Propagation of Electromagnetic Waves on a Rectangular Lattice of Polarizable Points

TL;DR

This paper derives the dispersion relation for electromagnetic waves on a lattice of polarizable points, providing a new method to assign dipole polarizabilities for accurate scattering simulations.

Contribution

It introduces a novel prescription for dipole polarizabilities that aligns the lattice's dispersion with that of a continuum medium, improving the discrete dipole approximation.

Findings

Derived dispersion relation for long-wavelength waves on a polarizable lattice.

Provided a new method for assigning dipole polarizabilities.

Validated the approach with selected numerical cases.

Abstract

We discuss the propagation of electromagnetic waves on a rectangular lattice of polarizable point dipoles. For wavelengths long compared to the lattice spacing, we obtain the dispersion relation in terms of the lattice spacing and the dipole polarizabilities. We also obtain the polarizabilities required for the lattice to have the same dispersion relation as a continuum medium of given refractive index m.; our result differs slightly from previous work by Draine & Goodman (1993). Our new prescription can be used to assign dipole polarizabilities when the discrete dipole approximation is used to study scattering by finite targets. Results are shown for selected cases.