Approached vectorial model for Fano resonances in guided mode resonance gratings

TL;DR

This paper introduces a self-consistent vectorial Green's function-based model to analyze Fano resonances in guided mode resonance gratings, providing intuitive formulas and numerical validation for complex polarization effects.

Contribution

The paper presents a novel vectorial method using Green's functions to accurately describe Fano resonances in guided mode resonance gratings, including polarization effects.

Findings

Validated the model numerically against known results.

Derived explicit expressions for reflectivity and transmittivity matrices.

Analyzed polarization effects in resonance configurations.

Abstract

We propose a self-consistent vectorial method, based on a Green's function technique, to describe the Fano resonances that appear in guided mode resonance gratings. The model provides intuitive expressions of the reflectivity and transmittivity matrices of the structure, involving coupling integrals between the modes of a planar reference structure and radiative modes. These expressions are used to derive a physical analysis in configurations where the effect of the incident polarization is not trivial. We provide numerical validations of our model. On a technical point of view, we show how the Green's tensor of our planar reference structure can be expressed as two scalar Green's functions, and how to deal with the singularity of the Green's tensor.