Emergence of Exceptional Points in Periodic Metastructures With Hidden ParityTime Symmetric Defects

Abstract

We study the elastodynamics of a periodic metastructure incorporating a defect pair that enforces a paritytime (PT) symmetry due to judiciously engineered imaginary impedance elements—one having energy amplification (gain) and the other having an equivalent attenuation (loss) mechanism. We show that their presence affects the initial band structure of the periodic Hermitian metastructure and leads to the formation of numerous exceptional points (EPs) which are mainly located at the band edges where the local density of modes is higher. The spatial location of the PTsymmetric defect serves as an additional control over the number of emerging EPs in the corresponding spectra as well as the critical nonHermitian (gain/loss) strength required to create the first EP—a specific defect location minimizes the critical nonHermitian strength. We use both finite element and coupledmodetheorybased models to investigate these metastructures and use a timeindependent secondorder perturbation theory to further demonstrate the influence of the size of the metastructure and the PTsymmetric defect location on the minimum nonHermitian strength required to create the first EP in a band. Our findings motivate feasible designs for the experimental realization of EPs in elastodynamic metastructures.