Ray theory of diffraction by a half‐sheet parallel to a flat earth

Abstract

In this paper, the diffraction by a half‐sheet parallel to a flat earth for H‐ and E‐polarized plane waves are discussed. The half‐sheet is assumed to be perfectly conducting, and the flat earth is an imperfectly conducting dielectric with the complex refractive index n. This problem is solved by using the angular spectrum proposed by Clemmow, which may be also solved by using the Wiener‐Hopf technique. When kd is large, the diffraction fields can be approximated by the geometrical rays even for small r except in the neighborhood of θ = π/2 and 3π/2. Here, r and θ are polar coordinates of the observation point, with the origin as the edge, and d is the distance between the half‐sheet and the flat earth. The far field can be approximated by the simple geometrical rays in all regions (0 < θ < π). The interaction between the edge and the flat earth can be evaluated even for small kd. Exact values by the numerical integration show that these approximate solutions can give very good accuracy even for small r except in the neighborhood of θ = π/2 and 3π/2. These results will give a fundamental concept to the understanding of the diffraction by a finite conducting plane over a flat earth.

Characterization of a resistive half plane over a resistive sheet

“…This field is due to currents excited on the half plane which can be represented by an angular spectral integral [9]. Accounting for the reflections from (and transmissions through) the resistive plane at y = -d, the total scattered field is given by [3] H: = L [1 + r(sina) e-j2kdsin a l…”

“…1). The corresponding exact diffraction coefficient is derived for this configuration with an H-polarized illumination using the dual integral equation method, following a development similar to that in [3], [4]. The encountered Wiener-Hopf split function is factorized via an efficient numerical procedure discussed in [7].…”

Characterization of a resistive half plane over a resistive sheet

“…The angular spectrum method set forth by Booker and Clemmow has been applied to many diffracting structures composed of a half plme over a substrate [l], [2]. In this paper we particularly consider the diffraction by a resistive half plane vertically displaced from a uniform resistive sheet (see Fig.…”

“…1). The corresponding exact diffraction coefficient is derived for this configuration with an H-polarized illumination using the dual integral equation method, following a development similar to that in [2], [3]. The encountered Wiener-Hopf split fun( tion is factorized via an efficient numerical procedure discussed in [3].…”