Parametric diffraction efficiency of non-paraxial sinusoidal reflection gratings

With the wide-spread availability of electromagnetic; i.e., vector, analysis codes for describing the diffraction of electromagnetic waves by periodic grating structures, the insight and understanding of non-paraxial parametric diffraction grating behavior afforded by approximate methods (i.e.; scalar diffraction theory) is being ignored in the education of most optical engineers today. In this paper we show how the recent linear systems formulation of non-paraxial scalar diffraction theory allows the development of a scalar parametric diffraction grating analysis for sinusoidal reflection (phase) gratings with arbitrary groove depths and arbitrary non-paraxial incident and diffracted angles. This scalar parametric analysis is remarkably accurate as it includes the ability to redistribute the energy from evanescent orders into the propagating ones, thus allowing the calculation of non-paraxial diffraction efficiencies to be predicted with an accuracy usually thought to require rigorous electromagnetic theory. These scalar parametric predictions of diffraction efficiency compare well with rigorous predictions for a variety of non-paraxial diffraction grating configurations.