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.

An analysis of wave guidance by surface-relief grating waveguides is presented for the case of oblique propagation. This analysis is based on the first-order differential equations expressing the coupling of the space harmonics and an improved differential method is applied to solve the equations in the grating region with arbitrary profile. The propagation constants are calculated for isotropic grating waveguids with sinusoidal profile and the calculated results indicate that the accurate solutions can be obtained by increasing the number of expansion terms and the number of segments. Moreover, this method is extended to the case of the analysis of obliquely propagating waves and it is shown that peculiar leaky waves and stop bands appear owing to the coupling between TE and TM waves.

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.

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.

A method for analyzing the scattering of electromagnetic waves by a general bianisotropic slab is presented by extending the author's previous approaches for anisotropic, chiral, and those periodic media. The analysis is formulated in a unified matrix form, so that scattering characteristics can be obtained by system matrix calculations. The method can be extended straightforwardly to multilayerd and periodic structures. The scattering efficiencies are obtained for the incidence of not only linearly polarized waves but also circularly polarized waves.