Poynting's theorem for planes waves at an interface: a scattering matrix approach

TL;DR

This paper applies Poynting's theorem to electromagnetic wave scattering at interfaces, defining a scattering matrix that accounts for energy conservation and losses, providing a simple model for complex dissipative systems.

Contribution

It introduces a natural definition of the scattering matrix based on energy conservation, including loss modeling at dielectric-conductor interfaces.

Findings

Scattering matrix is unitary for dielectric-dielectric interfaces.

Losses at conductors lead to a non-unitary scattering matrix.

A dissipative mode can be modeled as an absorbing channel in the scattering matrix.

Abstract

We apply the Poynting theorem to the scattering of monochromatic electromagnetic planes waves with normal incidence to the interface of two different media. We write this energy conservation theorem to introduce a natural definition of the scattering matrix S. For the dielectric-dielectric interface the balance equation lead us to the energy flux conservation which express one of the properties of S: it is a unitary matrix. For the dielectric-conductor interface the scattering matrix is no longer unitary due to the presence of losses at the conductor. However, the dissipative term appearing in the Poynting theorem can be interpreted as a single absorbing mode at the conductor such that a whole S, satisfying flux conservation and containing this absorbing mode, can be defined. This is a simplest version of a model introduced in the current literature to describe losses in more complex systems.