Direction-dependent non-Hermitian skin effect in modulated photonic waveguide arrays

Non-Hermitian skin effect (NHSE), where huge modes are accumulated at system boundaries, offers new possibility for steering the transport and localization of light by non-Hermiticity. Here, the direction-dependent NHSE is proposed in a photonic waveguide array via spatially complex modulation, where the skin modes tend to localize at different boundaries for opposite propagation directions. We utilize complex modulation to arouse anisotropic coupling between symmetric and anti-symmetric modes in multimode waveguides and further match the refractive index of adjacent waveguides. In this way, a non-Hermitian Su-Schrieffer-Heeger (SSH) lattice that supports NHSE is achieved. In particular, the anisotropic coupling is highly unidirectional. For forward direction, it allows mode conversion from antisymmetric modes to symmetric modes. However, the process is forbidden for backward direction. As a result, the skin modes tend to locate at lower boundary for forward propagation but the localization direction is reversed for backward injection. Our results provide a potential platform to investigate NHSE on photonic chips and may find applications in non-magnetic unidirectional devices.