6.3. RAMAN AMPLIFIERS 249
orthogonally polarized. The polarization problem can be solved by pumping a Raman
amplifier with two orthogonally polarized lasers. Another requirement for WDM sys-
tems is that the gain spectrum be relatively uniform over the entire signal bandwidth so
that all channels experience the same gain. In practice, the gain spectrum is flattened by
using several pumps at different wavelengths. Each pump creates the gain that mimics
the spectrum shown in Fig. 6.11. The superposition of several such spectra then creates
relatively flat gain over a wide spectral region. Bandwidths of more than 100 nm have
been realized using multiple pump lasers [46]–[48].
The design of broadband Raman amplifiers suitable for WDM applications requires
consideration of several factors. The most important among them is the inclusion of
pump–pump interactions. In general, multiple pump beams are also affected by the Ra-
man gain, and some power from each short-wavelength pump is invariably transferred
to long-wavelength pumps. An appropriate model that includes pump interactions,
Rayleigh backscattering, and spontaneous Raman scattering considers each frequency
component separately and solves the following set of coupled equations [48]:
dPf(ν)
dz=
∫μ>νgR(μ−ν)aμ−^1 [Pf(μ)+Pb(μ)][Pf(ν)+ 2 hνnsp(μ−ν)]dμ−
∫μ<νgR(ν−μ)a−ν^1 [Pf(μ)+Pb(μ)][Pf(ν)+ 2 hνnsp(ν−μ)]dμ,−α(ν)Pf(ν)+rsPb(ν) (6.3.10)whereμandνdenote optical frequencies,nsp(Ω)=[ 1 −exp(−h ̄Ω/kBT)]−^1 , and the
subscriptsfandbdenote forward- and backward-propagating waves, respectively. In
this equation, the first and second terms account for the Raman-induced power trans-
fer into and out of each frequency band. Fiber losses and Rayleigh backscattering are
included through the third and fourth terms, respectively. The noise induced by spon-
taneous Raman scattering is included by the temperature-dependent factor in the two
integrals. A similar equation can be written for the backward-propagating waves.
To design broadband Raman amplifiers, the entire set of such equations is solved
numerically to find the channel gains, and input pump powers are adjusted until the
gain is nearly the same for all channels. Figure 6.14 shows an example of the gain
spectrum measured for a Raman amplifier made by pumping a 25-km-long dispersion-
shifted fiber with 12 diode lasers. The frequencies and power levels of the pump lasers,
required to achieve a nearly flat gain profile, are also shown. Notice that all power
levels are under 100 mW. The amplifier provides about 10.5 dB gain over an 80-
nm bandwidth with a ripple of less than 0.1 dB. Such an amplifier is suitable for
dense WDM systems covering both the C and L bands. Several experiments have used
broadband Raman amplifiers to demonstrate transmission over long distances at high
bit rates. In one 3-Tb/s experiment, 77 channels, each operating at 42.7 Gb/s, were
transmitted over 1200 km by using the C and L bands simultaneously [49].
Several other nonlinear processes can provide gain inside silica fibers. An exam-
ple is provided by the parametric gain resulting from FWM [29]. The resulting fiber
amplifier is called aparametric amplifierand can have a gain bandwidth larger than
100 nm. Parametric amplifiers require a large pump power (typically>1 W) that may
be reduced using fibers with high nonlinearities. They also generate a phase-conjugated