WIENER-HOPF ANALYSIS OF THE H-POLARIZED PLANE WAVE DIFFRACTION BY A FINITE SINUSOIDAL GRATING (Invited Paper)

Abstract

Abstract-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.

Plane Wave Diffraction by a Finite Parallel-Plate Waveguide With Sinusoidal Wall Corrugation

“…The aim of this paper is to provide further generalization to our previous analysis carried out for the diffraction problems involving the semi-infinite parallel-plate waveguide with sinusoidal corrugation [32,33] and the finite sinusoidal grating [34][35][36]. We shall analyze in this paper the plane wave diffraction by a finite parallel-plate waveguide with sinusoidal wall corrugation for the E-polarized plane wave incidence.…”

“…In [32,33], we have analyzed the problem considered by Chakrabarti and Dowerah via a different Wiener-Hopf approach for both E and H polarizations, and derived various new expressions of the scattered field. We have also considered a finite sinusoidal grating as another important generalization to Das Gupta [30] and analyzed the plane wave diffraction for both E and H polarizations via a hybrid Wiener-Hopf and perturbation approach [34][35][36].…”

Complex eigenvalues of natural TM ‐oscillations in an open resonator formed by two sinusoidally corrugated metallic strips

“…Turning to the concrete content of the present article, our investigation focuses on perfectly conducting surface‐relief gratings with sinusoidal corrugation. For a long time, plane wave diffraction problems for both E‐ and H‐polarization for finite sinusoidal single gratings [16] and binary gratings [17] have been analysed by the Wiener–Hopf technique combined with a perturbation method. In these articles, the initial stage of the solution assumes that the depth of the grating is small compared with the wavelength.…”

Diffraction of EM-wave by a slit of finite width with Dirichlet conditions in cold plasma

“…In electromagnetic theory and optics, the phenomena of scattering and diffraction by periodic structures and gratings have great importance. Several numerical and analytical techniques such as Green's function-dual series approach, method of analytical regularization, mode-matching, Yasuura method, the finite difference time domain method and Wiener-Hopf techniques, have been developed so far and diffraction phenomena for many periodic structures have been studied [1][2][3][4][5][6][7][8][9][10]. Most of the diffraction problems for such types of complex geometries are tackled by using the Riemann-Hilbert approach, Mode-Matching and Wiener-Hopf technique.…”