Suppression of Anderson localization of light in one-dimensional disordered photonic superlattices

Abstract

The localization properties of electromagnetic modes in one-dimensional disordered photonic superlattices are theoretically studied. The multilayered system is considered to be composed of alternating stacks of two different random-thickness slabs, characterized by nondispersive and/or frequency-dependent electric permittivities and magnetic permeabilities. Results for the localization length are evaluated by using an analytical model for weakly disordered systems as well as its general definition through the transmissivity properties of the heterostructure. Good agreement between both results is observed only for small amplitudes of disorder. The critical frequencies at which the localization length diverges are correctly predicted in the whole frequency spectrum by the analytical model and confirmed via the corresponding numerical calculations. The ${\ensuremath{\lambda}}^{2}$ dependence of the localization length, previously observed in disordered heterostructures made of material of positive refractive indexes, are confirmed in the present work. In addition, new ${\ensuremath{\lambda}}^{4}$ and ${\ensuremath{\lambda}}^{\ensuremath{-}4}$ dependencies of the localization length in positive-negative disordered photonic superlattices are obtained, under certain specific conditions, in the long and short wavelength limits, respectively. The asymptotic behavior of the localization length in these limits is essentially determined by the particular frequency dispersion that characterizes the metamaterial used in the left-handed layers. When the effects of absorption are considered, then a divergence of the localization length is still observed, under some conditions, in the short wavelength limit.