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Non-Conventional Anderson Localization in Bilayered Structures with Metamaterials

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 $ω$. Within the fourth order of perturbation theory in disorder, $σ^2 \ll 1$, we derive the expression for $L_{loc}$ valid for any $ω$. In the limit $ω\rightarrow 0$ one gets a quite specific dependence, $L^{-1}_{loc} \propto σ^4 ω^8$. Our approach allows one to establish the conditions under which this effect can be observed.