Rigorous formulation of scattering and guidance by dielectric grating waveguides: general case of oblique incidence

First a rigorous formulation is presented for the scattering of a uniform plane wave by an infinite dielectric grating waveguide, under the most general condition of oblique incidence. The results are then applied to the analysis of the guidance of waves by the dielectric grating waveguide. By using a simple coordinate rotation, the TE and TM Floquet mode functions determined previously for the special case of principal-plane incidence are combined to treat the general case of oblique incidence. In terms of the coupling between the known Floquet mode functions of both polarizations, the general case of oblique incidence is formulated in an exact fashion, as a three-dimensional boundary-value problem, so that the hybrid nature of waves supported by the structure can be investigated rigorously.