On polarization interface conditions for time-harmonic Maxwell's equations

TL;DR

This paper analyzes the polarization interface conditions in time-harmonic Maxwell's equations, deriving limit equations, and establishing existence and Fredholm properties, with origins in homogenization of thin wire inclusions.

Contribution

It provides a rigorous analysis of the polarization interface conditions, including derivation of limit equations and mathematical properties like existence and Fredholm alternative.

Findings

Derived the limit equations for polarization interface conditions.

Proved existence of solutions for the limit equations.

Established Fredholm alternative for the problem.

Abstract

We consider the time-harmonic Maxwell's equations with a polarization interface condition. The interface condition demands that one component of the electric field vanishes at the interface and that the corresponding component of the magnetic field has no jump across the interface. These conditions have been derived in the literature as a homogenization limit for thin wire inclusion. We analyze the limit equations and provide an existence result and a Fredholm-alternative.