Bound states in one-dimensional acoustic parity-time-symmetric lattices for perfect sensing

• Two kinds of defect states have been systematically studied.
• Studying the eigenvalues of scattering matrix for non-dissipative and PT-symmetric system.
• Proposing a design of sensitive acoustic sensor.

In this letter, we study the propagation of acoustic waves through a one-dimensional multilayer structure composed of a thin defect layer sandwiched by two phononic crystals. Two kinds of defect states will generate in band gaps and both of them cause unitary transmission. However, they have very unlike field distributions due to the different contrasted acoustic impedances between the defect layer and its neighboring layers. Spectral positions of transmission peaks can be exactly determined by the resonant phase condition. In a non-dissipative system, these resonant states correspond to single crossing point of two eigenvalues of scattering matrix. When gain and loss are introduced to judiciously construct an acoustic parity-time-symmetric lattice, the crossing point will split into a pair of exceptional points (EPs). Interestingly, the EPs correspond to unidirectional zero reflection that is very sensitive to the thickness of defect layer. Taking advantage of this virtue, a very sensitive acoustic sensor can be designed, which has potentially applications in ultrasonic inspection, noise detection, ultrasonic medicine, etc.