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Cavity optomechanics is important in both quantum information processing andbasic physics research. In this paper, we propose an optomechanical latticewhich manifests non-Hermitian physics . We first use the non-Bloch band theoryto investigate the energy spectrum and transmission property of anoptomechanical lattice. The generalized Brillouin zone of the system iscalculated with the help of the resultant. And the periodical boundarycondition (PBC) and open boundary condition energy spectrum are given,subsequently. By introducing probe laser on different sites we observed thedirectional amplification of the system. The direction of the amplification isanalyzed combined with the non-Hermitian skin effect. The frequency thatsupports the amplification is analyzed by considering the PBC energy spectrum.By introducing probe laser on one site we investigate the onsite transmissionproperty. Optomechanically induced transparency (OMIT) can be achieved in oursystem. By varying the parameters and size of the system, the OMIT peak can beeffectively modulated or even turned into optomechanically inducedamplification . Our system shows its potential as the function of a single-waysignal filter. And our model can be extended to other non-Hermitian Bosonicmodel which may possess topological features and bipolar non-Hermitian skineffect.

Optomechanically induced transparency and directional amplification in a non-Hermitian optomechanical lattice