Nonlinear Fiber Optics - 4 ed. Agrawal

392 Chapter 10. Four-Wave Mixing
Figure 10.12: (a) Gain spectra of a single-pump FOPA for several values of pump detuning Δλ p
from the zero-dispersion wavelength. (b) Gain spectra for three different fiber lengths assuming
γP 0 L = 6 in each case. The pump wavelength is optimized in each case, and only half of the gain
spectrum is shown because of its symmetric nature.
gain in this case is about 8 dB, and the gain bandwidth is limited to 40 nm. When the
pump is detuned by −0.1 nm such that it experiences normal GVD, gain bandwidth
is reduced to below 20 nm. In contrast, both the peak gain and the bandwidth are
enhanced when the pump is detuned toward the anomalous-GVD side. In this region,
the gain spectrum is sensitive to the exact value of Δλ p . The best situation from a
practical standpoint occurs for Δλ p = 0.106 nm because the gain is nearly constant
over a wide spectral region.
An interesting feature of Figure 10.12(a) is that the maximum gain occurs when the
signal is detuned relatively far from the pump wavelength. This feature is related to the
nonlinear contribution to total phase mismatch κ. The linear part of phase mismatch is
negative for Δλ p > 0 and its magnitude depends on the signal wavelength. In a certain
range of signal wavelengths, it is fully compensated by the nonlinear phase mismatch
to yield κ = 0. When phase matching is perfect, FOPA gain increases exponentially
with the fiber length, as indicated in Eq. (10.4.9), resulting in an off-center gain peak
in Figure 10.12(a).
From a practical standpoint, one wants to maximize both the peak gain and the
gain bandwidth at a given pump power P 0 . Since the peak gain in Eq. (10.4.9) scales
exponentially with γP 0 L, it can be increased by increasing the fiber length L. However,
from Eq. (10.4.10) gain bandwidth scales inversely with L when L ≫ L NL . The only
solution is to use a fiber as short as possible. Of course, shortening of fiber length
must be accompanied with a corresponding increase in the value of γP 0 to maintain
the same amount of gain. This behavior is illustrated in Figure 10.12(b) where the
gain bandwidth increases considerably when large values of γP 0 are combined with
shorter fiber lengths such that γP 0 L = 6 remains fixed. The solid curve obtained for a
250-m-long FOPA exhibits a 30-nm-wide region on each side of the pump wavelength
over which the gain is nearly flat. The nonlinear parameter γ can be increased by
reducing the effective mode area. Such highly nonlinear fibers (see Chapter 11) with