Super-Gaussian approximation of the fundamental radial mode in nonlinear parabolic-index optical fibers

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Abstract
Using a direct variational technique involving super-Gaussian trial functions, we find approximate solutions for the fundamental radial mode of an optical wave propagating in a nonlinear parabolic-index fiber. A detailed examination is made of the amplitude, width, radial profile, and longitudinal phase shift of the stationary solutions that represent a two-dimensional balance among diffraction, nonlinear self-focusing, and linear wave guiding. For pulse powers below the self-focusing power, the stationary solutions are stabilized by the parabolic index variation.