EXACT SOLUTION OF PLANE WAVE DIFFRACTION IN SEMI INFINITE PARALLEL PLATE WAVEGUIDES USING THE MATRIX WIENER-HOPF EQUATION

Abstract

This paper investigates the diffraction of a time-harmonic plane electromagnetic wave by a parallel-plate waveguide with mixed boundary conditions, consisting of a Neumann upper plate and a Dirichlet lower plate. The waveguide geometry comprises a two-part impedance plane combined with a perfectly conducting plate, forming a semi-infinite structure. By applying Fourier transform techniques, the Helmholtz equation governing the wave field is reduced to a matrix Wiener–Hopf equation, which is solved using kernel factorization and analytic continuation. The solution leads to two coupled infinite systems of linear algebraic equations corresponding to the unknown spectral functions. The effects of waveguide height, incidence angle, and mixed boundary conditions on the diffracted field are analyzed. The results indicate that the Neumann–Dirichlet combination significantly modifies the field distribution compared to symmetric boundary cases, particularly in the far-field scattering pattern. The proposed methodology provides a coherent framework for investigating diffraction in waveguides with mixed boundaries and is applicable to electromagnetic shielding, waveguide irregularities, and acoustic systems. It also incorporates recent advances in Wiener-Hopf techniques, emphasizing the relevance and novelty of this extended formulation