Controlling light transport in non-Hermitian waveguide arrays

Controlling light propagation in scattering media remains a fundamental challenge in photonics. Non-Hermitian waveguide arrays offer a promising platform for advanced light manipulation, yet key questions persist regarding the roles of the non-Hermitian skin effect and topology in stabilizing transmission. We analytically investigate these phenomena using an extended Hatano-Nelson model with open boundaries, deriving exact solutions for both eigen-site and single-site excitations (n = 1) and asymptotic solutions for n ≥ 1. Our results demonstrate that the skin effect induces edge-localized propagation with energy-dependent gain/attenuation in eigen-site excitation and topological light funneling in single-site excitation. For n ≥ 1, we discover a unique 2n-directional Gaussian transport originating from single-site excitation, which can be extended to multi-site scenarios via superposition. These findings reveal three robust control mechanisms-gain/loss-modulated propagation, non-reciprocal funneling, and multi-directional spreading-providing design principles for topological photonic devices including scattering-resistant lasers and invisibility materials.