A resolution of the problem of additional boundary conditions

TL;DR

This paper resolves the longstanding issue of additional boundary conditions in Maxwell's equations by introducing a surface response function that captures non-local boundary effects, providing a more accurate physical description.

Contribution

It presents a generic theory for light-surface interactions, replacing ABCs with a surface response function that accounts for non-local effects in spatially dispersive media.

Findings

ABC can be fitted but are not intrinsic surface properties

Introduces a surface response function (SRF) for non-local effects

Proposes methods to experimentally determine SRF profile

Abstract

Maxwell's boundary conditions (MBCs) were long known insufficient to determine the optical responses of spatially dispersive medium. Supplementing MBCs with additional boundary conditions (ABCs) has become a normal yet controversial practice. Here the problem of ABCs is solved by analyzing some subtle aspects of a physical surface. A generic theory is presented for handling the interaction of light with the surfaces of an arbitrary medium and applied to study the traditional problem of exciton polaritons. We show that ABCs can always be adjusted to fit the theory but they can by no means be construed as intrinsic surface characteristics, which are instead captured by a \textit{surface response function} (SRF). Unlike any ABCs, a SRF describes essentially non-local boundary effects. Methods for experimentally extracting the spatial profile of this function are proposed.