Non-conventional Anderson localization in bilayered structures

¹ Instituto de Física, Universidad Autónoma de Puebla - Apartado Postal J-48, Puebla, Pue., 72570, México
² NSCL and Department of Physics and Astronomy, Michigan State University - East Lansing, MI 48824-1321, USA
³ Instituto de Ciencias, Universidad Autónoma de Puebla - Priv. 17 Norte No 3417, Col. San Miguel Hueyotlipan, Puebla, Pue., 72050, México

^a felix.izrailev@gmail.com

Received: 9 February 2012
Accepted: 15 March 2012

Abstract

We resolve the problem of non-conventional Anderson localization emerging in bilayered periodic-on-average structures with alternating layers of materials with positive and negative refraction indices. Recently, it was numerically discovered that in such structures with weak fluctuations of refractive indices, the localization length L_loc can be enormously large for small wave frequencies ω. Within a new approach allowing us to go beyond the second order of perturbation theory, we derive the expression for L_loc valid for any ω and small variance of disorder, σ²≪1. In the limit ω→0 one gets a quite specific dependence, L⁻¹_loc∝σ⁴ω⁸. Our approach allows one to establish the conditions under which this effect occurs.