Green's function method to study thin diffraction gratings

The anomalous features in diffraction patterns first observed by Wood over a century ago have been the subject of many investigations, both experimental and theoretical. The sharp, narrow structures---and the large resonances with which they are sometimes associated---arise in numerous studies in optics and photonics. In this paper we present an analytical method to study diffracted fields of optically thin gratings that highlights the nonanalyticities associated with the anomalies. Using this approach we can immediately derive diffracted fields for any polarization in a compact notation. While our equations are approximate, they fully respect energy conservation in the electromagnetic field, and describe the large exchanges of energy between incident and diffracted fields that can arise even for thin gratings.