Clustering diffused-particle method for simulating electromagnetic fields among large ensembles of electromagnetically polarizable particles

In this work, the Foldy-Lax equation is generalized for a medium that consists of particles with both electric and magnetic responses. The result is used to compute fields scattered from ensembles of particles with polarizabilities extracted from shape/size effects, self-interaction, and dipole fluctuations. The computational complexity is reduced by hierarchical clustering techniques to enable simulations with on the order of 10¹⁰ 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.