Scalar analysis of general dielectric waveguides by Fourier decomposition method and Lanczos reduction

The scalar Helmholtz eigenproblem for dielectric waveguides is solved by ex pressing the field in a series of sines in the transverse plane (Fourier de composition). A matrix eigenproblem is correspondingly built up, where the refractive index distribution is represented either by a grid of homogeneou s rectangles or by polynomial functions defined over rectangular domains. F inally, the Lanczos reduction technique is used to calculate the matrix eig enpairs corresponding to guided modes. This allows to examine very large-si zed cases without physically storing huge nonsparse matrices. In this work, a few examples of propagation analysis are shown referring to both step-in dex and graded-index integrated optical structures, and the calculation res ults are compared with those obtained by a commercial simulation software a nd the effective index method.