Electromagnetic Boundary Conditions Defined in Terms of Normal Field Components

TL;DR

This paper introduces a new set of electromagnetic boundary conditions based on normal field components, generalizes them to arbitrary surfaces, and relates them to classical PEC and PMC conditions, enhancing understanding of wave interactions at boundaries.

Contribution

It proposes a novel framework of boundary conditions using scalar normal field components and extends the theory to general boundary surfaces, linking to classical PEC and PMC conditions.

Findings

Four meaningful boundary condition pairs identified

Boundary conditions correspond to PEC and PMC for specific polarizations

Generalized boundary conditions apply to arbitrary surfaces

Abstract

A set of four scalar conditions involving normal components of the fields D and B and their normal derivatives at a planar surface is introduced, among which different pairs can be chosen to represent possible boundary conditions for the electromagnetic fields. Four such pairs turn out to yield meaningful boundary conditions and their responses for an incident plane wave at a planar boundary are studied. The theory is subsequently generalized to more general boundary surfaces defined by a coordinate function. It is found that two of the pairs correspond to the PEC and PMC conditions while the other two correspond to a mixture of PEC and PMC conditions for fields polarized TE or TM with respect to the coordinate defining the surface.