Nonlinear Fiber Optics - 4 ed. Agrawal

462 Chapter 12. Novel Nonlinear Phenomena
Figure 12.7: (a) Experimental and (b) numerical spectra plotted as a function of propagation
distance when 200-fs pulses are launched with 230-W peak power into a photonic crystal fiber
exhibiting two ZDWLs. A darker shading represents higher power. A vertical dashed line marks
the location of second frequency where β 2 = 0. (After Ref. [39]; c○2003 AAAS.)
frequency ω d associated with the NSR. As mentioned earlier, Eq. (12.1.7) predicts
that the frequency shift Ω d ≡ ω d −ω s becomes negative for solitons propagating in the
anomalous-GVD region near the second ZDWL (where β 3 < 0), resulting in the NSR
that lies in the infrared region beyond it. It turns out that spectral recoil from this NSR
cancels the RIFS as the soliton approaches the second ZDWL [40].
Figure 12.7(a) shows the spectral evolution of 200-fs pulses, launched with a peak
power of 230 W at a wavelength of 860 nm, into a photonic crystal fiber exhibiting β 2 =
0 at two wavelengths near 600 and 1300 nm [39]. Under these experimental conditions,
the launched pulse forms a fourth-order soliton (N = 4) that undergoes fission and
creates 4 fundamental solitons. The most intense soliton has a width of only about
28.6 fs and shifts rapidly toward the red side through the RIFS. The spectra of other
solitons shifted less because of their larger widths. The shortest soliton approaches
the second β 2 = 0 frequency (shown by a vertical dashed line) at a distance of about
1.25 m. As seen in Figure 12.7, its spectrum suddenly stops shifting, a clear indication
that the RIFS is cancelled beyond this point. At the same time, a new spectral peak
appears on the longer-wavelength side of the second ZDWL. This peak represents the
NSR emitted by the soliton. Its frequency is smaller (and wavelength is larger) than
that of the Raman soliton because of a change in the sign of β 3 .
The generalized NLS equation (2.3.36) was used to simulate pulse propagation under
experimental conditions [40], and the results are shown in Figure 12.7(b). The
agreement with the experimental data is excellent, although some quantitative differences
are also apparent. The main reason for these differences is related to the use of
the approximate form of the Raman response function h R (t) given in Eq. (2.3.40). As
discussed in Section 2.3.2, this form approximates the Raman-gain spectrum seen in
Figure 8.1 with a single Lorentzian profile. The use of h R (t) based on the actual gain
spectrum (see Figure 2.2) should provide a better agreement.
The question is why the emission of dispersive waves near the second ZDWL suppresses
the RIFS in Figure 12.7. To answer it, we need to understand how the energy