Nonreciprocal dynamic degeneracy splitting in non-Hermitian photonic crystals

Non-Hermitian dynamics offer promising ways to study the non-equilibrium phase of matter, such as chiral Zener tunneling, non-Bloch dynamics, and dynamic non-Hermitian skin effects, phenomena that cannot be fully captured by static eigenstate descriptions alone. Dynamic degeneracy splitting (DDS), which reveals the dynamic consequence caused by the uneven broadening of equal-frequency contours at a given excitation frequency, assists in investigating non-Hermitian dynamics. However, under reciprocity constraints, the theoretical and experimental studies of previous research on DDS have primarily focused on structures that exhibit centrosymmetric band structure and lifetime, leaving the distinctive phenomena associated with nonreciprocity largely unexplored. Here, we propose and realize nonreciprocal DDS through anisotropic damping of hyperbolic-like bands, induced by sequential symmetry breaking in a photonic crystal. This nonreciprocal DDS enables directional transmission via momentum-selective excitation in a stripe geometry and directional imaging in a slab geometry through anomalous negative refraction. These findings unify the concepts of nonreciprocity, non-Hermiticity, and dissipation anisotropy, demonstrating the opportunities enabled by artificial materials through symmetry engineering for tunable, highly directional wave propagation.