Abstract

A finite difference method usually gives rise to large matrix eigenvalue problems when it is used to discretize waveguide mode problems. Iterative methods exist and they typically have a slow convergence. We develop a domain decomposition method in connection with the Rayleigh Quotient Iteration. The method has a fast convergence, so that eigenvalues (of the discretized problem) are computed to full precision in only a few iterations. The required number of operations in each iteration is significantly reduced by the domain decomposition technique.

© 2006 Optical Society of America