PROPAGATION OF OPTICAL PULSES THROUGH NON LINEAR PLANAR WAVEGUIDES WITH JUNCTIONS

Abstract

Investigation of spatiotemporal dynamics of optical pulse in step-index planar waveguide with Kerr nonlinearity is presented which is based on numerical solution of a (2D+T) wave equation for slowly varying amplitude of the total field. Effect of emission of radiation field that is specific for open dielectric waveguides is taken into account. This emission can be observed, first, as a result of light beam propagation through waveguide junctions, and second, due to some effects that vary the temporal distribution of all Ultra-short optical pulse propagating in a regular nonlinear waveguide. Two types of junctions in weakly-guiding planar waveguides are under consideration: both wavegauides have the same width and refractive index profile but possess different nonlinear properties, and both waveguides have the same refractive index profile and nonlinearity but their widths are different. In the quasi-static approximation, the problem of optical Pulse propagation through the junctions is reduced to the solution of a 2D equation for the pulse envelope with time coordinate given as a parameter. Spatial transformations of the stationary components of the pulse behind the junctions are studied ill detail depending, on their power and waveguide width. The approach is based on general methods of the theory of Hamiltonian dynamical systems and consists of the following steps: (i) finding the set of stationary nonlinear modes, (ii) investigation of power-dispersion diagrams, and (iii) investigation of global dynamics. Transmittance versus power dependencies demonstrate the applicability of the junctions for pulse shaping and power controlling. In the case of ultrashort optical pulses, self-steepening effect and second-order group velocity dispersion effect are shown to prevent formation of stable spatiotemporal pulse distribution owing to the emission of radiation field outside the guiding region.