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
Original Manuscript: July 3, 2000
Revised Manuscript: October 30, 2000
Manuscript Accepted: November 2, 2000
Published: April 1, 2001
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)