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A modal expansion formalism is presented to solve the scalar-wave diffraction problem for a perfectly conducting reflection grating whose grooves are semi-circular in cross-section. The theory is given for both of the fundamental polarizations, together with efficiency calculations for the first-order Littrow mounting. Similarity between the results and those of other profile shapes is observed and the groove radius which produces optimum blazing performance is determined. Resonance anomalies are observed in the efficiency spectra and are attributed to complex poles in the mode amplitudes. The positions of these poles are traced as a function of groove radius.
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Andrewartha et al. (1981) studied this question.
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