Nonlinear Fiber Optics - 4 ed. Agrawal

8.2. Quasi-Continuous SRS 293
1
0.8
Pump Depletion, D p
0.6
0.4
r 0
= 0.5
1
0.2
2
0
1 1.5 2 2.5 3 3.5 4
Amplification Factor, G A
Figure 8.10: Pump-depletion characteristics showing variation of D p with G A for three values
of r 0 .
(8.1.3). These equations can be solved analytically if the fiber loss is assumed to be the
same for both channels (α s = α p ), an assumption easily justified for typical channel
spacings near 1.55 μm. The amplification factor G s for the longer-wavelength channel
is given by Eq. (8.2.7). The associated reduction in the short-wavelength channel power
is obtained from the pump-depletion factor
D p =
I p (L)
I p (0)exp(−α p L) = 1 + r 0
1 + r 0 G 1+r 0
A
, (8.2.9)
where G A and r 0 are defined by Eqs. (8.2.4) and (8.2.8), respectively. Figure 8.10 shows
the pump-depletion characteristics by plotting D p as a function of G A for several values
of r 0 . These curves can be used to obtain the Raman-induced power penalty defined as
the relative increase in the pump power necessary to maintain the same level of output
power as that in the absence of Raman crosstalk. The power penalty can be written as
(in decibels)
Δ R = 10 log(1/D p ). (8.2.10)
A 1-dB penalty corresponds to D p ≈ 0.8. If we assume equal channel powers at the
fiber input (r 0 ≈ 1), D p = 0.8 corresponds to G A ≈ 1.22. The input channel powers corresponding
to 1-dB penalty can be obtained from Eq. (8.2.4). If we use the typical values
for 1.55-μm optical communication systems, g R = 7×10 −14 m/W, A eff = 50 μm 2 ,
and L eff = 1/α p ≈ 20 km, G A = 1.22 corresponds to P 0 = 7 mW. If the Raman gain is
reduced by a factor of 2 to account for polarization scrambling, this value increases to
P 0 = 14 mW. The experimental measurements of the power penalty are in agreement
with the predictions of Eqs. (8.2.9) and (8.2.10).