Analysis of Nonlinear Multilayered Waveguides and MQW Structures: A Field Evolution Approach Using Finite-Difference Formulation

In this paper, we present a method of analyzing nonlinear multilayered-planar waveguides and multiple-quantum-well structures. The method is based on scalar and semi-vectorial solutions of Helmholtz's equation devised with a mode-field convergence technique in a finite-difference grid. The approach is general, simple to formulate, and applicable to any arbitrary structures with Kerr-like/non-Kerr-like nonlinearities for determining guided mode characteristics of both TE and TM polarizations and the dispersion relations. We analyze a number of known waveguide structures reported in the literature to test the accuracy and establish the efficacy of the algorithm as a useful analysis recipe for modeling and understanding the modal properties of such nonlinear multilayered waveguides.