Four-wave coupled-mode theory of obliquely incident plane waves on waveguide diffraction gratings

Diffraction of plane waves, obliquely incident on a (waveguide) grating with infinitely long grooves, is analyzed with the four-wave coupled-mode theory (CMT). Unlike the ordinary analysis that considers only coupling between pairs (i.e., TE⁺ ↔ TE, TE⁺ ↔ TM^™, TM⁺ ↔ TE^™, or TM⁺ ↔ TM^™), the simultaneous interaction among these waves is properly accounted for. The field variation along the grating and the impulse response representation of the grating (reflectivity and transmission as functions of the plane-wave incidence angle) are calculated. Significant differences between the ordinary (two-wave) CMT and the four-wave CMT are observed over a wide range of incident angles.