# Global polarizability matrix method for efficient modeling of light scattering by dense ensembles of non-spherical particles in stratified media

## TL;DR

This paper presents a numerical method that models light scattering by dense, non-spherical particle ensembles in stratified media efficiently, using a small set of fictitious dipoles characterized by a global polarizability matrix.

## Contribution

The method introduces a global polarizability matrix approach that accurately reproduces scattering by individual particles and efficiently solves multiple scattering in complex media.

## Key findings

- Effective modeling of large particle ensembles in stratified media.
- Low memory usage for dense systems near interfaces.
- Applicable to complex nanostructured surfaces.

## Abstract

We introduce a numerical method that enables efficient modelling of light scattering by large, disordered ensembles of non-spherical particles incorporated in stratified media, including when the particles are in close vicinity to each other, to planar interfaces and/or to localized light sources. The method consists in finding a small set of fictitious polarizable elements -- or numerical dipoles -- that quantitatively reproduces the field scattered by an individual particle for any excitation and at an arbitrary distance from the particle surface. The set of numerical dipoles is described by a global polarizability matrix that is determined numerically by solving an inverse problem relying on fullwave simulations. The latter are classical and may be performed with any Maxwell's equations solver. Spatial non-locality is an important feature of the numerical dipoles set, providing additional degrees of freedom compared to classical coupled dipoles to reconstruct complex scattered fields. Once the polarizability matrix describing scattering by an individual particle is determined, the multiple scattering problem by ensembles of such particles in stratified media can be solved using a Green tensor formalism and only few numerical dipoles, thereby with a low physical memory usage, even for dense systems in close vicinity to interfaces. The performance of the method is studied with the example of large high-aspect-ratio high-index dielectric cylinders. The method is easy to implement and may offer new possibilities for the study of complex nanostructured surfaces, which are becoming widespread in emerging photonic technologies.