Nonlinear Fiber Optics - 4 ed. Agrawal

8.2. Quasi-Continuous SRS 283
four equations that includes all nonlinear terms appropriately, as discussed in Section
7.1. The situation is even more complicated if the anti-Stokes wave is included: one
must then solve a set of six coupled equations. Polarization effects are discussed later
in Section 8.5.
For pump pulses propagating in the anomalous-GVD regime of optical fibers, one
should consider how modulation instability and SRS influence each other. As discussed
in Section 5.1, modulation instability can be thought of as a four-wave mixing
process phase-matched by SPM (see Section 10.3). It generates new waves at frequencies
ω p + Ω m and ω p − Ω m , where Ω m depends on the pump power and is generally
different than the Raman shift Ω. Thus, a unified analysis should consider five waves at
frequencies ω p , ω p ±Ω m , and ω p ±Ω. Each of these five waves can have two orthogonally
polarized components, resulting in a set of ten coupled-amplitude equations. The
analysis becomes simpler for ultrashort pump pulses whose spectrum is so broad that
the frequencies Ω m and Ω fall within its bandwidth. The propagation of such pump
pulses is described by a set of two coupled equations that include the effects of GVD,
SPM, XPM, fiber birefringence, four-wave mixing, and intrapulse SRS. A linear stability
analysis of such equations can be performed to obtain the effective gain spectrum
when a CW pump beam enters an optical fiber [31].
8.2 Quasi-Continuous SRS
Since the initial observation of SRS in optical fibers [9], SRS has been studied extensively
using pump pulses of widths in the range 1–100 ns, a situation that corresponds
to the quasi-CW regime [34]–[50]. In the single-pass geometry, each pump
pulse launched at one end of the fiber generates a Stokes pulse at the other end. In the
multipass geometry, the fiber is placed inside a cavity, resulting in a tunable Raman
laser. Another application consists of using SRS for signal amplification. This section
discusses all three aspects of SRS in optical fibers.
8.2.1 Single-Pass Raman Generation
The 1972 demonstration of SRS in silica fibers was carried out in the visible region
using 532-nm pulses from a frequency-doubled Nd:YAG laser [8]. About 75 W of
pump power was required to generate the Stokes radiation at 545 nm in a single-mode
fiber of 9-m length and 4-μm core diameter. In later experiments, 150-ns infrared pump
pulses, from a Nd:YAG laser operating at 1.06 μm, were used to initiate SRS [35]. In
one experiment, the first-order Stokes line at 1.12 μm was observed at a pump power of
70 W [37]. Higher-order Stokes lines appeared at higher pump powers when the Stokes
power became large enough to pump the next-order Stokes line. Figure 8.4 shows the
optical spectrum at a pump power of about 1 kW with five Stokes lines clearly seen.
Each successive Stokes line is broader than the preceding one. This broadening is due
to several competing nonlinear processes and limits the total number of Stokes lines.
Stokes line of up to the 15th order have been generated in the visible region [40].
In these experiments no attempt was made to resolve spectral details of each Stokes
line. In a subsequent experiment [45], the resolution was fine enough to resolve the