Método rigoroso das diferenças finitas em análise de estruturas de guias dielétricos anisotrópicos com perfil de índice de refração variável

Abstract

A rigorous, general and versatil finite-difference formulation for the analysis of the propagation characteristics in structures, having the dielectric waveguide as the basic element, is presented here. In this formulation, the finite-diff erence method is used in the numerical solution of the scalar wave equation, written in terms of the transverse components of the magnetic field. As a result, a conventional eigenvalue problem is obtained without the presence of spurious modes (present in previous formulations), due to the implicit inclusion of the divergence of the magnetic field equal to zero. The general case of biaxial anisotropic dielectrics is considered, with the refractive index profile varying arbitrarily in the waveguide cross section. Dispersion characteristics for isolated and parallel coupled dielectric waveguides are calculated. The theoretical development was then used to solve particular problems and the results agree with those available from other methods. Results were obtained for a variety of guiding wave structures, of much interest, particularly for the development of integrated optics.