1. Chapter 5: Optical Amplifiers
5.1 Basic Concepts
Introduction
Gain Spectrum and Bandwidth
Gain Saturation
Amplifier Noise
Amplifier Applications
5.2 Semiconductor Optical Amplifiers
Amplifier Design
Amplifiers Characteristics
Pulse Amplification
System Application
5.3 Raman Amplifier
Introduction
Raman Gain and Bandwidth
Amplifier Characteristics
Raman Amplifier Performance

2. Chapter 5: Optical Amplifiers
5.4 Erbium-Doped Fiber Amplifiers
Introduction
Pumping Requirement
Gain Spectrum
Simple Theory of EDFAs
Amplifier Noise
Multi-channel Amplification
Distributed-Gain Amplifiers
5.5 System Applications
Optical Pre-amplification
Noise Accumulation in Long-Haul System
ASE-Induced Timing Jitter
Accumulated Dispersive and Nonlinear Effects
WDM-Related Impairments

3. 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.

4. 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)

5. 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

6. 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.

7. 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

8. 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

9. 5.1: Basic Concepts

10. 5.2 Semiconductor Optical Amplifiers
Amplifier Design
Fabry-Perot amplifier: gain spectrum and its amplifier bandwidth
The condition of TW-type SOA

11. 5.2 Semiconductor Optical Amplifiers
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

12. 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)

13. 5.2 Semiconductor Optical Amplifiers
Pulse Amplification
The amplification factor is shape dependent, implying distortion
Saturation-induced SPM and the associated frequency chirp

14. 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.

15. 5.2 Semiconductor Optical Amplifiers
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, inter-channel 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

16. 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 m/W,
λ=1.55 mm, ap= 50 mm

17. 5.3 Raman Amplifier 5.3.2. Raman Gain and Bandwidth
gR/ap, a measure of Raman-gain efficiency
Raman Spectrum from SiO2 fiber

18. 5.3.3 Raman Amplifier Characteristics
Small-signal amplification factor GA & small-signal 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

19. 5.3.3 Raman Amplifier Characteristics

20. 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.

21. 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.

22. 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.

23. 5.4 Erbium-Doped Fiber Amplifiers
Introduction
Pumping Requirement
Gain Spectrum
Simple Theory
Amplifier Noise
Multi-channel Amplification
Distributed-Gain Amplifiers

24. 5.4 Erbium-Doped Fiber Amplifiers
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

25. 5.4 Erbium-Doped Fiber Amplifiers

26. 5.4 Erbium-Doped Fiber Amplifiers
PUMP PHOTON
980 nm
TRANSITION
METASTABLE STATE
SIGNAL PHOTON
1550 nm
STIMULATED
PHOTON
FUNDAMENTAL STATE
EXCITED
STATE

27. 5.4 Erbium-Doped Fiber Amplifiers

28. 5.4 Erbium-Doped Fiber Amplifiers

29. 5.4 Erbium-Doped Fiber Amplifiers

30. 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 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.

31. Pumping Requirement
In the saturation regime, the power-conversion efficiency is generally better in the backward-pumping 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.

32. Pumping Requirement

33. 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.

34. Gain Spectrum

35. Gain Spectrum

36. 5.4 Erbium-Doped Fiber Amplifiers
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,

37. 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.

38. 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.

39. 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 nm can be used if the gain spectrum is flattened by introducing wavelength-selective losses through an optical filter.
L-band: nm, C-band: nm,
S-band: nm

40. 5.4.6. Multi-channel Amplification

41. 5.4.6. Multi-channel Amplification

42. 5.4.6. Multi-channel Amplification
PUMP
Input
Signal
Output
Er3+
Doped Fiber
Optical
Isolator
1st Active Stage
Co-pumped
2nd Active Stage
Counter-pumped

43. 5.4.6. Multi-channel Amplification

44. 5.4 Erbium-Doped Fiber Amplifiers
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.

45. 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 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.

46. 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.

47. 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.

48. 5.5.2. Noise Accumulation in Long-Haul System
Amplifier-induced noise builds up due to the cascaded amplifiers

49. 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.

50. 5.5.2. Noise Accumulation in Long-Haul System
Degradation of OSNR
Noise at Rx
Popt l l
OSNR
Link Length

51. 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 post-compensation is

52. 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.

53. 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 < (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.

54. 5.5.5. WDM-Related Impairments
The advantages of EDFAs for WDM systems were demonstrated as early as 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.

55. 5.5.5. WDM-Related Impairments