Spectral level repulsion and Lifshitz-like states in hyperuniform disordered photonic networks.

Disorder is emerging as a design principle in nanophotonics, offering new ways to control light beyond the limits of periodic architectures. Hyperuniform disordered networks, positioned between order and randomness, offer a unique platform for this exploration. Using large-scale numerical simulations and hyperspectral near-field imaging, we uncover spectral level repulsion among delocalized modes - a universal signature of interacting states in complex systems, from nuclear physics to quantum chaos, experimentally observed here for the first time in correlated disordered photonics. Within the same platform, we provide a phenomenological identification of classes of localized modes in hyperuniform disordered networks: genuine Anderson states and defect-induced resonances associated with Lifshitz-like photonic states. Unlike their electronic counterparts, these Lifshitz-like states arise from architecture-encoded topological defects and can hybridize into coupled "photonic molecules". Our results reveal a potentially reconfigurable regime of disorder where localization, correlations, and coupling can be engineered, opening new opportunities for random lasing, optical filtering, and quantum photonics.