With the widespread availability of electromagnetic (vector) analysis codes for describing the diffraction of electromagnetic waves by periodic grating structures, the insight and understanding of nonparaxial parametric diffraction grating behavior afforded by approximate methods (i.e., scalar diffraction theory) is being ignored in the education of most optical engineers today. We show that the linear systems formulation of nonparaxial scalar diffraction theory enables the development of a scalar parametric diffraction grating model [for transverse electric (TE) polarization] for sinusoidal reflection gratings with arbitrary groove depths and arbitrary nonparaxial 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 nonparaxial diffraction efficiencies to be predicted with an accuracy usually thought to require rigorous electromagnetic theory. These scalar parametric predictions of diffraction efficiency are compared to paraxial scalar and rigorous electromagnetic (vector) predictions for a variety of nonparaxial diffraction grating configurations, thus providing quantitative limits of applicability of nonparaxial scalar diffraction theory to sinusoidal reflection gratings as a function of the grating period-to-wavelength ratio (λ / d).
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