Nonlinear Fiber Optics - 4 ed. Agrawal

232 Chapter 7. Cross-Phase Modulation
where different curves correspond to values of the power ratio P 2 /P 1 in the range 0–2.
The right graph shows the effect of group-velocity mismatch for equal beam powers
by varying the parameter δ = |v −1
g1 − v−1 g2
| in the range 0–3 ps/m. These results show
that XPM-induced modulation instability can occur in the normal-GVD regime for relatively
small values of δ. The peak gain of about 5 m −1 at the 100-W power level
implies that the instability can develop in fibers a few meters long.
7.2.2 Experimental Results
The experimental attempts to observe the XPM-induced modulation instability for normal
GVD have focused mostly on the case of two polarization components of a single
beam (see Section 6.4). It appears that this instability is difficult to observe in the case
of two beams with different wavelengths. The reason is related to the fact that Eqs.
(7.1.15) and (7.1.16) neglect four-wave mixing. The neglect of the four-wave-mixing
terms can be justified when the wavelength difference is so large that phase matching
cannot occur [16]–[18]. However, to observe modulation instability, the wavelength
difference needs to be reduced to ∼1 nm or less. Four-wave mixing then becomes
nearly phase matched and cannot be ignored. Indeed, a careful analysis that includes
GVD to all orders shows that XPM-induced modulation instability is not likely to occur
in the normal-dispersion region of conventional silica fibers [18]. It can occur in
especially designed dispersion-flattened fibers in which two normal-GVD regions are
separated by an intermediate wavelength region of anomalous GVD. In such fibers, it is
possible to match the group velocities even when the wavelengths of two beams differ
by 100 nm or more.
The XPM-induced modulation instability has been observed when one of the beams
propagates in the normal-GVD region while the other beam experiences anomalous
dispersion. In a 1988 experiment [21], a pump-probe configuration was used such
that the 1.06-μm pump pulses experienced normal GVD, while 1.32-μm probe pulses
propagated in the anomalous-GVD regime of the fiber. When the pump and probe
pulses were launched simultaneously, the probe developed modulation sidebands, with
a spacing of 260 GHz at the 0.4-W peak-power level of pump pulses, as a result of
XPM-induced modulation instability. This configuration can be used to advantage if
the pump beam is in the form of intense pulses whereas the other beam forms a weak
CW signal. The weak CW beam can be converted into a train of ultrashort pulses
because it is amplified through XPM-induced modulation instability only when the
two waves are present simultaneously [8].
In an experimental realization of the preceding idea [22], 100-ps pump pulses were
obtained from a 1.06-μm, mode-locked, Nd:YAG laser while an external-cavity semiconductor
laser provided the weak CW signal (power 500 W), the signal spectrum developed sidebands
indicative of the XPM-induced modulation instability. The experimental results were
in qualitative agreement with the numerical solutions of Eqs. (7.1.15) and (7.1.16) and
indicated that the CW signal was converted into a train of picosecond pulses.