Spatio-temporal dynamics of light beams in non-linear dielectric waveguides with sharp discontinuities

The goals of the work are conditioned mostly by elaboration of novel guiding structures, nonlinear materials and laser sources generating ultra-short optical pulses. The spatial dynamics of stationary light beams, as well as the spatio-temporal dynamics of non-stationary light beams, on step-like discontinuities of dielectric waveguides with embedded Kerr-like non-linearity is investigated in detail, taking account of the phenomenon of radiation field leakage outside the guiding region. The method of investigation is based on the reduction of the initial boundary problem to the solution of the non-linear parabolic wave equation. For numerical simulations, the FD-BPM and the TD-FD-BPM are applied.