Analysis of light scattering off photonic crystal slabs in terms of Feshbach resonances

TL;DR

This paper applies Feshbach resonance techniques to analytically describe light scattering in photonic crystal slabs, providing accurate, parameter-free expressions that relate resonance features to the structure and incident light properties.

Contribution

It introduces a novel analytical framework for resonant light scattering in photonic crystals using Feshbach resonance methods, applicable to overlapping resonances.

Findings

Derived explicit formulas for scattering amplitudes

Validated the approach's accuracy against numerical results

Demonstrated analysis of complex overlapping resonances

Abstract

Techniques to deal with Feshbach resonances are applied to describe resonant light scattering off one dimensional photonic crystal slabs. Accurate expressions for scattering amplitudes, free of any fitting parameter, are obtained for isolated as well as overlapping resonances. They relate the resonance properties to the properties of the optical structure and of the incident light. For the most common case of a piecewise constant dielectric function, the calculations can be carried out essentially analytically. After establishing the accuracy of this approach we demonstrate its potential in the analysis of the reflection coefficients for the diverse shapes of overlapping, interacting resonances.