Analytical scattering matrix of subwavelength infinitely conducting metallic gratings in TM polarization

TL;DR

This paper derives an analytical scattering matrix for subwavelength metallic gratings in TM polarization using a monomode approximation, enabling efficient diffraction calculations for multilayer structures.

Contribution

It introduces a new analytical expression for the scattering matrix of infinitely conducting metallic gratings in TM polarization based on the Monomode Modal Method.

Findings

Analytical scattering matrix expressions derived and validated.

The theory reveals an Airy-like form of the scattering matrix.

Numerical stability demonstrated for multilayer gratings.

Abstract

We obtain in TM polarization an analytical expression of the scattering matrix of one infinitely conducting metallic lamellar grating with subwavelength slits. The theory is based on the Monomode Modal Method which consists in considering only one propagative mode in grating slits. Two expressions are exposed. The first one comes directly from the theory equations and the second one clearly reveals the Airy-like form of the scattering matrix terms. The theory is validated on a multi-grating object and the stability of the numerical results are shown at the same time. This work provides a basic and very efficient theoretical tool to calculate the diffraction by a stack of subwavelength metallic gratings.