Universal transverse confinement and scaling of transmission eigenchannels in disordered photonic lattices

Harnessing subsets of scattering paths, particularly through the transmission eigenchannels, has recently become a crucial strategy to control wave transport in disordered media. While previous works are mainly focused on structures with both axial and horizontal disorders, the disordered photonic lattice—offering the unique advantage that its uniform axial direction acts as an effective time dimension—has remained largely unexplored. Here, we unveil the distinctive transverse profiles of transmission eigenchannels in disordered photonic lattices, which are inherently related to the intriguing long- and short-lived scattering modes by taking into account the effective temporal dimension. Interestingly, we demonstrate a remarkable localization-to-delocalization transition, i.e., high-transmission eigenchannels exhibit a strongly shrinking bell-shaped transverse profile, while low-transmission eigenchannels feature an extended profile with a characteristic central dip. Further theoretical analysis leads to a profound linear scaling between the transverse size and the transmission coefficient. Moreover, we find that the disorder strength can amplify the interference of scattering paths, leading to enhanced confinement for high-transmission channels but deepened central dip for the low-transmission counterparts. These results offer new perspectives on wave localization and energy flow in complex systems, with direct implications for enhancing performance in random lasers, photoluminescence, and nonlinear optical processes.