Hidden rays of diffraction

Abstract

The method of hidden rays was developed to provide approximate but accurate analytical solution to the diffraction coefficients of composite wedges. After ordinary ray-tracing in physical regions is terminated, hidden rays are traced only by applying the usual principle of geometrical optics in the complementary regions, which are defined by the formulation of dual integral equations. The diffraction coefficients are constructed routinely by sum of cotangent functions, which have one-to-one correspondence with not only the ordinary but also hidden rays. The angular period of the cotangent functions is adjusted to satisfy the edge condition at wedge tip. Compared to the physical optics diffraction coefficients, the presented diffraction coefficients show smooth transition from high to low dielectric constant cases due to total reflections on the complementary dielectric interface. The accuracy of the presented diffraction coefficients is assured by showing how closely the null field condition is satisfied in the complementary region.