The diffraction by a semi-infinite parallel-plate waveguide with sinusoidal wall corrugation is analyzed for the H-polarized plane wave incidence using the Wiener-Hopf technique combined with the perturbation method. Introducing the Fourier transform for the unknown scattered field and applying an approximate boundary condition together with a perturbation series expansion of the scattered field, the problem is formulated in terms of the zero-order and first-order simultaneous Wiener-Hopf equations. The Wiener-Hopf equations are solved via the factorization and decomposition procedure leading to the exact solutions. 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.
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