On a General Theory of Anomalies and Energy Absorption by Diffraction Gratings and Their Relation with Surface Waves

The authors generalize a previous theory to study the phenomenon of absorption of plane waves by a grating working with several spectral orders. The theory allows predicting, with the aim of a simple formula, the shape of various kinds of grating anomalies, as well as the shape of the total diffracted energy curve. The use of a convenient matrix, called S*S, leads to the introduction of the efficiency hyperellipsoid. This enables one to predict in a simple way a phenomenon of total absorption of a finite number of plane waves by a grating.