
406 Optical Fiber Communication Systems with MATLAB
®
and Simulink
®
Models
with
as the input pump power. Hence, the signal intensity at the output of the amplier
of length L is determined as
P L P
g P L
A
L
S S
R eff
eff
S
( ) ( )exp= −
0
0
α (10.6)
The effective length,
eff
is the length where the nonlinearities exist or SRS occurs in the
ber and is dened as
L
L
eff
P
P
=
− −1 exp( )α
α
(10.7)
As ber losses exist at the pump wavelength, it is less than the actual length and can be
approximated by
eff P
if
Hence, the gain amplication, the ratio of the power
of the signal with and without Raman amplication, is given by
G
P L
P