Localization in Correlated Bi-Layer Structures: From Photonic Cristals to Metamaterials and Electron Superlattices

TL;DR

This paper presents a unified analytical approach to study localization and transport properties in various layered structures, revealing how correlations influence anomalous transport behaviors across photonic, metamaterial, and electronic systems.

Contribution

It introduces a general analytical expression for localization length considering correlations in weakly disordered bi-layered structures, applicable to diverse physical systems.

Findings

Correlations can induce anomalous transport properties.

Specific correlations lead to a quadratic frequency dependence of the Lyapunov exponent.

The approach unifies analysis across photonic, metamaterial, and electronic superlattices.

Abstract

In a unified approach, we study the transport properties of periodic-on-average bi-layered photonic crystals, metamaterials and electron superlattices. Our consideration is based on the analytical expression for the localization length derived for the case of weakly fluctuating widths of layers, that also takes into account possible correlations in disorder. We analyze how the correlations lead to anomalous properties of transport. In particular, we show that for quarter stack layered media specific correlations can result in a $\omega^2$-dependence of the Lyapunov exponent in all spectral bands.