Non-conventional Anderson localization in a matched quarter stack with metamaterials

• Published in: New journal of physics Vol. 15; no. 5; pp. 55014 - 23
• Main Authors: Torres-Herrera, E J, Izrailev, F M, Makarov, N M
• Format: Journal Article
• Language: English
• Published: IOP Publishing 21.05.2013
• Subjects: Anderson localization; Disorders; Fluctuation; Localization; Mathematical models; Position (location); Refraction; Stacks
• DOI: 10.1088/1367-2630/15/5/055014
• ISSN: 1367-2630

We study the problem of non-conventional Anderson localization emerging in bilayer periodic-on-average structures with alternating layers of materials, with positive and negative refraction indices na and nb. Attention is paid to the model of the so-called quarter stack with perfectly matched layers (the same unperturbed by disorder impedances, Za = Zb, and optical path lengths, nada = |nb|db, with da and db being the thicknesses of basic layers). As was recently numerically discovered, in such structures with weak fluctuations of refractive indices (compositional disorder), the localization length Lloc is enormously large in comparison to the conventional localization occurring in the structures with positive refraction indices only. In this paper we develop a new approach, which allows us to derive the expression for Lloc for weak disorder and any wave frequency ω. In the limit ω → 0 one gets a quite specific dependence, L−1loc∝σ4ω8, which is obtained within the fourth order of perturbation theory. We also analyze the interplay between two types of disorder, when in addition to the fluctuations of na and nb, the thicknesses da and db slightly fluctuate as well (positional disorder). We show how conventional localization recovers with the addition of positional disorder.