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

This work examines a dielectric medium consisting of small, polarizable classical atoms arranged on a cubic lattice. Using a regularized variant of the discrete dipole approximation method (DDA), we derive the solution for the propagation of light in this medium in the long wavelength limit. Under typical conditions, the atoms remain effectively stationary, but acquire momentum. The analytical solution is used to calculate the mechanical contribution to the signal momentum from the electromagnetic stress tensor, as well as from the Lorentz and Coulomb force. The results essentially agree with that of R. Peierls from 1976, and disagree with commonly accepted expressions. Experiments tend to support the conventional values. We paraphrase the solution of the discrepancy presented by Peierls in his 1976 work.