This paper presents a rigorous analysis of the electromagnetic scattering and transmission of misaligned dual metallic grating screens. The Fourier transform and the mode-matching technique are employed to obtain an analytical solution. Numerical results show that misaligned dual metal grating screens exhibit asymmetric scattering and transmission properties with respect to the scattering and transmission angles. Parametric studies are conducted in terms of the lateral displacement and vertical distance between the dual metallic grating screens. For validation, the proposed method is compared with a numerical simulation and good agreement has been achieved.

The scattering problem by metallic gratings has become one of fundamental problems in electromagnetics. In this paper, a thin metallic grating placed in conical mounting is treated as a lossy dielectric grating expressed by complex permittivity and thickness. The solution of the metallic grating by using the matrix eigenvalue calculations is compared with that of the plane grating by using the resistive boundary condition and the spectral Galerkin procedure, and the availability of the resistive boundary condition for thin metallic gratings in conical mounting is investigated. In order to improve the convergence of the solutions of thin metallic gratings, the spatial harmonics of flux densities which are continuous function instead of electromagnetic fields are used.

The growth and saturation characteristics of an electromagnetic (EM) wave in a Smith-Purcell free-electron laser (FEL) with a Bragg cavity are investigated in detail with the aid of numerical simulation based upon the fluid model of the electron beam. To analyze the problem, a two-dimensional (2-D) model of the Smith-Purcell FEL is considered. The model consists of a planar relativistic electron beam and a parallel plate metallic waveguide, which has a uniform grating carved on one plate. For confinement and extraction of EM waves, a Bragg cavity is formed by a couple of reflector gratings with proper spatial period and length, which are connected at both ends of the waveguide. The results of numerical simulation show that a compact Smith-Purcell FEL can be realized by using a Bragg cavity composed of metallic gratings.