Abstract

The simulation of photonic circuit elements, such as diode lasers, waveguides, couplers, and turning mirrors, has in the past depended to a great extent upon the use of the paraxial beam propagation method. This method, although easy to use and efficient in terms of computer resources, is entirely inadequate to model many of the devices now being fabricated, because of the restricting assumptions employed in its derivation. In order to overcome these limitations, we solve the 2-D (or 3-D) harmonic Helmholtz equation prior to the introduction of restrictions, resulting in a formulation that includes the following three important features: (1) treatment of adjacent regions of widely different indices of refraction, (2) wide-angle (non-paraxial) beam propagation, and (3) reflection. The solution is obtained by using an iterative technique in order to minimize the required storage. Although the method is numerically intensive at present, future progress in solution techniques coupled with the advent of larger and faster computers is expected to make this method more attractive for a variety of applications. We illustrate the capability of this technique by solving several problems of interest, including energy loss resulting from propagation through a large-angle Y-guide splitter, reflectivity of a facet-terminated waveguide, and the performance of waveguides etched with both first and second order Bragg gratings.

© 1992 Optical Society of America