Plane wave diffraction by a finite parallel-plate waveguide with sinusoidal wall corrugation

The diffraction by a finite parallel-plate waveguide with sinusoidal wall corrugation is analyzed for the E-polarized plane wave incidence using the Wiener-Hopf technique combined with the perturbation method. Assuming that the corrugation amplitude of the waveguide walls is small compared with the wavelength and expanding the boundary condition on the waveguide surface into the Taylor series, the problem is reduced to the diffraction by a flat, finite parallel-plate waveguide with a certain mixed boundary condition. Introducing the Fourier transform for the unknown scattered field and applying an approximate boundary condition together with a perturbation series expansion for the scattered field, the problem is formulated in terms of the zero-order and the first-order Wiener-Hopf equations. The Wiener-Hopf equations are solved via the factorization and decomposition procedure leading to the exact and asymptotic solutions. Taking the inverse Fourier transform and applying the saddle point method, a scattered far field expression is derived explicitly. Scattering characteristics of the waveguide are discussed in detail via numerical examples of the radar cross section (RCS).