Exceptional Ring by Non-Hermitian Sonic Crystals

Exceptional point (EP) and exceptional ring (ER) are unique features for non-Hermitian systems, which have recently attracted great attentions in acoustics due to their rich physical significances and various potential applications. Despite the rapid development about the study of the EP and ER in one-dimensional acoustic systems, the realization of them in two-dimensional (2D) non-Hermitian structures is still facing a great challenge. To overcome this, we numerically and theoretically realize an ER in 2D reciprocal space based on a square-lattice non-Hermitian sonic crystal (SC). By introducing radiation loss caused by circular holes of each resonator in a Hermitian SC, we realize the conversion between a Dirac cone and the ER. Based on the theoretical analysis with the effective Hamiltonian, we obtain that the formation of the ER is closely related to different radiation losses of dipole and quadrupole modes in the resonators. Additionally, in the non-Hermitian SC, two eigenfunctions can be merged into a single self-orthogonal one on the ER, which does not exist in the Hermitian SC. Finally, by verifying the existence of the EP with topological characteristics in every direction of 2D reciprocal space, we further demonstrate the ER in the proposed non-Hermitian SC. Our work may provide theoretical schemes and concrete methods for designing various types of non -Hermitian acoustic devices.