Wiener-Hopf Analysis of the H-Polarized Plane Wave Diffraction by a Finite Sinusoidal Grating

The diffraction by a finite sinusoidal grating is analyzed for the H-polarized plane wave incidence using the Wiener-Hopf technique combined with the perturbation method. Assuming the depth of the grating to be small compared with the wavelength and approximating the boundary condition on the grating surface, the problem is reduced to the diffraction problem involving a flat strip 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 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, the scattered field expression is explicitly derived. Scattering characteristics of the grating are discussed in detail via numerical examples of the far field intensity.