Non-Hermitian topological coupler for elastic waves

Non-Hermitian topological systems, by combining the advantages of topological robustness and sensitivity induced by non-Hermiticity, have recently emerged and attracted much research interest. Here, we propose a device based on the topological coupler in elastic waves with non-Hermiticity, which contains two topological domain walls and four ports. In this device, topological robustness routes the transmission of waves, while non-Hermiticity controls the gain or loss of waves as they propagate. These mechanisms result in continuous and quantitative control of the energy distribution ratio of each port. A non-Hermitian Hamiltonian is introduced to reveal the coupling mechanism of the topological coupler, and a scattering matrix is proposed to predict the energy distribution ratio of each port. The proposed topological coupler, which provides a new paradigm for the non-Hermitian topological systems, can be employed as a sensitive beam splitter or a coupler switch. Moreover, the topological coupler has potential applications in information processing and logic operation in elastic circuits or networks, and the paradigm also applies to other classical systems.