A New Theory of Wood’s Anomalies on Optical Gratings

Abstract

A new theory of Wood’s anomalies is presented which is based on a guided wave approach rather than the customary multiple scattering procedure. This approach provides both new insight and a method of calculation. It is shown that two distinct types of anomalies may exist: a Rayleigh wavelength type due to the emergence of a new spectal order at grazing angle, and a resonance type which is related to the guided complex waves supportable by the grating. A general theoretical treatment is presented which makes use of a surface reactance to take into account the standing waves in the grating grooves, and which derives the locations and detailed shapes of the anomalies. Rigorous results are obtained for a specific example; the amplitudes of all of the spectral orders are determined explicitly, and the Wood’s anomaly effects are demonstrated clearly in graphical form for a variety of cases.