Non-Conventional Anderson Localization in Bilayered Structures with Metamaterials

TL;DR

This paper develops a theoretical approach to analyze non-conventional Anderson localization in bilayered structures with both right-handed and left-handed materials, revealing conditions for extremely large localization lengths at low frequencies.

Contribution

The authors derive a perturbation theory-based expression for localization length in bilayered metamaterial structures, capturing the unique low-frequency behavior.

Findings

Localization length can be enormously large at small frequencies.

Derived an explicit formula for localization length valid for any frequency.

Identified specific conditions for observing the non-conventional localization effect.

Abstract

We have developed an approach allowing us to resolve the problem of non-conventional Anderson localization emerging in bilayered periodic-on-average structures with alternating layers of right-handed and left-handed materials. Recently, it was numerically discovered that in such structures with weak fluctuations of refraction indices, the localization length $L_{loc}$ can be enormously large for small wave frequencies $\omega$. Within the fourth order of perturbation theory in disorder, $\sigma^2 \ll 1$, we derive the expression for $L_{loc}$ valid for any $\omega$. In the limit $\omega \rightarrow 0$ one gets a quite specific dependence, $L^{-1}_{loc} \propto \sigma ^4 \omega^8$. Our approach allows one to establish the conditions under which this effect can be observed.