Page 318 - Fiber Optic Communications Fund

Optical Amplifiers 299

6.5 The OSNR (within a bandwidth of 0.1 nm) at the output of an amplifier operating at 1550 nm is 22 dB.
The output of the amplifier passes through an ideal photo-detector ( = 1). Calculate the electrical
SNR at the photodetector. Ignore the thermal noise and ASE–ASE beat noise. Assume that the input
power of the amplifier is −20 dBm, gain G = 23 dB, B ≪ B , R = 0.8 A/W, and B = 8 GHz.
o
e
e
(Ans: 20.92 dB.)
6.6 In a cavity-type SOA, R = R = 0.3, FSR = 30 GHz, and the single-pass gain G = 4.75 dB. Find (a)
2
s
1
the peak gain and (b) the gain G at frequency Δf = 5 GHz, where Δf is the frequency shift from the
resonant frequency. Assume n = 3.3.
(Ans: (a) 21.28 dB; (b) 2.07 dB.)
6.7 Explain the gain–bandwidth trade-off in semiconductor amplifiers.

6.8 In a cavity-type SOA, the maximum and minimum gains are 20.78 dB and 4.43 dB, respectively. The
geometric mean of the reflectivities, R, is 0.32. Calculate the single-pass gain G .
s
(Ans: 4.47 dB.)
6.9 In a cavity-type SOA, FSR = 300 GHz, refractive index n = 3.3, G = 4.3 dB. (a) Calculate the peak
s
gain G and the 3-dB bandwidth if R = R = 0.3, (b) repeat if R = R = 0.1.
peak 1 2 1 2
(Ans: (a) G peak (dB)= 17.62 dB and f 3dB = 16.06 GHz; (b) G peak (dB)= 6.4 dB and f 3dB =
141.8 GHz.)

6.10 Explain how population inversion is achieved in an EDFA.

6.11 Explain the meaning of absorption cross-section.
6.12 Solve Eqs. (6.187) and (6.189) numerically and plot the signal power as a function of amplifier length
−3
for various pump powers, P (0)= 10 mW and P (0)= 10 μW. Assume N = 1.1 × 10 25 m , Γ = 0.4,
p
s
s
T
−2
−2
−2
Γ = 0.64, 13 = 2.7 × 10 −25 m , 12 = 1.8 × 10 −25 m , 21 = 12 ms, A eff = 3.4 × 10 −12 m .
p
6.13 Explain the difference between spontaneous Raman scattering and stimulated Raman scattering.
6.14 Solve Eqs. (6.200) and (6.201) numerically. Plot the gain as a function of the length for pump powers
P (0)= 200 mW and P (0)= 1 mW. Plot the gain obtained by the undepleted pump approximation
p
s
given by Eq. (6.207) and compare the analytical result (Eq. (6.207)) and that obtained by the numerical
solution of Eqs. (6.200 ) and (6.201). Assume = 0.2 dB/km and = 0.5dB/km.
p
s
6.15 Provide an explanation as to why gain saturates for large signal powers in any type of amplifier.
6.16 In a distributed Raman amplifier system, the pump power of the input = 250 mW, effective area of
−1
2
the pump mode = 30 μm , loss coefficient at the pump wavelength = 9.5 × 10 −5 m , Raman gain
coefficient g = 6 × 10 −14 m/W, and length = 50 km. Calculate the gain of the amplifier under the
R
undepleted pump approximation.
(Ans: 7.17 dB.)