A solvable microscopic model for the propagation of light in a dielectric medium

TL;DR

This paper presents a solvable microscopic model based on a regularized discrete dipole approximation to analyze light propagation and momentum in dielectric media, aligning with classical theory.

Contribution

Introduces a solvable microscopic electrodynamic model using a regularized DDA to study light propagation and momentum in dielectrics, bridging microscopic details with classical theory.

Findings

Model agrees with Peierls' classical theory on light momentum.

Provides detailed analysis of electromagnetic and mechanical momentum.

Demonstrates the effectiveness of a regularized DDA approach.

Abstract

Maxwell's equations resemble Schr\"odinger's equation in that an exact solution for a well-defined model delivers all physically relevant details. Solvable microscopic electrodynamic models, however, are rare. An exception is the discrete dipole approximation (DDA), which models a medium as a lattice of point dipoles. We use a regularized DDA variant to examine mechanical and electromagnetic momentum of light signals in such a medium in detail. The results agree in essential parts with that of the theory of R. Peierls from 1976.