Three-Dimensional Scattering of Dielectric Gratings Under Plane-Wave Excitation

Abstract—In this letter, the problem of scattering of electro-magnetic plane waves by one-dimensional (1-D) periodic dielec-tric gratings, under the most general condition of oblique inci-dence [three-dimensional (3-D) incidence], is rigorously solved. A recently developed vectorial modal method for obtaining the modal spectrum of 1-D dielectric periodic guiding media has been ex-tended for considering 3-D incidence. Polarization coupling effects are included in this analysis, just demonstrating the impossibility of the separation between the transverse electric and transverse magnetic polarizations traditionally employed in the two-dimen-sional (2-D) case. A study of the scattering parameters of a multi-layered dielectric periodic structure is accomplished by imposing the boundary conditions in terms of the multimode scattering ma-trix. The effect of changing the azimuthal angle of excitation is shown in the dispersion curves of the periodic dielectric medium. For 3-D incidence on a dielectric waveguide grating, it is found that total reflection can be predicted by imposing the phase-match con-dition, analogous to the bi-dimensional incidence case. Index Terms—Dielectric waveguide grating, frequency-selective surfaces, hybrid modes, resonance frequency, three-dimensional (3-D) incidence. I