Dielectric resonances in disordered media

TL;DR

This paper investigates dielectric resonances in disordered media, analyzing impedance spectra of resistor-capacitor and resistor-inductor-capacitor systems near percolation thresholds, revealing sharp frequency-specific absorption features.

Contribution

It introduces two independent methods to calculate impedance in disordered systems and characterizes their complex spectral features, especially in LR-C composites with small conducting clusters.

Findings

Impedance spectra show intricate structures near percolation thresholds.

Sharp resonance lines are identified at specific frequencies.

Signature patterns of small conducting clusters ('animals') are characterized.

Abstract

Binary disordered systems are usually obtained by mixing two ingredients in variable proportions: conductor and insulator, or conductor and super-conductor. and are naturally modeled by regular bi-dimensional or tri-dimensional lattices, on which sites or bonds are chosen randomly with given probabilities. In this article, we calculate the impedance of the composite by two independent methods: the so-called spectral method, which diagonalises Kirchhoff's Laws via a Green function formalism, and the Exact Numerical Renormalization method (ENR). These methods are applied to mixtures of resistors and capacitors (R-C systems), simulating e.g. ionic conductor-insulator systems, and to composites consituted of resistive inductances and capacitors (LR-C systems), representing metal inclusions in a dielectric bulk. The frequency dependent impedances of the latter composites present very intricate structures in the vicinity of the percolation threshold. We analyse the LR-C behavior of compounds formed by the inclusion of small conducting clusters (``$n$-legged animals'') in a dielectric medium. We investigate in particular their absorption spectra who present a pattern of sharp lines at very specific frequencies of the incident electromagnetic field, the goal being to identify the signature of each animal. This enables us to make suggestions of how to build compounds with specific absorption or transmission properties in a given frequency domain.