Improved scalar analysis of integrated optical structures by the mapped Galerkin method and Arnoldi iteration

A modified Galerkin method is used to study the modal behavior of generic i ntegrated optical waveguides down to first-order mode cutoff. The scalar He lmholtz equation is solved through nonlinear mapping of the transverse plan e and subsequent Fourier decomposition. The differential equation is thus t ransformed into the eigenproblem for a specific finite-dimension linear ope rator. The largest eigenvalues, corresponding to the lowest-order guided mo des, are in turn determined by an iterative Arnoldi procedure. Therefore ac tual diagonalization of a huge coefficient matrix is avoided, and a very la rge number of field frequency components can be considered. (C) 2001 Optica l Society of America.