We introduce a fundamental concept and a pragmatic approach to effectively realize negative refraction for elastic waves using a parity-time ($\mathcal{P}\mathcal{T}$)-symmetric plate. In contrast to existing strategies that can achieve this property by making use of complex configurations of phononic crystals or metamaterials, the proposed $\mathcal{P}\mathcal{T}$-symmetric system enables tunable elastic loss and gain, by which the negative refraction can be directly realized and tuned. We demonstrate that, for elastic waves, this tunability can be achieved by piezoelectric units when they are shunted by electric circuits with serially-connected inductance and positive/negative electric resistance. Because the phase and energy flow in the space between the loss and gain units of the system should both be negative, the condition for the $\mathcal{P}\mathcal{T}$-symmetric-based negative refraction is searched by the scattering matrix method. This fundamental concept and its engineering implementation may pave the way toward tunable negative refraction based on the $\mathcal{P}\mathcal{T}$-symmetry approach.

• Received 5 April 2018
• Revised 29 August 2018

DOI:https://doi.org/10.1103/PhysRevApplied.10.044071