Abstract

A Monte Carlo path integral approach to the treatment of propagation problems in integrated optics is presented. Unlike the many methods that work very well for slab waveguides but require orders of magnitude more computer time for channel waveguides, Monte Carlo simulation requires a comparatively modest increase (typically a factor of 2-4) in computer time to treat a channel waveguide to the same degree of accuracy as a slab. We have used Monte Carlo simulation to obtain the propagation constants of the fundamental and first-order modes of a number of dielectric waveguide structures. Excellent agreement has been found in 1-D and 2-D with the fundamental mode propagation constants of the analytically soluble refractive-index profiles involving 1/cosh². For realistic air/Ti:LiNbO₃ diffused waveguides, excellent predictions are obtained for the propagation constant of the fundamental mode. The Monte Carlo evaluation of the first-order mode requires more time, and predictions are obtained with a fair degree of accuracy. These preliminary results are very encouraging for future use of Monte Carlo techniques to describe the optical characteristics of waveguide structures with arbitrary refractive-index profiles.

© 1987 Optical Society of America