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Frontiers in Phononics: Parity-Time Symmetric Phononic Metamaterials

Periodic Reporting for period 4 - PHONOMETA (Frontiers in Phononics: Parity-Time Symmetric Phononic Metamaterials)

Reporting period: 2021-06-01 to 2022-11-30

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 I identified that active phononic control was but still is at the cutting edge of the current research on phononic metamaterials. The overall objectives were formulated very broad, yet initially they were all stated in the context of exploring 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 and geometrical arrangements, 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. Further, we added topological phases of quantum matter as an objective for the analogue case of sound and vibrations.

Overall, the objectives can be categorized as follows. Our aim was, based on the aforementioned quantum aspects, in a classical wave-based context to explore novel routes for one-wave reflective materials, one-way invisibility cloaks, artificial lattice effects in the context of non-Hermiticity and topology. Regarding the latter, we explored acoustic sasers (acoustic laser analogies) and unusual waveguides and resonators.

Beyond the idea to bring forth knowledge regarding sound wave physics, deeply inspired by notions in quantum mechanics, a strong driving force was the ability to develop materials providing reflectionless behavior. This property has the potential to facilitate for society new paradigms to improve the soundscape in rooms, halls, urban environments where parasitic and disturbing echoes and undesired.
In the initiating phase of the PHONOMETA project we advanced with actions comprise studies in: 1. Artificial lattices, 2. One-way acoustic diodes, Cloaks of unhearability. In the following, an overview of the major milestones achieved is listened. Those findings are based on theoretical predictions, numerical computations, and experimental verifications as conducted by external collaborators.

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.

One-way acoustic diodes and cloaks of unhearability
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. 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.


1. Acoustic “saser”
In the proposal I used the term “acoustic resonator” and “ring cavity” to describe my aim at developing a device whose properties would resemble the one of a conventional laser, just for sound waves. For this action, the aim was to generate sound wave amplification, i.e. acoustic gain through the so-called acoustoelectric (AE) effect in piezoelectric semiconductors. The teams theoretical predictions revealed its viability, but my external experimental partners had difficulties to demonstrate anything meaningful for the project. Therefore, we decided to use a different approach to realize acoustic gain. We took advantage of the so-called electro-thermoacoustic coupling (ETAC) in thin conductors that could be used in connection to resonators or cavities to resemble as close as possible the acoustic counterpart of a laser. From the literature it was known that the ETAC is particularly efficient in thin materials such as carbon nanotube (CNT) films, which led to the design of an artificial acoustic lattice (see action 2) using these CNT films. In the condensed matter community, adding “gain” (or loss) is know as the non-Hermitian component. Hence, creating a lattice whose topology is dictated by the underlying symmetry, gave birth to the first acoustic non-Hermitian topological lattice with analogue lasing (sasing) effects.

B. Hu, Z. Zhang, H. Zhang, L. Zheng, W. Xiong, Z. Yue, X. Wang, J. Xu, Y. Cheng, X. Liu, and J. Christensen, “Non-Hermitian topological whispering gallery”, Nature 597, 655 (2021).

2. Lattice effects (extenstion of the above)
Furthermore, we expanded upon the notion of exotic lattice effects in an acoustic setting where the Hermitian (loss and gain-free) cases were studied extensively, however, the non-Hermitian counterparts (including gain, loss, or both), are still ongoing. Thus, we focused on twisted elastic and acoustic bilayers, complex Dirac media analogies, and even discussed a direct sound-based analogy of the aforementioned CNT.
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.

For audible sound, no sound laser exist. What we call an saser would require an acoustic gain medium inside which sound amplification takes places. We found that electro-thermoacoustic coupling in very thin conducting materials functions as a highly efficient acoustic source. Adding the concept of topology, we explored acoustic sasing excitations that were protected by the symmetry of underlying lattice arrangement. Such a system has never been realized before.

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