Nonlinear Fiber Optics - 4 ed. Agrawal

114 Chapter 4. Self-Phase Modulation
Figure 4.25: (a) Experimental spectrum of 109-fs input pulses at the output of a 6-m-long fiber
and predictions of the generalized NLS equation with (b) s = τ R = 0, (c) s = 0, and (d) both s
and τ R nonzero. Letters (A)–(E) mark different spectral features observed experimentally. (After
Ref. [107]; c○1999 OSA.)
in the trace (c). All experimental features, marked as (A)–(E), were reproduced only
when both higher-order nonlinear effects were included in the numerical model. Inclusion
of the fourth-order dispersion was also necessary for a good agreement. Even
the predicted pulse shapes were in agreement with the cross-correlation traces obtained
experimentally.
The SPM and other nonlinear effects such as stimulated Raman scattering and fourwave
mixing, occurring simultaneously inside optical fibers, can broaden the spectrum
of an ultrashort pulse so much that it may extend over 100 nm or more. Such extreme
spectral broadening is called supercontinuum, a phenomenon that has attracted considerable
attention in recent years because of its potential applications [110]–[116]. Pulse
spectra extending over as much as 1000 nm have been generated using the so-called
highly nonlinear fibers (see Chapter 11). Chapter 12 is devoted to the phenomenon of
supercontinuum generation and other novel nonlinear effects that have become possible
with highly nonlinear fibers. In particular, Section 12.1 shows that, under suitable
conditions, the RIFS can be both enhanced and suppressed in such fibers.
Problems
4.1 A 1.06-μm Q-switched Nd:YAG laser emits unchirped Gaussian pulse with 1-nJ
energy and 100-ps width (FWHM). Pulses are transmitted through a 1-km-long
fiber having a loss of 3 dB/km and an effective mode area of 20 μm 2 . Calculate
the maximum values of the nonlinear phase shift and the frequency chirp at the
fiber output.