectrum is flattened by introducing wavelengthselective losses through an optical filter.
 L-band: 1570-1610 nm, C-band: 1530-1570nm,
S-band:1470-1520nm
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5.4.6. Multi-channel Amplification
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5.4.6. Multi-channel Amplification
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5.4.6. Multi-channel Amplification
2nd Active Stage
Counter-pumped
1st Active Stage
Co-pumped
Input
Signal
Optical
Isolator
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Output
Signal
Optical
Isolator
Optical
Isolator
PUMP
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Er3+
Doped Fiber
Er3+
Doped Fiber
PUMP
5.4.6. Multi-channel Amplification
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5.4 Erbium-Doped Fiber Amplifiers
5.4.7. Distributed-Gain Amplifiers
 Lumped amplifier:
most EDFAs provide 20-25dB amplification over a length ~10m
through a relatively high density of dopants (~500 parts per
million)
 Distributed amplifier ~ distributed Raman amplifier
the transmission fiber itself is lightly doped (dopant density ~ 50
part per billion) to provide the gain distributed over the entire
fiber length such that it compensates for fiber loss locally.
 Distributed EDFA ~ distributed Raman amplifier
except that the dopants provide the gain instead of the nonlinear
phenomenon of SRS.
 Pumping at 980nm is ruled out due to fiber loss > 1dB/km
 Pumping loss > 0.4dB/km for 1480nm
 This scheme has not yet been used commercially as it requires
special fibers.
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5.5 System Applications
5.5.1. Optical Pre-amplification
 After 1995, due to low insertion loss, high gain, large
BW, low noise, and low crosstalk, EDFAs are used
as preamplifier at the receiver.
 The receiver sensitivity can be improved by 10-20 dB
using an EDFA as a preamplifier.
 The most important performance issue in designing
optical preamplifier is the contamination of the
amplified signal by the ASE.
 The receiver sensitivity is
Prec = hnFnDf[Q4+Q(Dnopt/Df)1/2]
where BER = (1/2)erfc(Q/√2);
Dnopt is the BW of the optical filter, and Df is the
electrical noise BW of the receiver.
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5.5.1. Optical Pre-amplification
 The receiver sensitivity is written in terms of the average
number of photon/bit, Np, by Prec=Nphn and Df = B/2,
Np = (1/2)Fn[Q2+Q(2Dnopt/B)1/2]
 It shows clearly why amplifiers with a small noise figure
must be used.
 It also shows how optical filters can improve the receiver
sensitivity by reducing Dnopt
 The minimum optical BW is equal to the bit rate to avoid
blocking the signal.
 For Q = 6 (BER=10-9), Np = 44.5
 Np > 1000 for PIN with amplifier. Np < 100 can be realized
when optical amplifiers are used to pre-amplify the signal.
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5.5.2. Noise Accumulation in
Long-Haul System
 The amplifier-induced noise builds up due to the
cascaded amplifiers in a long-haul lightwave system
 Two disadvantages of ASE noise
(1) degrading SNR
(2) saturating optical amplifier and reducing the gain of
amplifiers located further down the fiber link.
(3) self-regulating behavior that the total power obtained
by adding the signal and ASE powers remains relatively
constant.
 Electrical SNR is dominated by the signal-spontaneous
beat noise generated at the photodetector
SNR = PinLA/(4nsphn0LTexp(aLA)] ~ 20dB
when nsp= 1.6, a = 0.2 dB/km, Df =10 Gbps
 Typically, LA~ 50km for undersea systems and LA~ 80km
for terrestrial systems with link lengths under 3000km.
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5.5.2. Noise Accumulation in
Long-Haul System
 Amplifier-induced noise builds up due to the
cascaded amplifiers
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5.5.2. Noise Accumulation in
Long-Haul System
 Self-regulating behavior that the total power
obtained by adding the signal and ASE powers
remains relatively constant.
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5.5.2. Noise Accumulation in
Long-Haul System
Popt
 Degradation of OSNR
 Noise at Rx
Popt
l
l
OSNR
Link Length
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5.5.3. ASE-Induced Timing Jitter
 The amplifier noise (ASE) can induce timing jitter in the
bit stream by shifting optical pulses from their original
time slot in a random fashion.
 The post-compensation technique :
a fiber is placed at the end of the last amplifier to reduce
the net accumulated dispersion
 The timing jitter for a CRZ system employing postcompensation is
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5.5.3. ASE-Induced Timing Jitter
 With post-compensation, the ASE jitter ~ NA3d2
 With zero average dispersion, the ASE jitter ~ NA
 When NAd+C0+df =0, zero net dispersion the entire
link
 Assume an error occurs whenever the pulse has
moved out of the bit slot, then
 To reduce the BER < 10-9, the st/TB should be < 8%
of the bit slot, resulting in a tolerable value of the
jitter of 8 ps for 10 Gbps system and only 2 ps for 40
Gbps.
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5.5.4. Accumulated Dispersive
and Nonlinear Effects
 Neglecting nonlinear effects,
(1) β2LT< 3000 (Gbps)2-km for β2 ~ -20ps2/km at
1.55 mm,
(2) β2LT < 60000 (Gbps)2-km for DSF at 1.55 mm,
(3) to extend the distance to beyond 5000 km at 10 Gbps,
the average GVD along the link should be smaller
than β2 < -0.1 ps2/km
 The role of dispersion can be minimized either by
operating close to the zero-dispersion wavelength of the
fiber or by using a dispersion management technique.
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5.5.5. WDM-Related Impairments
 The advantages of EDFAs for WDM systems were
demonstrated as early as 1990. By 2001, transmission at
120 x 20 Gbps over 6200 km has been realized within the
C band using EDFAs every 50 km.
 Polarization multiplexing : the adjacent channels were
orthogonally polarized for reducing the nonlinear effects
resulting from a relatively small spacing of 42 GHz.
 FWM can be avoided by using dispersion management
such that the GVD is locally high all along the fiber but
quite small on average. But it also enhanced in L-band
amplifiers due to their long lengths (>100m)
 SPM and XPM lead to considerable power fluctuations
within an L-band amplifier due to the relatively small
effective core area.
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5.5.5. WDM-Related Impairments
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