Abstract

A modified Galerkin method is used to study the modal behavior of generic integrated optical waveguides down to first-order mode cutoff. The scalar Helmholtz equation is solved through nonlinear mapping of the transverse plane and subsequent Fourier decomposition. The differential equation is thus transformed into the eigenproblem for a specific finite-dimension linear operator. The largest eigenvalues, corresponding to the lowest-order guided modes, are in turn determined by an iterative Arnoldi procedure. Therefore actual diagonalization of a huge coefficient matrix is avoided, and a very large number of field frequency components can be considered.

© 2001 Optical Society of America

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