Nonlinear Fiber Optics - 4 ed. Agrawal

410 Chapter 10. Four-Wave Mixing
circularly). As noted earlier, optical fields with different frequencies change their SOPs
at different rates in the presence of PMD. As a result of this frequency dependence,
the two pumps will not remain orthogonally polarized and would produce gain that
depends on the signal SOP to some extent. Indeed, such a behavior has been observed
for a dual-pump FOPA [67]. Figure 10.20(b) shows the average gain spectra for three
different signal SOPs for a specific value of D p = 0.1 ps/ √ km. The two pumps are
launched with SOPs that are linear and orthogonal to each other. The signal is also
linearly polarized with its SOP inclined at an angle of 0, 45, or 90 ◦ from that of the
shorter-wavelength pump. The gain spectrum expected in the absence of PMD is also
shown as a dotted curve.
Two features of Figure 10.20(b) are noteworthy. First, at signal wavelengths close
to the pump, gain can change by as much as 12 dB as signal SOP is varied; variations
are much smaller in the central region. The reason for this behavior can be understood
as follows. If the signal has its wavelength close to that of a pump, their relative
orientation does not change much along the fiber. As a result, it experiences the highest
or smallest gain depending on whether it is initially polarized parallel or orthogonal to
the that pump. Second, the PMD effects enhance the gain considerably compared
with the case of an isotropic fiber with no birefringence. The reason is understood by
recalling from Figure 10.19 that the FWM efficiency is the smallest when the pumps
are orthogonally polarized. However, because of the PMD, pump SOPs do not remain
orthogonal along the fiber, and may even become parallel occasionally; this results in
a higher gain at all signal wavelengths.
PMD effects can be made negligible for FOPAs designed with a relatively short
length (∼100 m) of low-PMD fibers and pumped at wavelengths spaced apart by