Anderson localization of light in disordered superlattices containing graphene layers

Abstract

We theoretically investigate light propagation and Anderson localization in one-dimensional disordered superlattices composed of dielectric stacks with graphene sheets in between. Disorder is introduced either on graphene material parameters (e.g. Fermi energy) or on the widths of the dielectric stacks. We derive an analytic expression for the localization length ξ, and compare it to numerical simulations using transfer matrix technique; a very good agreement is found. We demonstrate that the presence of graphene may strongly attenuate the anomalously delocalised Breswter modes, and is at the origin of a periodic dependence of ξ on frequency, in contrast to the usual asymptotic decay, ξ ∝ ω −2 . By unveiling the effects of graphene on Anderson localization of light, we pave the way for new applications of graphene-based, disordered photonic devices in the THz spectral range.

Anderson localization of classical waves in weakly scattering one-dimensional Levy lattices

“…At short wavelengths the localization length tends to a constant given by relation (19) The solid red curve is the numerical Monte Carlo calculation, while the dotted blue curve is the analytical prediction (18). The horizontal dashed line is the derived shortwavelength asymptote (19), while the green dashed curve is the long-wavelength asymptote (21).…”

“…3) the localization length tends to a constant. The horizontal dashed line is based on the short-wavelength asymptote (19). So at the short wavelength the localization length depends on the Fresnel reflection coefficient and on the mean layer thickness.…”

“…For example, the effects of absorption on Anderson localization have been considered in [11,12], while the effects of gain have been considered in [13,14]. The properties of Anderson localization have been considered in different media as well, such as disordered periodic media [15,16], metamaterials [17,18], graphene [19], and gyrotropic media [20]. It has been established that metamaterials can suppress Anderson localization.…”

Scattering of surface plasmon polaritons in a graphene multilayer photonic crystal with inhomogeneous doping

“…Also it is interesting that the graphene stacks exhibit the properties of hyperbolic metamaterials [36][37][38] . Finally, the study of propagation of radiation in a disordered graphene stack when light impinges perpendicularly to the graphene surface has recently been considered 17 , showing that graphene can control Anderson localization of radiation.…”

“…The above-mentioned zeroth approximation for p also can be used for approximating the spatial profile function (17), namely:…”