Abstract

I present an improved approach to numerical path integration that expands the scope of the method I discussed recently1 and yields the propagation constants and field distributions of all the modes of a dielectric waveguide structure while retaining the ease of implementation, computational simplicity, and ability to accommodate arbitrarily graded refractive-index profiles characteristic of the previous approach. This approach follows that of Yevick and Hermansson² in that the propagation properties are obtained by diagonalizing the propagator of the optical wave equation. It differs from their method in the manner by which the propagator is calculated: they use the propagating beam method, I use the Trotter product formula to obtain a closed form expression for the matrix elements of the propagator. The spectral properties calculable using this method are discussed, and the utility of this method in waveguide design is illustrated by calculating the propagation properties of slab waveguide structures.

© 1987 Optical Society of America