Universal Theory of Light Scattering of Randomly Oriented Particles: A Fluctuational-Electrodynamics Approach for Modeling of Light Transport in Disordered Nanostructures

Disordered nanostructures are commonly encountered in many nanophotonic systems, from colloid dispersions for sensing, to heterostructured photocatalysts. Randomness, however, imposes severe challenges for nanophotonics modeling, often constrained by the irregular geometry of the scatterers involved or the stochastic nature of the problem itself. In this article, we resolve this conundrum by presenting a universal theory of averaged light scattering of randomly oriented objects. Specifically, we derive formulas of orientation-and-polarization-averaged absorption cross section, scattering cross section and asymmetry parameter, for single or collection of objects of arbitrary shape, and that can be solved by any electromagnetic scattering method. These three parameters can be directly integrated into traditional unpolarized radiative energy transfer modelling, enabling a practical tool to predict multiple scattering and light transport in disordered nanostructured materials. Remarkably, the formulas of average light scattering can be derived under the principles of fluctuational electrodynamics, allowing analogous mathematical treatment to the methods used in thermal radiation, non-equilibrium electromagnetic forces, and other associated phenomena. The proposed modelling framework is validated against optical measurements of polymer composite films with metal-oxide microcrystals. Our work sets a new paradigm in the theory of light scattering, that may contribute to a better understanding of light-matter interactions in applications such as, plasmonics for sensing and photothermal therapy, photocatalysts for water splitting and CO$_2$ dissociation, photonic glasses for artificial structural colours, diffuse reflectors for radiative cooling, to name just a few.