Nonlinear Fiber Optics - 4 ed. Agrawal

124 Chapter 5. Optical Solitons
Figure 5.2: Autocorrelation trace and optical spectrum of 100-ps input pulses showing evidence
of modulation instability at a peak power of 7.1 W. (After Ref. [12]; c○1986 APS.)
One may wonder whether modulation instability can occur in the normal-dispersion
region of optical fibers under certain conditions. It turns out that cross-phase modulation,
occurring when two optical beams at different wavelengths or with orthogonal
polarizations propagate simultaneously, can lead to modulation instability even in normally
dispersive fibers. This case is discussed in Chapters 6 and 7. Even a single CW
beam can become unstable in a normally dispersive medium if it responds slowly [24].
Modulation instability can also occur for β 2 > 0 if the fiber has two zero-dispersion
wavelengths. This is the case for dispersion-flattened fibers [25]. This is also the case
for tapered and other microstructured fibers in which a narrow core changes dispersive
properties of the fiber considerably [26]. In such fibers, the gain spectrum of modulation
instability exhibits a second peak even in the case of anomalous dispersion.
5.1.3 Experimental Results
Modulation instability in the anomalous-dispersion regime of optical fibers was first
observed in an experiment in which 100-ps (FWHM) pulses from a Nd:YAG laser
operating at 1.319 μm were transmitted through a 1-km-long fiber having β 2 ≈−3
ps 2 /km [12]. Figure 5.2 shows the autocorrelation trace and the optical spectrum measured
at the fiber output for a peak power P 0 = 7.1 W. The location of spectral sidebands
is in agreement with the prediction of Eq. (5.1.9). Furthermore, the interval
between the oscillation peaks in the autocorrelation trace is inversely related to Ω max
as predicted by theory. The secondary sidebands seen in Figure 5.2 are also expected
when pump depletion is included. In this experiment, it was necessary to use 100-ps
pulses rather than CW radiation to avoid stimulated Brillouin scattering (see Chapter
9). However, as the modulation period is ∼1 ps, the relatively broad 100-ps pulses
provide a quasi-CW environment for the observation of modulation instability.
In a related experiment, modulation instability was induced by sending a weak
CW probe wave together with the intense pump pulses [13]. The probe was obtained
from a single-mode semiconductor laser whose wavelength could be tuned over a few
nanometers in the vicinity of the pump wavelength. The CW probe power of 0.5 mW
was much smaller compared with the pump-pulse peak power of P 0 = 3 W. However,
its presence led to breakup of each pump pulse into a periodic pulse train whose period
was inversely related to the frequency difference between the pump and probe waves.