Emergence of Exceptional Points in Periodic Metastructures with Hidden PT-symmetric Defects

TL;DR

This paper investigates how PT-symmetric defects in periodic elastodynamic metastructures induce exceptional points, revealing control over their emergence and critical gain/loss parameters through defect positioning and structure size.

Contribution

It demonstrates the formation and control of exceptional points in elastodynamic metastructures with engineered PT-symmetric defects, combining theoretical and numerical analyses.

Findings

PT-symmetric defects create multiple exceptional points at band edges.

Defect location influences the number of EPs and the critical gain/loss strength.

Metastructure size and defect position affect the EP formation threshold.

Abstract

We study the elastodynamics of a periodic metastructure incorporating a defect pair that enforces a parity-time (PT) symmetry due to a 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 PT-symmetric defect serves as an additional control over the number of emerging EPs in the corresponding spectra as well as the critical non-Hermitian (gain/loss) strength required to create the first EP - a specific defect location minimizes the critical non-Hermitian strength. We use both finite element and coupled-mode-theory-based models to investigate these metastructures, and use a time-independent second-order perturbation theory to further demonstrate the influence of the size of the metastructure and the PT-symmetric defect location on the minimum non-Hermitian strength required to create the first EP in a band. Our findings motivate feasible designs for the experimental realization of EPs in elastodynamic metastructures.