Analysis of integrated optical waveguides: variational method and effective-index method with built-in perturbation correction

We show analytically that for the modal analysis of rectangular waveguides, the recently developed effective-index method with built-in perturbation correction is identical to the first-iteration cycle of the variational method that we had developed earlier [Opt. Quantum Electron. 12, 517 (1989)]. We also show that in a number of cases the accuracy improves considerably through iteration beyond the first cycle.