Nonlinear Fiber Optics - 4 ed. Agrawal

394 Chapter 10. Four-Wave Mixing
the signal or idler falls within the Raman-gain bandwidth [83]. In spite of these factors,
noise figures of 4.2 dB for an FOPA with 27.2-dB gain [80] and of 3.7 dB with a 17-dB
gain [81] were realized in two 2002 experiments. Such noise levels are close to the
fundamental quantum limit of 3 dB for an ideal amplifier.
Another factor that affects FOPAs is the onset of stimulated Brillouin scattering
(SBS). As was seen in Section 9.2.2, the SBS threshold is around 5 mW for long fibers
(>10 km) and increases to near 50 mW for fiber lengths of 1 km or so. Since FOPAs
require pump power levels approaching 1 W, a suitable technique is needed that raises
the threshold of SBS and suppresses it over the FOPA length. The techniques used in
practice (i) control the temperature distribution along the fiber length [75] or (ii) modulate
the pump phase either at several fixed frequencies [72], or over a broad frequency
range using a pseudorandom bit pattern [82]. The pump-phase modulation technique
suppresses SBS by broadening the pump spectrum, but it should not affect FOPA gain
much. In practice, gain is affected to some extent because the phase-mismatch parameter
κ depends on the phase of the pump [84]. Moreover, dispersive effects within
the fiber convert pump-phase modulation into amplitude modulation of the pump. As
a result, the SNR of both the signal and the idler is reduced because of undesirable
power fluctuations [85]. Pump-phase modulation also leads to broadening of the idler
spectrum, making it twice as broad as the pump spectrum. Such broadening of the idler
is of concern when FOPAs are used as wavelength converters. As seen later, it can be
avoided in dual-pump FOPAs.
An important issue associated with single-pump FOPAs is that their gain spectrum
is far from being uniform over its entire bandwidth (see Figure 10.12). The reason is
that it is hard to maintain the phase-matching condition over a wide bandwidth in a
single-pump FOPA. Since the linear contribution Δk → 0 when signal wavelength approaches
the pump wavelength, κ ≈ 2γP 0 in the pump vicinity. This value of κ is quite
large and results in only a linear growth of the signal, resulting in G = 1 + γP 0 L.As
a result, the gain spectrum exhibits a dip in the vicinity of the pump wavelength. Although
amplification over a range as wide as 200 nm is possible [70], the gain spectrum
remains highly nonuniform, and the usable bandwidth is limited to a much smaller region
of the gain spectrum. This problem can be solved to some extent by manipulating
fiber dispersion [71]. Theoretically, a fairly flat gain spectrum is possible by using
several fiber sections of suitable lengths and properly selecting dispersive properties of
these fiber sections [86]. However, such a scheme is difficult to implement in practice
because dispersive properties of fibers are rarely known with sufficient precision. A
practical solution is to make use of the dual-pump configuration discussed next.
10.4.4 Dual-Pump Configuration
Dual-pump FOPAs use the nondegenerate FWM process and employ two pumps at
different wavelengths [87]–[92]. With a proper choice of the pump wavelengths, they
can provide a relatively uniform gain over a wider bandwidth than that is possible with
a single pump. The parametric gain in the dual-pump case is given by Eq. (10.2.19).
Using r from Eq. (10.2.20), it can be written as
g(ω 3 )=[4γ 2 P 1 P 2 − κ 2 (ω 3 )/4] 1/2 , (10.4.14)