Non-Hermitian reconstruction of photonic hierarchical topological states

Abstract Higher-order topological phases featured by hierarchical topological states (HTSs) have spawned a paradigm for developing robust multidimensional wave manipulation. While non-Hermitian skin effects (NHSEs) entail that bulk states collapse to open boundaries as local skin modes, the topological transport properties at the interplay between HTS and NHSE are still at early stage of exploration. Here, we report the non-Hermitian reconstruction of HTSs by incorporating the interplay of NHSEs and HTSs, which manifests robust and controllable topological transport properties. By a feasible design in coupled resonant optical waveguides, we demonstrate that zero-dimensional topological states of HTSs only undergo non-Hermitian reconstruction at finitely small system sizes, while nonzero-dimensional topological states of HTSs undergo non-Hermitian reconstruction independent of bulk states. We link the behaviour of zero-dimensional topological states to the restriction of their spatially non-negligible couplings under a macroscopic non-reciprocal framework. Our study unveils the interplay mechanism between NHSEs and HTSs, and underpins topological applications in various wave systems.