Subdiffusive light transport in three-dimensional subrandom arrays

Abstract

We investigate light transport in novel three-dimensional scattering systems generated according to subrandom sequences and demonstrate subdiffusive behavior typical of wave transport in disordered systems at the critical point for metal-insulator-transitions but in a wider range of parameters. Specifically, we solve the electromagnetic multiple scattering problem using the Green's matrix spectral theory for aperiodic systems based on Halton, Sobol, and stochastic Latin-Hypercube sequences. By studying the Thouless number and the level spacing statistics of the electromagnetic resonances at different scattering density we demonstrate that light transport in deterministic Halton and Sobol structures exhibit multifractal behavior characterized by inverse power law scaling of level spacing statistics across a wide range of densities of dipolar scatterers. On the other hand, this scenario is absent in the stochastic Latin-Hypercube array, whose behavior resembles instead standard diffusion in uniform random media. Our findings establish a connection between subdiffusion and subrandom aperiodic order and provide a novel strategy to design three-dimensional structures with multifractal properties over a broad spectral range.