Ray-optical prediction of radio-wave propagation characteristics in tunnel environments. 1. Theory

TLDR: In this paper, a right-angle wedge with different impedance boundary conditions at its two surfaces is considered, where a functional transformation is used to simplify the boundary conditions, and the eigenfunction solutions for the transformed functions are replaced by integral representations, which are then evaluated by the modified Pauli-Clemmow method of steepest descent.

Abstract: A tunnel is modeled as congregates of walls, with the wall being approximated by a uniform impedance surface. The aim is to get a solution for a canonical problem of a wedge with uniform impedance surface. The diffraction by a right-angle wedge with different impedance boundary conditions at its two surfaces is first considered. A functional transformation is used to simplify the boundary conditions. The eigenfunction solutions for the transformed functions are replaced by integral representations, which are then evaluated asymptotically by the modified Pauli-Clemmow method of steepest descent. The asymptotic solution is interpreted ray optically to obtain the diffraction coefficient for the uniform geometrical theory of diffraction (UTD). The obtained diffraction coefficients are related directly to the Keller diffraction coefficients in the uniform version. The total field is continuous across the shadow of the geometrical optics fields.