Localization in Correlated Bilayer Structures: From Photonic Crystals to Metamaterials and Semiconductor Superlattices

Abstract

In a unified approach, we study the transport properties of periodic-on-average bilayered photonic crystals, metamaterials, and semiconductor superlattices. Our consideration is based on the analytical expression for the localization length derived for the case of weakly fluctuating widths of layers and 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.

Analytical theory of light localization in one-dimensional disordered photonic crystals

“…While some problems, like coherent backscattering of light from disordered photonic crystals, can be treated perturbatively using Green function technique [48]- [50], the problem of localization of light by such structures requires summation of all the diagrams or application of the different approaches as done in Refs. [51]- [53]. Unfortunately, the methods suggested in Refs.…”

“…regions of the most interest), as stated in Ref. [53]. Recently the problem of light localization in the one-dimensional case has been considered in more strict manner using the Fokker-Planck equation [54] similar to considered in Ref.…”

“…Even a one-dimensional model of Ref. [53] restricted to the case of purely geometric disorder was not solved exactly but using a kind of heuristic assumption, namely uniform distribution of some angle variable θ. Unfortunately, this assumption is certainly wrong for the center and edges of the photonic band gap (i.e.…”

Anderson localization in metamaterials and other complex media (Review Article)

“…Note that for considered alternated stack, it is natural to join each pair of subsequent layers with numbers j = 2n − 1 and j = 2n into one effective cell number n. Then the total transfer matrix factorizes to the product of N/2 transfer matrices of separate cells 43,[51][52][53][54] .…”

“…Detailed investigation of Lyapunov exponent (and therefore localization length l ξ ) in various multilayered metamaterials was presented in [51][52][53][54] . In the weak disorder limit, explicit expressions for Lyapunov exponent valid in all region of wavelengths for various kinds of correlated disorder were obtained 53,54 and analytical explanation of anomalous suppression of localization was done 51,52 .…”