Scattering matrix of elliptically polarized waves

TL;DR

This paper derives the scattering matrix for elliptically polarized waves at dielectric interfaces, considering both dielectric-dielectric and dielectric-conductor cases, highlighting basis choices and energy conservation.

Contribution

It provides a comprehensive derivation of the scattering matrix using boundary conditions and Poynting's theorem, including the treatment of absorption via parasitic channels.

Findings

Scattering matrix formulated for dielectric-dielectric interface.

Unitary scattering matrix constructed for dielectric-conductor interface.

Absorption quantified through parasitic channels in the scattering matrix.

Abstract

We analyze the scattering of elliptically polarized plane waves normally incident at the planar interface between two different materials; we consider two cases: dielectric-dielectric and dielectric-conductor interfaces. The scattering matrix S in both cases is obtained using the boundary conditions and Poynting's theorem. In the dielectric-dielectric case we write S using two different basis, the usual xy and a rotated one. For the dielectric-conductor interface, the use of the rotated basis together with an energy balance argument leads us, in a natural way, to construct a unitary S matrix after recognizing the need to introduce two equivalent parasitic channels due to dissipation in the conductor, and the transmission coefficient into these parasitic channels measures the absorption strength.