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The finite element method as applied to the diffraction by an anisotropic grating.

Guillaume Demésy¹, Frédéric Zolla, André Nicolet

¹Institut Fresnel, UMR CNRS 6133, Faculté de Saint Jérôme, case 162, 13397 Marseille Cedex 20, France. uillaume.demesy@fresnel.fr

|June 25, 2009

Summary

This study introduces a new Finite Element Method (FEM) formulation for analyzing anisotropic gratings on isotropic substrates. The method accurately models complex grating behaviors, revealing non-symmetric diffracted fields even in symmetric configurations.

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Area of Science:

Optics and Photonics
Materials Science
Computational Electromagnetics

Background:

Anisotropic gratings on isotropic substrates present complex electromagnetic behavior.
Accurate numerical modeling is crucial for understanding light-matter interactions in such structures.
Existing methods may face challenges with infinite issues inherent to grating problems.

Purpose of the Study:

To develop and present a novel Finite Element Method (FEM) formulation for the numerical study of anisotropic gratings.
To analyze gratings without constraints on geometry or electromagnetic properties.
To investigate the diffraction of plane waves by anisotropic gratings on isotropic substrates.

Main Methods:

A new Finite Element Method (FEM) formulation is proposed.
The FEM formulation rigorously addresses infinite issues in grating analysis.
2D numerical experiments are conducted for specific anisotropic grating configurations.

Main Results:

The proposed FEM formulation successfully models various anisotropic gratings on isotropic substrates.
Numerical experiments demonstrate the diffraction of plane waves by an aragonite grating on a silica substrate.
A key finding is the non-symmetric nature of the diffracted field in geometrically symmetric configurations.

Conclusions:

The new FEM formulation provides a robust tool for analyzing complex anisotropic grating structures.
The study highlights unique electromagnetic properties of anisotropic gratings, such as non-symmetric diffraction patterns.
This research contributes to a deeper understanding of light interaction with advanced optical materials.