Propagator-based calculation of the propagation properties of dielectric waveguide structures

A simple expression for the propagator of a dielectric waveguide structure with an arbitrarily graded refractive-index profile is presented. This expression simplifies considerably the calculation of the propagation properties of dielectric waveguide structures described by z-independent paraxial optical Hamiltonians. The expression is based on the use of a short-distance approximation to simplify the formal path integral solution to the paraxial optical wave equation. The expression is incorporated into a simple and efficient numerical method for calculation of the propagation properties of dielectric waveguides with arbitrarily graded refractive-index profiles. The accuracy of this approach and its potential for use in optical design are illustrated by calculating the propagation constants and optical field distributions for a graded-index slab waveguide and a slab waveguide array.