  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 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.
