Spectral representation of the effective dielectric constant of graded composites

TL;DR

This paper extends the spectral representation method to graded composites, enabling analysis of their effective dielectric properties, with applications to optical absorption and nonlinear optics.

Contribution

It generalizes the Bergman-Milton spectral representation to graded composites, allowing for the extraction of spectral density functions in continuously varying materials.

Findings

Spectral density function becomes continuous for graded composites.

Analytic generalization to 3D graded structures is discussed.

Numerical calculations demonstrate application to multilayered composites.

Abstract

We generalize the Bergman-Milton spectral representation, originally derived for a two-component composite, to extract the spectral density function for the effective dielectric constant of a graded composite. This work has been motivated by a recent study of the optical absorption spectrum of a graded metallic film [Applied Physics Letters, 85, 94 (2004)] in which a broad surface-plasmon absorption band has been shown to be responsible for enhanced nonlinear optical response as well as an attractive figure of merit. It turns out that, unlike in the case of homogeneous constituent components, the characteristic function of a graded composite is a continuous function because of the continuous variation of the dielectric function within the constituent components. Analytic generalization to three dimensional graded composites is discussed, and numerical calculations of multilayered composites are given as a simple application.