Scalar analysis of general dielectric waveguides by Fourier decomposition method

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