Random matrix approach to plasmon resonances in the random impedance network model of disordered nanocomposites

TL;DR

This paper applies random matrix theory, specifically the Jacobi ensemble, to analyze plasmon resonances in disordered nanocomposite networks, providing analytical density of states expressions that align well with numerical simulations.

Contribution

It introduces the Jacobi ensemble as the appropriate random matrix model for plasmon resonances in disordered nanocomposites, offering analytical insights.

Findings

Analytical density of states matches numerical simulations across various metal fractions.

The Jacobi ensemble effectively models the spectral properties of the network.

A link between the spectral results and the effective medium approximation is established.

Abstract

Random impedance networks are widely used as a model to describe plasmon resonances in disordered metal-dielectric and other two-component nanocomposites. In the present work, the spectral properties of resonances in random networks are studied within the framework of the random matrix theory. We have shown that the appropriate ensemble of random matrices for the considered problem is the Jacobi ensemble (the MANOVA ensemble). The obtained analytical expressions for the density of states in such resonant networks show a good agreement with the results of numerical simulations in a wide range of metal filling fractions $0<p<1$. A correspondence with the effective medium approximation is observed.