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
Michele A. Forastiere and Giancarlo C. Righini, "Improved scalar analysis of integrated optical structures by the mapped Galerkin method and Arnoldi iteration," J. Opt. Soc. Am. A 18, 966-974 (2001)