Power conservation and field structures in uniform dielectric gratings

Moharam and Gaylord [ J. Opt. Soc. Am.71, 811 ( 1981)] have recently found a neat new way of numerically analyzing the coupled-wave equations describing light propagation in thick, uniformly modulated dielectric gratings with parallel planar boundaries. This interesting new contribution has raised some important questions about power conservation in coupled-wave theory and about how the behavior of symmetrical reflection gratings (pure reflection gratings) relates to that of nearly symmetrical ones. The new-found accuracy of Moharam and Gaylord’s method has in part contributed to the debate, allowing as it does fine testing of power conservation. A detailed rigorous discussion is given here of power conservation in dielectric gratings, based on the time-averaged Poynting vector. It is shown that truncated coupled-wave theories do not rigorously conserve power.