Abstract
A nonstationary two-dimensional problem of propagation of a femtosecond pulse in a planar waveguide comprised of linear and nonlinear sections connected in series is solved using the finite-difference method. The accuracy of the finite-difference techniques is analyzed as applied to solution of stationary and nonstationary two-dimensional quasi-linear equations of light propagation in step-index waveguides. The effects of wave instability on the dynamics of the spatiotemporal pulse distribution in a nonlinear waveguide are studied. It is shown that, due to the retarded nonlinear response of the medium and the dependence of the group velocity of the pulse on its intensity, radiation continuously leaks from the fiber core to the cladding as the pulse propagates along the fiber.
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