Transverse spreading Anderson Localization in two and three dimensional disordered correlated dielectric materials with bandgap regimes

Strong Anderson Localization manifests itself as an interference wave phenomenon, potentially leading to completely localized states under infinite extension. We propose a framework for characterizing light transmission through two-dimensional high-refractive disordered materials, showcasing both localization and photonic band gaps (PBG). Leveraging advanced numerical techniques and recent advancements in Finite-Difference Time Domain (FDTD) simulations, we explore how light behaves in complex dielectric materials and how these effects interact near the bandgap. Based on FDTD numerical simulations, we studied the transverse spreading of a focused beam through various realizations of 2D Stealthy Hyperuniform (SHU) patterns silicon rods. For frequencies close to the bandgap, the transverse confinement of the transmitted intensity indicates the presence of Anderson localization, while far from the gap we observe rapid spreading of the intensity toward to the edges of the slabs suggesting diffusive behavior. We identified all transport regimes: bandgap, pseudotunneling, Anderson localization, and diffusion, and we present our findings in transport phase diagrams.