A New Theory of Wood’s Anomalies on Optical Gratings

TLDR

The paper introduces a guided‑wave theory for Wood’s anomalies, replacing the traditional multiple‑scattering approach. The theory employs a surface reactance model to account for standing waves in grating grooves, deriving anomaly locations and shapes. The model predicts two anomaly types—Rayleigh and resonance—provides explicit spectral‑order amplitudes, and demonstrates clear anomaly effects in simulations.

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.