Abstract
We investigate the modulational instability of optical pulses
propagating in a lossless fiber where both effects of relaxation and
saturation of the nonlinearity are taken simultaneously into account.
The saturation of the nonlinearity is incorporated in the relaxation
dynamics of the Kerr response. We calculate the exact dispersion
relation for harmonic perturbations over the stationary solution. In the
anomalous dispersive regime, the gain spectrum exhibits two bands in the
fast relaxation regime. The low energy band is reduced by the saturation
of the nonlinearity but is roughly insensitive to the nonlinearity
response time. The high energy band is mainly due to the Raman response.
These frequency bands superpose for fast relaxation responses and a new
behavior sets up. In the normal dispersive regime, a single instability
band sets up associated with the finite response time of the
nonlinearity with distinct features for fast and slow nonlinear
relaxation. (c) 2008 Optical Society of America
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