Evolution of exceptional points and anisotropic transmission resonance phenomenon for one-dimensional local resonant phononic crystal

In this study, a spring–mass physical model is proposed to study the complex band structure of a one-dimensional parity-time (PT)-symmetric local resonant phononic crystal. By solving the kinetic equations, the analytical solutions of the dispersion relation and effective mass are obtained. As is known, the infinite effective mass would appear at the resonant frequency in a Hermitian system without any gain or loss. Once the balanced gain and loss are added to form a PT-symmetric system, the infinite effective mass would become finite, and the exceptional points can be observed in the subwavelength realm. With the increase in gain and loss, exceptional points would coalesce and form a higher order one. The numerical simulations in a practical structure agree well with the analytical analysis. In addition, the simulated transmission/reflection spectrum and field distribution clearly demonstrate the anisotropic transmission resonances. Our investigation enriches the physical connotation of local resonant phononic crystals in non-Hermitian systems.