Analysis Of A Dielectric Channel Waveguide Diffused In An Anisotropic Substrate With A Gaussian-Gaussian Index Of Refraction Profile Using The Finite-Difference Method

Abstract

A dielectric channel waveguide diffused in an isotropic (or anisotropic) substrate wjith an index of refraction profile itrarily in the wav ide cross section is analyzed a sigorous formu e finite-difference method. In this formulation the finite-dif ference method is used in the numerical solution of the wave equation written in terms of the transverse corn onents of the magnetic field. As a result, a conventional eigenvalue problem is obtained. The elimination of the spurious modes (observed in previous formulations) is obtained by the implicit inclusion of the divergence of the magnetic field equal to ze ro . The formulation is general and may be applied in the analysis of various structures of practical interest such as in millimeter and optical integrated circuits.