Chain-matrix analysis of arbitrary-thickness dielectric reflection gratings

A simple but rigorous chain-matrix analysis is used to determine the plane-wave diffraction efficiencies and angular selectivities of planar pure-reflection gratings (zero-slant angle) of arbitrary thickness, arbitrary-starting and arbitrary-ending conditions, and arbitrary incidence angle. The results from rigorous coupled-wave theory in the angular limit as the fringes become parallel to the surfaces are shown to approach these results in a particular average sense.