Nonlinear Fiber Optics - 4 ed. Agrawal

Problems 321
Figure 8.25: (a) Average gain and (b) standard deviation of signal fluctuations at the output of a
Raman amplifier as a function of PMD parameter in the cases of forward and backward pumping.
The solid and dashed curves correspond to the cases of copolarized and orthogonally polarized
signals, respectively. (After Ref. [189]; c○2003 OSA.)
The level of signal fluctuations in Figure 8.25 increases quickly with the PMD
parameter, reaches a peak value, and then decreases slowly toward zero with a further
increase in D p because of an averaging effect produced by the PMD. The location of the
peak depends on the pumping scheme as well as on the initial polarization of the pump;
the noise level near this peak exceeds 40%. If a fiber with low PMD is used, the noise
level can exceed 70% under some operating conditions. The behavior for backward
pumping is similar to those for forward pumping but the peak shifts to smaller D p
values. This shift is due to a much larger value of |Ω| = ω p + ω s . Since the diffusion
length scales as |Ω| −2 , it is smaller by about a factor of (ω p + ω s )/(ω p − ω s ) ≈ 30 in
the backward-pumping case. A smaller diffusion length results in rapid averaging over
birefringence fluctuations and reduces the noise level.
An important question is which pumping configuration is better from a practical
viewpoint. The answer depends on the value of D p . For fibers with values of D P <
0.001 ps/ √ km, forward pumping is the appropriate choice. However, D p exceeds 0.01
ps/ √ km for most fibers. In this situation, backward pumping produces the least signal
degradation in practice. It also reduces the polarization dependence of the Raman gain
in optical communication systems where the SOP of the input signal itself may change
with time in a random fashion.
Problems
8.1 What is meant by Raman scattering? Explain its origin. What is the difference
between spontaneous and stimulated Raman scattering?
8.2 Solve Eqs. (8.1.2) and (8.1.3) neglecting pump deletion. Calculate the Stokes
power at the output of a 1-km-long fiber when 1-μW power is injected together