Abstract

We present a constrained variational finite-difference method for calculating the modal properties of dielectric waveguide structures and compare the predictive results of the method with measurements of the coupling lengths of semiconductor directional couplers. The method is based on a finite-difference treatment of a functional of the scalar Helmholtz equation and contains no adjustable parameters. The functional is minimized subject to a field normalization constraint whereby the functional becomes the modal propagation constant. This minimization is implemented numerically using successive overrelaxation of a Gauss-Seidel iteration scheme. The resulting numerical method is easily implemented numerically and rather efficiently: the 2-D modal field distribution and propagation constants are typically calculated within a minute of CPU time on a VAX 8650. To illustrate the utility of this method in waveguide design, we compared calculated and measured coupling lengths for a variety of GaAs-AlGaAs rib waveguide directional couplers. (For this set of experiments the average experimental standard deviation was 13% of the mean.) The difference between the predicted and measured coupling lengths was less than the experimental uncertainty (one standard deviation) in all cases.

© 1987 Optical Society of America