Three-dimensional scattering of dielectric gratings under plane-wave excitation

The problem of scattering of electromagnetic plane waves by one-dimensional (1D) periodic dielectric gratings, under the most general condition of oblique incidence (3D incidence), is rigorously solved. A recently developed vectorial modal method for obtaining the modal spectrum of 1D dielectric periodic guiding media has been extended to consider 3D incidence. Polarization coupling effects are included in the analysis, just demonstrating the impossibility of the separation between the transverse electric and transverse magnetic polarizations traditionally employed in the two-dimensional (2D) case. A study of the scattering parameters of a multilayered dielectric periodic structure is accomplished by imposing the boundary conditions in terms of the multimode scattering matrix. The effect of changing the azimuthal angle of excitation is shown in the dispersion curves of the periodic dielectric medium. For 3D incidence on a dielectric waveguide grating, it is found that total reflection can be predicted by imposing the phase-match condition, analogous to the bidimensional incidence case.