Inherent non-Hermitian Chern insulators with PT-symmetry and synthetic translation dimension

The introduction of non-Hermiticity provides photonic systems with more design degrees of freedom, along with unique properties, which have aroused widespread interest. On the other hand, the concept of synthetic dimensions has also been introduced into non-Hermitian topological physics. In this work, we theoretically investigate the two-dimensional (2D) band structure of a 1D non-Hermitian photonic crystal (PC) by introducing globally a translation deformation as a synthetic dimension. The resulting two-dimensional photonic crystal is a Chern insulator, which is numerically verified by calculated Chern numbers and edge dispersions. We find that this property stems from the inherent topology of synthetic space ( k x ,Δ x ), which does not depend on the crystal’s structural and material parameters. It guarantees robust edge states traversing the gap along the synthetic dimension. To provide deeper insight, we derive the reflection phase of a 1D crystal using the plane wave expansion method and give a clear physical picture of the topological edge states generated by translation deformation. These findings may pave the way for translation-based photonic devices, including topological filters and lasers.