Nonlinear Fiber Optics - 4 ed. Agrawal

396 Chapter 10. Four-Wave Mixing
Figure 10.14: Gain spectrum of a dual-pump FOPA when all five idlers are included (solid
curve). The dashed spectrum is obtained when only a single idler generated through the dominant
nondegenerate FWM process is included in the model.
A complete description of dual-pump FOPAs becomes quite complicated [90] if
one were to include all underlying FWM processes. Fortunately, the phase-matching
conditions associated with these processes are quite different. When the two pumps
are located symmetrically far from the zero-dispersion wavelength of the fiber, the
ten FWM processes indicated in Eqs. (10.4.17)–(10.4.21) can only occur when the
signal is in the vicinity of one of the pumps. For this reason, they leave unaffected
the central flat part of the FOPA gain spectrum resulting from the the process ω 1 +
ω 2 → ω 3 +ω 4 . Figure 10.14 compares the FOPA gain spectrum calculated numerically
using all five idlers (solid curve) with that obtained using this sole nondegenerate FWM
process. Other FWM processes only affect the edges of gain spectrum and reduce the
gain bandwidth by 10 to 20%. The FOPA parameters used in this calculation were
L = 0.5 km, γ = 10 W −1 /km, P 1 = P 2 = 0.5W,β 30 = 0.1ps 3 /km, β 40 = 10 −4 ps 4 /km,
λ 1 = 1502.6 nm, λ 2 = 1600.6 nm, and λ 0 = 1550 nm.
Dual-pump FOPAs provide several degrees of freedom that make it possible to realize
a flat gain spectrum using just a single piece of fiber. A 2002 experiment employed
a 2.5-km-long highly nonlinear fiber having its zero-dispersion wavelength at 1585 nm
with γ = 10 W −1 /km [92]. It also used two pumps with their wavelengths at 1569 and
1599.8 nm. Such a FOPA exhibited a gain of 20 dB over 20-nm bandwidth when pump
powers were 220 and 107 mW at these two wavelengths, respectively. The gain could
be increased to 40 dB by increasing pump powers to 380 and 178 mW. It was necessary
to launch more power at the shorter wavelength because of the Raman-induced
power transfer between the two pumps within the same fiber used to amplify the signal
through FWM. A bandwidth of close to 40 nm was realized for a dual-pump FOPA
in a 2003 experiment [93]. Figure 10.15 shows the experimental data together with a
theoretical fit. In this experiment, two pumps were launched with powers of 600 mW
at 1559 nm and 200 mW at 1610 nm. The 1-km-long highly nonlinear fiber had its