Abstract
The nonstationary (time-dependent) problem of the longitudinal modulation instability of the fundamental mode of a cylindrical waveguide with a nonlinear (Kerr-law) dielectric susceptibility is analyzed numerically and analytically using some integral relations. The cases of low and high intensities for the initial cw beam for different core radii are considered. In the case of high intensities, diffraction has an important role, and the growth-rate curves have special features corresponding to the effect of modulation instability in an unbounded nonlinear medium. These features are investigated analytically using integral relations. In the case of low intensities, diffraction is suppressed and the effect is known to be described by the nonlinear Schr\"odinger equation. The explicit procedure for deriving the growth-rate curves, as well as the equation for the field-envelope function based on the integral relations, is suggested for this case.
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