Acoustic response in a a one-dimensional layered pseudo-Hermitian metamaterial containing defects

TL;DR

This paper investigates the acoustic response of layered pseudo-Hermitian metamaterials with defects, revealing unidirectional behaviors, symmetry-breaking phenomena, and potential for highly-sensitive sensor applications across a broad frequency spectrum.

Contribution

It introduces the analysis of pseudo-Hermitian acoustic metamaterials with defects, highlighting their unidirectional responses and symmetry-breaking effects, expanding understanding beyond traditional PT-symmetric systems.

Findings

Unidirectional reflection responses in PH-symmetric phases.

Defects can induce high sensitivity and symmetry-breaking.

Wide spectral range of stable PH-symmetric pass-band oscillations.

Abstract

Using transfer-matrix methods, we investigate the response of a multilayered metamaterial system containing defects to an incident acoustic plane wave at normal or oblique incidence. The transmission response is composed of pass-bands with oscillatory behaviour, separated by band gaps and covers a wide frequency range. The presence of gain and loss in the layers leads to the emergence of symmetry breaking and re-entrant phases. In the general case, a system containing defects will display a more general property, pseudo-Hermiticity (PH), of which $\mathcal{PT}$ systems are a subset. In the PH-symmetric phase, unidirectional responses of the reflection, accomplished by reversing the parity $\mathcal{P}$, can be found but the response sometimes deviates from the predictions of simple scattering theory which call for a pseudo-unitarity relation relating the transmission and the two directions of reflections to hold. The converse of reversing the parity, reversing the time operator $\mathcal{T}$ in a spatially-asymmetric system within the PH-symmetric regime can lead to different transmissions: a pass-band versus a stop-band. As regions of stable PH-symmetric pass-band transmission oscillations occur over a wide spectral range, there is a large flexibility in system parameters such as layer thicknesses, for leading to the desired unidirectional traits. In addition, we find that while defects in general lead to a near or complete loss of PH symmetry at all frequencies, they can be exploited to produce highly-sensitive responses, making such systems good candidates for sensor applications.