Diffraction by a Semi-Infinite Parallel-Plate Waveguide With Sinusoidal Wall Corrugation: Combined Perturbation and Wiener-Hopf Analysis

Abstract—The diffraction by a semi-infinite parallel-plate waveguide with sinusoidal wall corrugation is analyzed for the E-polarized plane wave incidence using the Wiener-Hopf technique together with the perturbation method. The problem is formulated in terms of the simultaneous Wiener-Hopf equations by introducing the Fourier transform for the unknown scattered field and applying approximate boundary conditions in the transform domain. Employing the factorization and decomposition procedure together with a perturbation series expansion, the zero- and first-order solutions of the Wiener-Hopf equations are obtained. Explicit expressions of the scattered field inside and outside the waveguide are derived analytically by taking the inverse Fourier transform and applying the saddle point method. Far field scattering characteristics of the waveguide are discussed in detail via representative numerical examples. 1.