Impact of non-Hermiticity and nonlinear interactions on disorder-induced localized modes

In non-Hermitian photonics, introducing gain and loss offers new degrees of freedom to control optical systems and a unique approach to explore fundamental concepts. Random lasers are a natural class of non-Hermitian open optical systems where spatial confinement, leakage, and non-orthogonality of the modes are further controlled by the degree of scattering. How Anderson localization is impacted by complex potentials, gain and loss and, more generally, nonlinearities has been the subject of numerous theoretical debates, without any conclusive experimental demonstration yet. Indeed, in systems where localized modes have sufficient spatial extension to be observed and investigated, their mutual interaction and coupling to the sample boundaries make it extremely difficult to isolate them spectrally and investigate them alone. Here, the degree of non-Hermiticity of an active scattering medium is controlled by shaping the pump. By imaging the intensity distribution of individual localized lasing modes, we demonstrate experimentally their insensitivity to local pumping; a signature that orthogonality is preserved between modes localized away from the system boundaries, as theoretically established. Demonstration of the one-to-one correspondence between lasing modes and localized states of the passive system opens the route to investigate the robustness of localized states in the presence of nonlinear gain and nonlinear modal interactions. Interestingly, gain saturation and mode competition for gain do not affect the spatial distribution of the modes, demonstrating their orthogonality in an otherwise strongly non-Hermitian system.