Integral Method for Gratings

TL;DR

This paper presents a comprehensive surface integral theory for modeling light diffraction by one-dimensional periodic gratings, including various approaches, numerical techniques, and applications to different grating profiles and materials.

Contribution

It introduces multiple integral equation formulations, addresses kernel singularities, and discusses convergence acceleration methods for accurate diffraction modeling.

Findings

Effective integral equation approaches for gratings.

Techniques for handling kernel singularities.

Numerical methods for convergence acceleration.

Abstract

The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading either to a single integral equation, or to a system of coupled integral equations. Special attention is paid to the singularities of the kernels, and to different techniques to accelerate the convergence of the numerical computations. The theory is applied to gratings having different profiles with or without edges, to real metal and dielectrics, and to perfectly conducting substrates.