Electromagnetic Energy, Momentum, and Angular Momentum in an Inhomogeneous Linear Dielectric

TL;DR

This paper develops a framework for analyzing electromagnetic energy, momentum, and angular momentum in inhomogeneous dielectric media with spatially varying refractive index, extending previous uniform-medium models.

Contribution

It introduces a symmetric energy-momentum tensor for inhomogeneous dielectrics and derives conservation laws considering spatially varying refractive indices.

Findings

Constructed a symmetric energy-momentum matrix for inhomogeneous media

Derived global conservation laws for energy, momentum, and angular momentum

Extended previous uniform-medium models to inhomogeneous cases

Abstract

In a previous work, Optics Communications 284 (2011) 2460--2465, we considered a dielectric medium with an anti-reflection coating and a spatially uniform index of refraction illuminated at normal incidence by a quasimonochromatic field. Using the continuity equations for the electromagnetic energy density and the Gordon momentum density, we constructed a traceless, symmetric energy--momentum tensor for the closed system. In this work, we relax the condition of a uniform index of refraction and consider a dielectric medium with a spatially varying index of refraction that is independent of time, which essentially represents a mechanically rigid dielectric medium due to external constraints. Using continuity equations for energy density and for Gordon momentum density, we construct a symmetric energy--momentum matrix, whose four-divergence is equal to a generalized Helmholtz force density four-vector. Assuming that the energy-momentum matrix has tensor transformation properties under a symmetry group of space-time coordinate transformations, we derive the global conservation laws for the total energy, momentum, and angular momentum.