Localization of scattering resonances in aperiodic Vogel spirals

Abstract

By using the dyadic Green's matrix spectral method, we demonstrate that aperiodic deterministic Vogel spirals made of electric dipoles support a light localization transition in three dimensions, an effect that does not occur in traditional uniform random media. We discover a light localization transition in Vogel spiral arrays embedded in three-dimensional space by evaluating the Thouless conductance, the level spacing statistics, and by performing a finite-size scaling. We probe light localization in the plane of the array by analyzing the behavior of the scattering resonances in three-dimensional space. This light localization transition is different from the Anderson transition because Vogel spirals are aperiodic deterministic structures characterized by nonuniform geometries. Moreover, this transition occurs when the vector character of light is fully taken into account, in contrast to what is expected for traditional uniform random media of pointlike scatterers. We show that light localization in Vogel arrays is a collective phenomenon that involves the contribution of multiple length scales. Vogel spirals are suitable photonic platforms to localize light thanks to their distinctive structural correlation properties that enable collective electromagnetic excitations with strong light-matter coupling. Our results unveil the importance of aperiodic correlations for the engineering of photonic media with strongly enhanced light-matter coupling compared to the traditional periodic and homogeneous random media.