Hyperuniformity and wave localization in pinwheel scattering arrays

We investigate the structural and spectral properties of deterministic aperiodic arrays designed from statistically isotropic pinwheel tiling. By studying scaling cumulative integral its structure factor in combination with higher-order correlation analysis we conclude that belong to weakly hyperuniformity class. Moreover, by solving multiple scattering problem for electric point dipoles using rigorous Green's matrix theory, demonstrate a clear transition diffusive transport localization behavior. This is shown Thouless number as function strength statistics resonances. Surprisingly, despite absence sharp diffraction peaks, gaps are discovered density states manifest distinctive long-range order. Furthermore, level spacing at large optical exhibits repulsion Poisson behavior, consistently onset wave regime. Our findings reveal importance hyperuniform structures k-space engineering enhanced light-matter interaction properties.