Three-dimensional vector coupled-wave analysis of planar-grating diffraction

TLDR

Diffraction by arbitrarily oriented planar gratings with slanted fringes is analyzed using rigorous three‑dimensional vector coupled‑wave analysis applicable to any sinusoidal or nonsinusoidal amplitude or phase grating, any plane‑wave incidence angle, and any linear polarization. The analysis shows that all space‑harmonic TE and TM fields inside the grating are mutually coupled, enabling near‑100 % diffraction efficiency when the incident field is perpendicular to the grating vector (with maximum coupling under the same condition), that the diffracted waves are elliptically polarized, and that the model reduces to conventional coupled‑wave theory when the grating vector lies in the plane of incidence.

Abstract

Diffraction by an arbitrarily oriented planar grating with slanted fringes is analyzed using rigorous three-dimensional vector coupled-wave analysis. The method applies to any sinusoidal or nonsinusoidal amplitude and/or phase grating, any plane-wave angle of incidence, and any linear polarization. In the resulting (conical) diffraction, it is shown that coupling exists between all space-harmonic vector fields inside the grating (corresponding to diffracted orders outside the grating). Therefore the TE and TM components of an incident wave are each coupled to all the TE and TM components of all the forward- and backward-diffracted waves. For a general Bragg angle of incidence, it is shown that the diffraction efficiency can approach 100% for a lossless grating if either the incident electric field or the magnetic field is perpendicular to the grating vector. Maximum coupling between incident and diffracted waves is shown to occur when the incident electric field is perpendicular to the grating vector. In general, the diffracted waves are shown to be elliptically polarized. The three-dimensional vector coupled-wave analysis presented is shown to reduce to ordinary rigorous coupled-wave theory when the grating vector lies in the plane of incidence.