Ray Theory of Diffraction by Open-Ended Waveguides. I. Field in Waveguides

Abstract

This paper presents an extension of Keller's ray method to problems involving two or more parallel plates. The approach used here is to solve a canonical problem (two staggered plates) in a rigorous manner, and then extract its dominant asymptotic terms so that the result admits ray interpretation. It is found that the coupling effect between two plates may be accounted for by introducing two multiplicative factors G₊(k cos θ₀) and G₊(k cos θ) to the conventional half‐plane diffraction coefficients, where (θ₀, θ) are the directions of incoming and outgoing rays at the edge. The function G₊(α) is the ``plus part'' of the transformed Green's function G(α) = 1 − exp [−2b(α² − k²)^½] in the Wiener‐Hopf technique, and b is the guide width. A table for G₊(k cos θ) is provided so that the calculation of the modified field on the rays can be accomplished even with a slide rule. An application of the present ray method to the problem of radiation from an unflanged open‐ended parallel‐plate waveguide recovers the exact solution obtainable by the Wiener‐Hopf technique. In Paper I of this series of papers, we present the main theory and discuss the field in waveguide, while in Paper II the field in free space, particularly that on the shadow boundary, will be examined.