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 light localization 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. This light localization transition is different from the Anderson transition because Vogel spirals are deterministic structures. 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 point-like 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 lightmatter 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. arXiv:1810.01909v2 [cond-mat.dis-nn]

Aperiodic Photonics of Elliptic Curves

“…The subradiant dark states, also called proximity resonances, are characterized by MSE=2 [67,70] (see also Fig.4 (a-b)). Interestingly, the absence of these scattering resonances in a class of aperiodic spirals, called Vogel spirals, was recently connected to the ability of these structures to localize vector waves thanks to their peculiar correlation properties [31].…”

“…This frequency stripe selection is necessary due to the strong frequency dependence of the light localization behavior [31]. On the other hand, averaging over all scattering frequencies will produce biased results due to mixing of different types of light regimes [75].…”

“…This is due to two factors: the presence of degenerate proximity resonances (like the ones shown in Fig.4 (e-f)) and the absence of any structural correlations. The absence of structural correlations was recently identified as the factor preventing light localization to occur in uniform random arrays when the vector nature of light is taken into account [20,31,66].…”

“…However, the level statistics of deterministic aperiodic systems displays different features with respect to the uniform random scenario. In our previous works, we have investigated the transition from the presence to the absence of level repulsion by increasing ρλ 2 in different open, deterministic, and aperiodic planar systems [25,31,43]. We have found that the distribution obeys at ρλ 2 ¡1 the critical cumulative probability density:…”

“…Deterministic structures with aperiodic though long-range ordered distributions of scattering potentials have a long history in the electronics and optics communities due to significant advantages in design and compatibility with standard fabrication technologies compared to random systems [22,23]. These structures manifest unique spectral characteristics that lead to physical properties that cannot be found in either periodic or uniform random media, such as multifractal density of eigenstates with varying degrees of spatial localization, known as critical modes [24][25][26][27][28], anomalous photon transport regimes [29,30], and distinctive wave localization transitions [31,32]. Critical modes feature highly-fragmented envelopes characterized by local power-law scaling that reflects the multi-scale geometry of certain deterministic aperiodic potentials that found recent applications to light emission and lasing, optical sensing, photo-detection, and nonlinear optical devices [24,26,[33][34][35][36][37][38][39][40][41].…”