Abstract
"New features of the light localization in a nonlinear and graded-index medium in the case of radial symmetry are described analytically. The model of nonlinear graded-index fiber assumes that the dielectric permittivity changes abruptly when the electric field amplitude reaches a certain level. The dielectric permittivity depends on the polar radius according to a parabolic law, in the regions where the electric field amplitude exceeds a certain level. Explicit exact solution to the wave equation is found, in terms of the Whittaker function and the modified Bessel function of the second kind, describing a new type of optical localized structure. The influence of the propagation constant and parameters of the nonlinear graded-index dielectric permittivity on the field profile over the fiber radius is analyzed. It is derived that the core radius and the dielectric permittivity of the core depend on the propagation constant. The dependence of the core radius on the propagation constant causes the appearance of local dispersion."
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