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Frontiers in Phononics: Parity-Time Symmetric Phononic Metamaterials

Periodic Reporting for period 3 - PHONOMETA (Frontiers in Phononics: Parity-Time Symmetric Phononic Metamaterials)

Reporting period: 2019-12-01 to 2021-05-31

The boost experienced by acoustic and elastic (phononic) metamaterial research during the past years has been driven by the ability to sculpture the flow of sound waves at will. Thanks to recent developments at the frontiers of phononic metamaterials it can be identified that active phononic control is at the cutting edge of the current research on phononic metamaterials.

The aim is to explore novel properties of sound and the ability to design Parity-Time (PT) symmetric systems that define a consistent unitary extension of quantum mechanics. Through innovative media sculpturing balanced loss and gain units, these structures have neither parity symmetry nor time-reversal symmetry, but are nevertheless symmetric in the product of both. PHONOMETA is inspired and driven by these common notions of quantum mechanics that I wish to translate into classical acoustics with unprecedented knowledge for the case of sound.

I expect that the successful realization of PHONOMETA has the potential to revolutionize acoustics in our daily life. Environmental and ambient noise stem from multiple scattering and reflections of sound in our surrounding. The extraordinary properties of PT acoustic metamaterials have the groundbreaking potential to push forward physical acoustics with new paradigms to design tunable diode-like behaviour with zero reflections, which is applicable for noise pollution mitigation. Also I anticipate to impact the progress on invisibility cloaks by introducing PT symmetry based acoustic stealth coatings for hiding submarines.
1.1 Overview
In the initiating 30 months of the project we have taken on 4 actions of the PHONOMETA project dealing with parity-time symmetric phononic metamaterials. In brief, those actions comprise studies in: 1. Artificial lattices, 2. One-way acoustic diodes, 3. Alternative acoustic gain, and 4. Cloaks of unhearability.

1.2 Major achievements
In the following, an overview of the major milestones achieved is listened. Further, we also list partial works that have not yet reached completion but belong in the category of the utter most contributions. Those findings are based on theoretical predictions, numerical computations, and experimental verifications as conducted by external collaborators.

1.2.1 – Artificial lattices
Ordinary media (described through Hermitian systems) and those that are PT symmetric (described through non-Hermitian systems) have been studied in man-made lattices with special emphasis on topological insulators. We have found new ways to engineer acoustic surface and interface states in Hermitian structures, but also for the non-Hermitian counterpart leading to both wave amplification and attenuation. Further, we have found new possibilities to control wave propagation, in that for the first time, we explored ways to generate supersonic wave transports. Interestingly, along side the growing interest of topological insulators (TIs), we dedicated our efforts in designing both Hermitian and non-Hermitian TIs that have lead to a close collaboration with experimentalists from the Nanjing University, China who have implemented many of our numerical key findings. In fact, we were the first ones to explore higher order TIs for sound waves containing non-Hermiticity. In this regard we developed a multiple scattering theory formalism to compute those exotic properties.

1.2.2 – One-way acoustic diodes
We conducted numerical studies in piezoelectric semiconductors and found a novel way to engineer acoustic rectification permitting ultrasonic waves to propagate along a one-way path only. Along the same frontier we explored that this acoustic diode could overcome visco-thermal and lattice losses.

1.2.3 – Alternative acoustic gain
In order to ease the implementation of acoustic gain that is essential in non-Hermitian systems we investigated two alternative routes: 1. We explored an optomechanical solution that surprisingly led to PT symmetric optical forces and force rectifiers and 2. We designed a model to elaborate a passive acoustic PT symmetric system not relying on gain. Experiments have been undertaken through external collaboration from Le Mans University.

1.2.4 - Cloaks of unhearability
We developed a theoretical model to design the acoustic counterpart of an invisibility cloak. By designing PT symmetry in a single layer shell-structure, our predictions sparked a fruitful collaboration with experimentalists from the Nanjing University, China who build this device. To date, our proposal is the largest unhearability cloak that could hide a human from incoming sound at audible frequencies. This paper is currently revised for publication in the journal SPJ Research.
Invisibility cloaks for sound waves that we call: Cloaks of unhearability, is one of our important contribution to the scientific community. Theoretically we employed a model to explore the needed acoustical ingredients to diminish the scattering of an object to be hidden and what it took, to reconstruct the field on the far-side of the object. Numerical computations verify the model and experiments have successfully verified our predictions.
Non-Hermitian acoustic edge states from a Phys. Rev. Lett. publication 2018