A New Formalism for Transmission Gratings

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Abstract
A new formalism for diffraction gratings consisting of a single grating surface surrounded by a number of planar films is presented. The diffraction problem is shown to reduce to the solution of a Fredholm integral equation of the first kind. The numerical implementation has been thoroughly tested using the constraints of energy conservation and reciprocity. A new constraint relating the phases and efficiencies of the propagating orders excited when a lossless symmetric transmission grating is operated in a first-order Littrow mount has been derived theoretically and verified numerically. The theory has been used to optimize the selective performance of a solar absorber consisting of a thin graphite layer deposited on a copper substrate. The superposition of a grating absorption feature on the primary resonance minimum of the absorptivity curve is shown to improve the integrated absorptivity by approximately 10 per cent.

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