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

Vectorial analysis of optical waveguides by the mapped Galerkin method based on E fields

Jinbiao Xiao, Xiaohan Sun, and Mingde Zhang
J. Opt. Soc. Am. B 21(4) 798-805 (2004)

Propagation of nonparaxial beams with a modified Arnoldi method

Q. Luo and C. T. Law
Opt. Lett. 26(21) 1708-1710 (2001)

Wavelet-Galerkin solver for the analysis of optical waveguides

Samit Barai and Anurag Sharma
J. Opt. Soc. Am. A 26(4) 931-937 (2009)

Helmholtz beam propagation in rib waveguides and couplers by iterative Lanczos reduction

R. P. Ratowsky, J. A. Fleck, and M. D. Feit
J. Opt. Soc. Am. A 9(2) 265-273 (1992)

Scattering of the transverse magnetic modes from an abruptly ended strongly asymmetrical slab waveguide by an accelerated integral equation technique

Alexander B. Manenkov, George P. Latsas, and Ioannis G. Tigelis
J. Opt. Soc. Am. A 18(12) 3110-3118 (2001)