Abstract

We study the simple approximation for the fundamental mode of a rectangular channel waveguide by a Gaussian field distribution. This method is based on determining the value of the propagation constant for the mode by using variational principles, along with a wave field approximation. The propagation constant is an important quantity, because the properties of guided modes and their interactions are determined by their propagation constants. The method presented results in a simple and fast approximation for the propagation constant and a best fit wave field approximation. For initial demonstration of the theory, the symmetric planar slab waveguide was studied. The data shows that the results from this method are consistent with previously published results. The approximations can be improved by adding more accuracy to the wave field approximation via adding offset or width parameters, which can be easily calculated. Although this initial paper discusses planar slab and rectangular geometries specifically, the method allows for different index profiles and cross-sectional geometries.

© 1991 Optical Society of America