Exceptional concentric rings in a non-Hermitian bilayer photonic system

We establish the bilayer non-Hermitian theory with interlayer coupling between two graphenelike lattices described by non-Hermitian Hamiltonians. Two exceptional rings (ERs) and an exceptional concentric ring (ECR) in this system are discovered. A topological classification has been identified for such non-Hermitian Hamiltonians via their global topological invariants. We find that two ERs and the ECR correspond to the global Z(3) topological invariant V = +1 and V = -1, respectively, whose topological properties are determined by the four-level bands and go beyond the topological properties of a single ER. It is shown that in contrast to the Hermitian case, the topological surface arcs with gain and loss are both present and redistributed in the two ERs and the ECR systems. We further propose an experimental design with bilayer photonic crystals (PCs) to realize the ECR. Our work can potentially pave the way for unveiling the unusual topological properties in such stacked two-dimensional materials and trigger further theoretical and experimental investigations.