In this paper, electromagnetic scattering by infinite double two-dimensional periodic array of resistive upper and lower elements is considered. The electric field equations are solved by using the moment method in the spectral domain. Some numerical results are shown and frequency selective properties are discussed.

Frequency Selective Screens (FSS) with conductor or complementary aperture array are investigated. The electric current distribution on conductor or the magnetic current distribution on aperture is determined by the moment method in the spectral domain. In addition, the power reflection coefficients are calculated and the scattering properties are considered.

A full-wave analysis for the scattering problem of infinite periodic arrays on dielectric substrates excited by a circularly-polarized incident wave is presented. The impedance boundary condition is solved by using the moment method in the spectral domain. Numerical results are given and scattering properties are discussed.

In the scattering problem of dielectric gratings in conical mounting, we have considered and formulated scattering fields using transverse electric (TE) and transverse magnetic (TM) waves. This paper formulates scattering fields by superpositions of right-circularly (RC) and left-circularly (LC) polarized waves through the matrix eigenvalue method.

In the shadow theory, a new description and a physical mean at a low grazing limit of incidence on gratings in the two dimensional scattering problem have been discussed. In this paper, by applying the shadow theory to the three dimensional problem of multilayered dielectric periodic gratings, we formulate the oblique primary excitation and introduce the scattering factors through our analytical method, by use of the matrix eigenvalues. In terms of the scattering factors, the diffraction efficiencies are defined for propagating and evanescent waves with linearly and circularly polarized incident waves. Numerical examples show that when an incident angle becomes low grazing, only specular reflection occurs with the reflection coefficient -1, regardless of the incident polarization. It is newly found that in a circularly polarized incidence case, the same circularly polarized wave as the incident wave is specularly reflected at a low grazing limit.

We propose a new analytical method for a composite dielectric grating embedded with conducting strips using scattering factors in the shadow theory. The scattering factor in the shadow theory plays an important role instead of the conventional diffraction amplitude. By specifying the relation between scattering factors and spectral-domain Green's functions, we derive expressions of the Green's functions directly for unit surface electric and magnetic current densities, and apply the spectral Galerkin method to our formulation. From some numerical results, we show that the expressions of the Green's functions are valid, and analyze scattering characteristics by composite gratings.

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.

In the scattering problem of periodic gratings, at a low grazing limit of incidence, the incident plane wave is completely cancelled by the reflected wave, and the total wave field vanishes and physically becomes a dark shadow. This problem has received much interest recently. Nakayama et al. have proposed “the shadow theory”. The theory was first applied to the diffraction by perfectly conductive gratings as an example, where a new description and a physical mean at a low grazing limit of incidence for the gratings have been discussed. In this paper, the shadow theory is applied to the analyses of multilayered dielectric periodic gratings, and is shown to be valid on the basis of the behavior of electromagnetic waves through the matrix eigenvalue problem. Then, the representation of field distributions is demonstrated for the cases that the eigenvalues degenerate in the middle regions of multilayered gratings in addition to at a low grazing limit of incidence and some numerical examples are given.

The relative permittivity and permeability are discontinuous at the grating profile, and the electric and magnetic flux densities are continuous. As for the method of analysis for scattering waves by surface relief gratings placed in conical mounting, the spatial harmonic expansion approach of the flux densities are formulated in detail and the validity of the approach is shown numerically. The present method is effective for uniform regions such as air and substrate in addition to grating layer. The matrix formulations are introduced by using numerical calculations of the matrix eigenvalue problem in the grating region and analytical solutions separated for TE and TM waves in the uniform region are described. Some numerical examples for linearly and circularly polarized incidence show the usefulness of the flux densities expansion approach.