Effective Macroscopic Response of a Composite with Small Deviations from Periodicity: Application to Colloidal Crystals

TL;DR

This paper uses spectral methods to study how small deviations from perfect periodicity in colloidal crystals affect their macroscopic dielectric properties, revealing resonance broadening and new spectral features.

Contribution

It introduces a spectral approach to analyze composites with slight deviations from periodicity, specifically applied to colloidal crystals.

Findings

Resonances in periodic composites are broadened with random displacements.

Additional branch cuts appear in the spectral response due to deviations.

Effective dielectric constant is significantly affected by small positional deviations.

Abstract

Using the spectral approach, we analyze the effective properties of a composite which deviates slightly from periodicity. We find that, when the inclusions are randomly displaced from their equilibrium positions, the sharp resonances seen in the periodic case are broadened, and an additional branch cut appears. We use these results to analyze the effective dielectric constant of a colloidal crystal.