# Electromagnetic Wave Reflection from Surface with General Boundary Conditions

## TL;DR

This paper derives an analytic reflection dyadic for electromagnetic waves at boundaries with the most general linear, local boundary conditions, including special cases and potential realizations in bi-anisotropic media.

## Contribution

It introduces a comprehensive theory for wave reflection at boundaries with general conditions, including new boundary types and their properties.

## Key findings

- Derived an analytic expression for the reflection dyadic.
- Identified and analyzed special boundary cases like E-boundary, H-boundary, and EH-boundary.
- Discussed possible physical realizations of the general boundary conditions.

## Abstract

The most general linear and local set of boundary conditions, involving relations between the normal components of the D and B vectors and tangential components of the E and H vectors at each point of the boundary, are considered in this paper. Reflection of a plane wave from a boundary defined by general conditions in an isotropic half space is analyzed and an analytic expression for the reflection dyadic is derived. It is shown that any plane wave can be decomposed in two components which do not interact in reflection. Properties of plane waves matched to the general boundary are given. Certain special cases of boundary conditions, arising naturally from the general theory and labeled as E-boundary, H-boundary and EH-boundary conditions, are introduced as interesting novelties and some of their properties are studied. Previously known special cases are considered in verifying the theory. A possible realization of the general boundary in terms of an interface of a general bi-anisotropic medium is discussed in an Appendix.