Nonlinear Fiber Optics - 4 ed. Agrawal

468 Chapter 12. Novel Nonlinear Phenomena
Figure 12.13: Measured phase-matched wavelengths (dashed lines) as a function of pump wavelength
for a birefringent photonic crystal fiber when pump light is polarized along the major or
minor axis of the fiber. The solid curves show the theoretical prediction based on the average
dispersion. (After Ref. [54]; c○2004 OSA.)
out a linear stability analysis of the coupled NLS equations for the two orthogonally
polarized modes [52]. The two cases of low and high birefringence were studied for a
narrow-core tapered fiber with two ZDWLs, and new instability bands were found to
occur.
In a 2004 experiment, a 20-m-long photonic crystal fiber with a relatively low birefringence
was used to study the FWM process by launching into it CW light from a
Ti:sapphire laser tunable from 650 to 830 nm [54]. This fiber exhibited two ZDWLs
near 755 and 1235 nm that were different for the two orthogonally polarized modes.
The first set of these occurred near 755 and 785 nm for the fast and slow modes, respectively.
Multiple semiconductor lasers operating at 975, 1064, 1312, and 1493 nm
were employed to seed the FWM process. Figure 12.13 shows the phase-matched
wavelengths (square data points) measured as a function of pump wavelength when
the pump and seed fields were polarized along one of the principal axes of the fiber.
The solid curve is identical to that in Figure 12.12 and is based on the average dispersion
values, as it was not possible to characterize the dispersion separately for the fast
and slow modes. Even though a quantitative agreement is not expected, the qualitative
behavior agrees well with the predictions of a scalar theory.
The birefringence of the 4-m-long microstructured fiber used in another experiment
was characterized carefully before observing the vector modulation instability [44].
Figure 12.14(a) shows the measured optical spectra when nanosecond pulses with 90-
W peak power at a wavelength of 624.5 nm were launched into the fiber such that the
two orthogonally polarized modes were equally excited. Under such conditions, the
two sidebands at the signal and idler wavelengths should be orthogonally polarized, a
feature verified experimentally. Moreover, the predicted frequency shift of 3.85 THz
at which the instability gain peaked in Figure 12.14(b) agreed well with the measured
value of 3.9 THz. Such a large frequency shift of sidebands at relatively low pump
powers was possible because of a relatively large value of the nonlinear parameter