Exceptional points and chiral mode conversion in non-Hermitian elastic media

Non-Hermitian behaviors for elastic waves, including the parity-time (PT) symmetric and anti-PT symmetric exceptional points (EPs) as well as chiral mode conversion via the dynamic encircling of them, are realized in a unified model based on anisotropic elastic media with complex modulus. Based on the tight-binding approximation of elastodynamic equations, the coupling interaction between elastic wave modes is described by the non-Hermitian Hamiltonian, which is used to derive the existence condition of PT-symmetric and anti-PT-symmetric EPs in different parameter systems. Eigenmode evolution of elastic waves in the process of dynamic encircling of EPs is studied in the spatially modulated model consisting of the multilayered anisotropic media. Chiral mode conversion for elastic waves as dominated by the encircling direction is disclosed by the developed model. The dynamical encircling of a PT-symmetric EP can lead to chiral mode conversion for the symmetric phase, while encircling an anti-PT-symmetric EP results in chiral mode switching for the broken phase. Dynamic evolution along regular and irregular paths are analyzed to demonstrate the topological robustness of chiral mode conversion.