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The anomalous features in diffraction patterns first observed by Wood over acentury ago have been the subject of many investigations, both experimental andtheoretical. The sharp, narrow structures - and the large resonances with whichthey are sometimes associated - arise in numerous studies in optics andphotonics. In this paper we present an analytical method to study diffractedfields of optically thin gratings that highlights the nonanalyticitiesassociated with the anomalies. Using this approach we can immediately derivediffracted fields for any polarization in a compact notation. While ourequations are approximate, they fully respect energy conservation in theelectromagnetic field, and describe the large exchanges of energy betweenincident and diffracted fields that can arise even for thin gratings.

A Green function method to study thin diffraction gratings