Abstract

A finite-difference method (FDM) algorithm has been developed to solve for the eigenvalues, the system effective indices, along with field distributions directly from the scalar Helmholtz equation for both graded-index and step-index waveguides. The algorithm for the FDM is presented along with a summary of the results from the standard programs using the transverse resonance condition to evaluate the optical parameters for step-index waveguides and the WKB method for graded-index waveguides. FDM results are also compared with those obtained from the zero-element method and the propagating beam method for graded-index waveguides. The FDM algorithm developed in this program is evaluated as a tool for use in designing integrated optical circuit elements.

© 1991 Optical Society of America