Beyond ClausiusMossotti: Wave Propagation on a Polarizable Point Lattice and the Discrete Dipole Approximation
Abstract
We derive the dispersion relation for electromagnetic waves propagating on a lattice of polarizable points. From this dispersion relation we obtain a prescription for choosing dipole polarizabilities so that an infinite lattice with finite lattice spacing will mimic a continuum with dielectric constant. The discrete dipole approximation is used to calculate scattering and absorption by a finite target by replacing the target with an array of point dipoles. We compare different prescriptions for determining the dipole polarizabilities. We show that the most accurate results are obtained when the lattice dispersion relation is used to set the polarizabilities.
 Publication:

The Astrophysical Journal
 Pub Date:
 March 1993
 DOI:
 10.1086/172396
 Bibcode:
 1993ApJ...405..685D
 Keywords:

 Cosmic Dust;
 Dielectric Polarization;
 Electromagnetic Absorption;
 Electromagnetic Scattering;
 Electromagnetic Wave Transmission;
 Interstellar Extinction;
 Lattices (Mathematics);
 Cubic Lattices;
 Fast Fourier Transformations;
 Finite Element Method;
 Wave Dispersion;
 Space Radiation;
 POLARIZATION;
 ISM: DUST;
 EXTINCTION