Conditionally extraordinary transmission in periodic parity-time symmetric phononic crystals

Parity-time (PT) symmetry originating from quantum mechanics has extended to other branches, such as optics and acoustics. In acoustics, the studies have mainly focus on fluids, such as air, and, in particular, they have not involved periodicity of structure, as seen in phononic crystals (PC). The current work introduces loss-gain PT symmetry into periodic elastic PC lattice systems that can simultaneously realize unidirectional zero reflection and extraordinarily high transmission under the condition: a certain number of unit cells of PC. In particular, it is shown that the infinite periodic PT symmetric PC (PT-S-PC) shows coalescence of band structure. Interface response theory of the system is used to investigate the scattering matrix of finite PT-S-PCs. The results show that the transmittance is extraordinarily high, reaching hundreds, at the frequency associated with the coalescence point of the infinite periodic PT-S-PC. The extraordinary transmission appears periodic-like with respect to the number of cells of the PT-S-PC system, and this extraordinary transmission resonance has an ultrahigh quality factor. Moreover, the scattering characteristics of the PT-S-PC system in the locally resonant band gap are explored. This work provides a new way to manipulate elastic waves and opens the path to design new devices, for example, for non-destructive testing.