First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

TL;DR

This paper develops a comprehensive first-principles theoretical framework for electromagnetic scattering by discrete and heterogeneous random media, enabling accurate modeling and deeper physical insights beyond phenomenological methods.

Contribution

It formulates a general Maxwell-Lorentz based formalism for scattering, integrating analytical and numerical approaches, and connects classical theories as specific cases within this framework.

Findings

Derivation of the first-order scattering approximation from Maxwell equations

Validation of radiative transfer and weak localization theories as special cases

Enhanced understanding of the mesoscopic origins of scattering regimes

Abstract

The main objective of this Report is to formulate the general theoretical framework of electromagnetic scattering by discrete random media rooted in the Maxwell-Lorentz electromagnetics and discuss its immediate analytical and numerical consequences. Starting from the microscopic Maxwell-Lorentz equations, we trace the development of the first-principles formalism enabling accurate calculations of monochromatic and quasi-monochromatic scattering by static and randomly varying multiparticle groups. We illustrate how this general framework can be coupled with state-of-the-art computer solvers of the Maxwell equations and applied to direct modeling of electromagnetic scattering by representative random multi-particle groups with arbitrary packing densities. This first-principles modeling yields general physical insights unavailable with phenomenological approaches. We discuss how the first-order-scattering approximation, the radiative transfer theory, and the theory of weak localization of electromagnetic waves can be derived as immediate corollaries of the Maxwell equations for very specific and well-defined kinds of particulate medium. These recent developments confirm the mesoscopic origin of the radiative transfer, weak localization, and effective-medium regimes and help evaluate the numerical accuracy of widely used approximate modeling methodologies.