Nonlinear Fiber Optics - 4 ed. Agrawal

164 Chapter 5. Optical Solitons
RIFS (THz)
7
6
5
4
3
2
1
(a)
250
C = 0
(b)
0
0.1 200
0.2
0.2
Pulse width (fs)
150
100
50
0.1
C 0
= 0
0
0 2 4 6 8 10
Distance (m)
0
0 2 4 6 8 10
Distance (m)
Figure 5.20: Evolution of (a) Raman-induced frequency shift and (b) pulse width when a fundamental
soliton with T 0 = 50 fs propagates inside a 10-m-long fiber. The input chirp parameter
C 0 is varied in the range of 0 to 0.2.
The solid curve in Figure 5.20 shows the case C 0 = 0 that corresponds to standard
solitons. The pulse width is indeed maintained in the beginning, as expected, but begins
to increase after 2 m because of the RIFS and TOD effects.
The most important feature seen in Figure 5.20 is that the RIFS grows linearly
with z at the early stages of pulse evolution and then becomes saturated. The physical
reason behind this saturation is related to chirping of solitons. For an unchirped soliton
(C 0 = 0), the magnitude of RIFS becomes comparable to the spectral width of the
pulse (about 2 THz) at a distance of about 2 m, and it begins to affect the soliton
by chirping it, as evident from the last term in Eq. (5.5.18). The use of Eq. (5.5.19)
becomes inappropriate under such conditions. The dashed and dash-dotted lines show
that even a relatively small chirp affects the RIFS considerably. For positive values of
C p , the pulse is initially compressed, as expected for β 2 C p < 0, and then broadens after
attaining its minimum width at a distance of about 1 m. For this reason, Ω p initially
increases faster than the unchirped case, but also saturates at a lower value because
of pulse broadening. The main point to note is that the chirp can increase the RIFS
when C p > 0. For C p < 0, pulse begins to broaden immediately, and RIFS is reduced
considerably.
The RIFS of solitons was observed in 1986 using 0.5-ps pulses obtained from a passively
mode-locked color-center laser [189]. The pulse spectrum was found to shift as
much as 8 THz for a fiber length under 0.4 km. The observed spectral shift was called
the soliton self-frequency shift because it was induced by the soliton itself [190]. However,
as discussed in Section 4.4.3, RIFS is a general phenomenon and occurs for all
short pulses, irrespective of whether they propagate as a soliton or not [167]. The shift
is relatively large if a pulse maintains its width along the fiber. In recent years, RIFS
has attracted considerable attention for producing femtosecond pulses whose wavelength
can be tuned over a wide range by simply propagating them through tapered or
other microstructured fibers [211]–[214]. This scheme is discussed in more detail in
Section 12.1.