Optical Solitons in Hatano-Nelson Systems

Since the discovery of the non-Hermitian skin effect [1], [2] in Hatano-Nelson systems [3], a plethora of experimental realizations from disordered media [4] to topological lasers [5] has emerged. From the theoretical point of view such results are counterintuitive with respect to the bulk-boundary correspondence and thus lead to new definitions of topological invariants for non-Hermitian systems [2]. From the experimental point of view, a lot of new and intriguing characteristics have been demonstrated. Despite being non-Hermitian, Hatano-Nelson systems can exhibit entirely real spectra with all the corresponding eigenmodes being localized at the surface, the so-called non-Hermitian skin effect [1], [2]. Most of these studies are devoted to the linear Hatano-Nelson Hamiltonian.