Novel acoustic flat focusing based on the asymmetric response in parity-time-symmetric phononic crystals.

We present a two-dimensional (2D) parity-time-symmetric (PT-symmetry) phononic crystals (PCs) with balanced gain and loss medium. Using the super cell method of rectangular lattice, we exhibit the thresholdless spontaneous PT-symmetry breaking in the band structure. The numerical results show that the asymmetric scattering properties obviously occur in a non-Hermitian system. At two specific incident frequencies, unidirectional reflectionless and perfect transmission behaviors exist individually in opposite directions, which are accompanied by a phase transition of π. Based on the generalized Snell's law, combining such a PT-symmetric medium, we design a novel metamaterial crystal for PT-symmetric acoustic flat focusing. Its focus frequency can also be modulated by the gain/loss parameter. The novel flat focusing based on the PT-symmetry that we propose opens a new door for high-dimensional applications of non-Hermitian metamaterials in acoustic wave manipulation.