Ray-optical analysis of reflection in open-ended parallel plane waveguide. I: TM case

The reflection problem for a TM mode traveling toward the open end of a semi-infinite parallel-plane waveguide, is solved by ray methods. Unlike a previous solution due to Yee, Felsen and Kelley, the present ray-optical solution is a rigorous asymptotic result, i.e., it is identical with the asymptotic expansion of the exact solution when the width of the waveguide is large compared to the wavelength. Numerical results for the modal reflection coefficients are presented and are compared with calculations based on the exact solution. It is found that the agreement between ray-optical and exact values is excellent and even better than in the approach of Yee et al., especially in the vicinity of cutoff frequencies of higher order modes