Nonlinear Fiber Optics - 4 ed. Agrawal

464 Chapter 12. Novel Nonlinear Phenomena
a 80-MHz repetition rate) for three input wavelengths of 1400, 1510, and 1550 nm.
In case (a), a Raman soliton is generated through fission, but its spectrum stops shifting
beyond 1470 nm because of the RIFS suppression induced by the NSR appearing
in the normal-GVD regime lying beyond 1510 nm. In case (b), a part of the pulse
lies in the normal-GVD regime, and it disperses without forming a soliton. The remaining
part propagates in the anomalous-GVD regime, and its spectrum shifts toward
shorter wavelengths with increasing power. At a certain value of the input power, soliton
effects begin to dominate, and the spectrum shifts through the RIFS toward longer
wavelengths, resulting in the comma-like shape (marked by an arrow). At even higher
powers, the RIFS is arrested by the spectral-recoil mechanism. In case (c), the pulse
propagates in the normal-GVD regime and mostly experiences SPM-induced spectral
broadening. At high powers, the spectrum broadens enough that a part of the pulse
energy lies in the anomalous regime and begins to form a soliton.
12.2 Four-Wave Mixing
The phenomenon of FWM has been discussed extensively in Chapter 10. The unusual
dispersive properties of highly nonlinear fibers affect the FWM process through the
phase-matching condition. For example, as already mentioned in Section 10.3.3, the
inclusion of higher-order dispersive effects offers the possibility of phase matching
even when pump wavelength lies in the normal-GVD regime. In this section, we focus
on such features of FWM in more detail.
12.2.1 FWM in Highly Nonlinear Fibers
Highly nonlinear fibers were used for FWM soon after their development [43]–[58].
In a 2001 experiment, a single-pump configuration was employed to amplify signals
by 13 dB over a 30-nm bandwidth with a pump peak power of only 6 W using a
6.1-m-long microstructured fiber [43]. A 2.1-m section of such a fiber was used in
a 2002 experiment to realize a fiber-optic parametric oscillator that was tunable over
40 nm [45]. The threshold for this laser was reached when pump pulses had a peak
power of only 34.4 W. In another experiment, a 100-m-long highly nonlinear fiber
was pumped continuously at 1565 nm [46], and two fiber gratings were used to form a
cavity. Such a parametric oscillator reached threshold at a pump power of 240 mW and
was tunable over a 80-nm bandwidth. In these experiments, the pump wavelength lay
in the anomalous-GVD regime of the fiber, and the signal and idler frequencies were
set by Eq. (5.1.9) of Section 5.1.
As discussed in Section 10.3.3, higher-order dispersive effects often become important
and should be included for highly nonlinear fibers. It was found there that
only the even-order dispersion terms affect the phase-matching condition. Thus, the
fourth-order dispersion becomes important in setting the signal and idler frequencies.
If dispersion to all orders is included, the phase-matching condition in Eq. (10.3.10)
becomes
∞
∑
m=2,4,...
β m (ω p )
Ω m s + 2γP 0 = 0, (12.2.1)
m!