Clustering Diffused-Particle Method for Scattering from Large Ensembles of Electromagnetically Polarizable Particles

TL;DR

This paper introduces a hierarchical clustering method to efficiently simulate electromagnetic scattering from extremely large ensembles of particles with electric and magnetic responses, revealing bulk medium behavior and validating effective medium theories.

Contribution

It generalizes the Foldy-Lax equation for particles with both electric and magnetic responses and reduces computational complexity for large-scale simulations.

Findings

Simulations with up to 10^10 particles are feasible.

Effective medium parameters match Clausius-Mossotti relation for non-magnetic materials.

Results agree with generalized effective medium theory for particles with magnetic responses.

Abstract

The Foldy-Lax equation is generalized for a medium which consists of particles with both electric and magnetic responses. The result is used to compute fields scattered from ensembles of particles. The computational complexity is reduced by hierarchical clustering techniques to enable simulations with on the order of 10^10 particles. With so many particles we are able to see the transition to bulk media behavior of the fields. For non-magnetic materials, the observable index, permittivity, and permeability of the effective bulk medium are in good agreement with the Clausius-Mossotti relation. The fields simulated for particles with both electric and magnetic responses are in good agreement with new analytical results for a generalized effective medium theory.