Plane-Wave Diffraction by a Slit Formed by Two Semi-Infinite Parallel-Plate Waveguides—Part I: The Case of H Polarization

Abstract

The diffraction by a slit formed by two semi-infinite parallel-plate waveguides is rigorously analyzed using the WienerÀHopf technique for the H-polarized plane-wave incidence. Introducing the Fourier transform for the scattered field and applying boundary conditions in the transform domain, the problem is formulated in terms of the simultaneous WienerÀHopf equations, which are solved via the factorization and decomposition procedure leading to exact and highfrequency asymptotic solutions. Taking the inverse Fourier transform and applying the saddle point method, the scattered field in real space is derived. Numerical examples of the far-field intensity are presented and scattering characteristics of the slit are discussed.

Plane-Wave Diffraction by a Slit Formed by Two Semi-Infinite Parallel-Plate Waveguides—Part II: The Case of E Polarization

“…In this two-part article, we have rigorously analyzed the plane-wave diffraction by a slit formed by two semi-infinite parallel-plate waveguides for both H polarization (Part I [6]) and E polarization (Part II, this article) using the WienerÀHopf technique. The geometry considered here is of the modified WienerÀHopf geometry of the first kind; hence, we have applied the method of solution developed in our previous article [7] to obtain a high-frequency asymptotic solution for this waveguide slit problem.…”

“…Numerical examples are presented for various physical parameters, and the scattering characteristics of the waveguide slit are discussed. Some comparisons with the results for H polarization [6] are given. The time factor is assumed to be expðÀixtÞ and suppressed throughout the article.…”

“…By using the method of asymptotic solutions developed by [7,8] and making some manipulations, as was done in Part I [6], we finally obtain that…”

“…In Part I of this two-part article [6], we considered the same waveguide slit geometry as in [3] and rigorously analyzed the H-polarized plane wave diffraction using the WienerÀHopf technique. As a result, we successfully have obtained a novel high-frequency solution to the waveguide slit problem in the form of a complete asymptotic series by using rigorous asymptotics [7,8] developed by the authors for the analysis of modified WienerÀHopf geometries.…”