A Green function method to study thin diffraction gratings

TL;DR

This paper introduces an analytical Green function method for studying thin diffraction gratings, capturing anomalous diffraction features and energy exchanges with a compact, polarization-inclusive formulation.

Contribution

The paper presents a novel Green function approach that analytically describes diffraction anomalies in thin gratings, respecting energy conservation and applicable to any polarization.

Findings

Accurately models diffraction anomalies in thin gratings.

Provides a compact analytical expression for diffracted fields.

Ensures energy conservation in approximate solutions.

Abstract

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.