Wavelet-Galerkin solver for the analysis of optical waveguides

Abstract

A new set of basis functions based on truncated Gaussian wavelets is proposed for optical waveguide analysis using the well-known Galerkin method. A spatially limited Gaussian wavelet train is formed by judiciously truncating the tails of Gaussian functions. The proposed set of basis functions produces a sparse eigenvalue equation when the wave equation is solved by the Galerkin method. The limited span of the basis functions makes the computation of integrals associated with matrix elements very fast with lower memory requirements. The effectiveness of the proposed basis functions is tested by comparing the results with those obtained by other methods and other basis functions for diffused and step index planar and channel waveguides. The results show a significant reduction in computation time while maintaining good accuracy.