Nonlinear Fiber Optics - 4 ed. Agrawal

12.1. Intrapulse Raman Scattering 455
Figure 12.1: Left Panel: Measured (a) spectrum and (b) autocorrelation trace of the Raman
soliton at the output of a tapered fiber. Right Panel: Numerically simulated (a) evolution of pulse
spectrum and (b) output spectrum. Dashed curves show the input spectrum. (After Ref. [13];
c○2001 OSA.)
damental solitons of different widths and peak powers. The inverse scattering method
(see Section 5.2.1) shows that their widths and peak powers are related to N as [6]
T k =
T 0
2N + 1 − 2k , P (2N + 1 − 2k)2
k =
N 2 P 0 , (12.1.2)
where k = 1to ¯N. As an example, when N = 2.1, two fundamental solitons created
through the fission process have widths of T 0 /3.2 and T 0 /1.2. The narrower soliton
exhibits a much larger RIFS compared with the broader one because of the T0 −4 dependence
seen in Eq. (12.1.1). For the N = 2.1 example, the enhancement factor for
the narrower soliton is about 105. Figure 12.1 agrees with this scenario as the Raman
soliton, whose spectrum has been shifted by 250 nm, has a width of 62 fs, about 3.3
times smaller than the input pulse width of 205 fs. Numerical simulations reveal that
fission occurs within 2 cm of propagation inside the tapered fiber. The spectrum of the
ultrashort soliton shifts rapidly toward the red side, as dictated by Eq. (12.1.1). After
15 cm, the spectrum has shifted to near 1550 nm. This predicted behavior agrees with
the experimental data qualitatively.
A 60-cm-long photonic crystal fiber having its zero-dispersion wavelength (ZDWL)
at 690 nm was used in a 2002 experiment [16]. Figure 12.2 shows the experimentally
measured output spectra at several average power levels when 70-fs pulses with a 48-
MHz repetition rate at a wavelength of 782 nm were launched into this fiber. After
the input power exceeds a value large enough to ensure N > 1, a Raman soliton is
generated, and its wavelength shifts continuously through RIFS inside the fiber. The
total shift at the output of fiber becomes larger as the input power is increased. The