Continuum Electrodynamics of a Piecewise-Homogeneous Linear Medium

TL;DR

This paper extends the continuum electrodynamics framework to piecewise-homogeneous linear media, deriving equations of motion, boundary conditions, and momentum separation, with implications for understanding radiation forces at interfaces.

Contribution

It introduces a formalism for electromagnetic fields in piecewise-homogeneous media, including boundary conditions and momentum transfer, advancing the theoretical understanding of electromagnetic interface phenomena.

Findings

Derived equations of motion for piecewise-homogeneous media

Explicit separation of total momentum into field and material components

Reinterpretation of Jones and Richards experiment results

Abstract

The energy--momentum tensor and the tensor continuity equation serve as the conservation laws of energy, linear momentum, and angular momentum for a continuous flow. Previously, we derived equations of motion for macroscopic electromagnetic fields in a homogeneous linear dielectric medium that is draped with a gradient-index antireflection coating (J. Math Phys. 55, 042901 (2014) ). These results are consistent with the electromagnetic tensor continuity equation in the limit that reflections and the accompanying surface forces are negligible thereby satisfying the condition of an unimpeded flow in a thermodynamically closed system. Here, we take the next step and derive equations of motion for the macroscopic fields in the limiting case of a piecewise-homogeneous simple linear dielectric medium. The presence of radiation surface forces on the interface between two different homogeneous linear materials means that the energy--momentum formalism must be modified to treat separate homogeneous media in which the fields are connected by boundary conditions at the interfaces. We demonstrate the explicit separation of the total momentum into a field component and a material motion component, we derive the radiation pressure that transfers momentum from the field to the material, we derive the electromagnetic continuity equations for a piecewise homogeneous dielectric, and we provide a lucid reinterpretation of the Jones and Richards experiment.