Light Propagation in Binary Kagome Ribbons With Evolving Disorder

Abstract

Recently, considerable attention has been paid to investigation of light localization in quenched disordered quasi-one and two dimensional photonic lattices (PLs) hosting one or more fl at bands (FBs) [1,2]. Emergence of diff erent energy-dependent scaling laws for localization lengths have been observed, with respect to mutual position of fl at and dispersive bands [1]. While eff ects of nonlinearity on light localization have also been explored in FB PLs with quenched disor-der [2], FB PLs with evolving disorder have not been studied so far. We investigate light propagation in uniform and binary kagome ribbons in the presence of evolving disorder. Th e particularity of binary structure is opening of gaps in the eigenvalue spectrum around FB [3]. Our intention is to clarify energy-dependent properties of the light spreading under the mutual infl uence of binarism and evolving disorder by initially exciting diff erent modes in eigenvalue spectrum of studied PLs. Binary kagome ribbons are modeled with system of coupled diff erential-diff erence linear equations in tight binding approximation. We consider only the case of on-site diagonal disorder in system. Evolving disorder is modeled by changing realization of on-site disorder in light propaga-tion direction aft er a defi ned step . We perform an extensive investigation of the light spreading dynamics in such disordered lattices, by exploring diff erent values of the dephasing step and disorder strength d. Observed light propagation regimes are classifi ed based on the behavior of sta-tistical measures (participation ratio and second moment) of light beam along propagation directions of PLs.