# Averaged optical characteristics of an ensemble of metal nanoparticles

## TL;DR

This paper develops a comprehensive theory to describe the averaged optical properties of metal nanoparticle ensembles with varying shapes, accounting for size-dependent conductivity and shape distribution effects.

## Contribution

It introduces a new theoretical framework for calculating optical characteristics of shape-varied metal nanoparticles, including a novel shape distribution function.

## Key findings

- Derived dependencies of magnetic absorption on nanoparticle shape and orientation.
- Proposed a new shape distribution function combining Gaussian and hat functions.
- Analyzed the influence of shape and size on optical conductivity and depolarization factors.

## Abstract

A theory for the averaged optical characteristics of an ensemble of metal nanoparticles with different shapes has been developed. The theory is applicable both for the nanoparticle size at which the optical conductivity of the particle is a scalar and for the nanoparticle size at which the optical conductivity should be considered as a tensor. The averaged characteristics were obtained taking into account the influence of nanoparticle shape on the depolarization coefficient and the components of the optical conductivity tensor. The dependences of magnetic absorption by a spheroidal metal nanoparticle on the ratio between its curvature radii and the angle between the spheroid symmetry axis and the magnetic field vector were derived and theoretically considered. An original variant of the distribution function for nanoparticle shapes, which is based on the combined application of the Gaussian and \textquotedblleft hat\textquotedblright\ functions, was proposed and analyzed.