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Acoustic resonances in non-Hermitian open systems

Nature Reviews Physics volume 6, pages 11–27 (2024)Cite this article

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Abstract

Acoustic resonances in open systems, which are usually associated with resonant modes characterized by complex eigenfrequencies, play a fundamental role in manipulating acoustic wave radiation and propagation. Notably, they are accompanied by considerable field enhancement, boosting interactions between waves and matter, and leading to various exciting applications. In the past two decades, acoustic metamaterials have enabled a high degree of control over tailoring acoustic resonances over a range of frequencies. Here, we provide an overview of recent advances in the area of acoustic resonances in non-Hermitian open systems, including Helmholtz resonators, metamaterials and metasurfaces, and discuss their applications in various acoustic devices, including sound absorbers, acoustic sources, vortex beam generation and imaging. We also discuss bound states in the continuum and their applications in boosting acoustic wave–matter interactions, active phononics and non-Hermitian acoustic resonances, including phononic topological insulators and the acoustic skin effect.

Key points

  • Acoustic resonances in open systems are associated with eigenmodes characterized by complex eigenfrequencies. These resonances arise in various acoustic systems whose features can be precisely engineered, making them promising for advanced sound manipulation with resonant metastructure devices.

  • An emerging class of non-Hermitian resonances is that of acoustic bound states in the continuum, which are exotic resonances with a theoretically unbounded Q-factor, providing a versatile and powerful means of enhancing acoustic wave–matter interactions.

  • By making use of the properties of active metamaterials and metasurfaces, acoustic resonances can be precisely engineered to feature active, nonlinear and non-reciprocal properties, as well as parity–time-symmetric wave phenomena, showing great potential for applications in enhanced acoustic wave control.

  • Non-Hermitian Hamiltonians extend the common Hermitian dispersion to the complex plane, resulting in additional exotic features of the band structure. Among these, exceptional degeneracies and bandgaps with unconventional topologies yield exciting and unusually robust wave phenomena.

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Fig. 1: Acoustic resonances in non-Hermitian open systems.
Fig. 2: Types of acoustic resonance.
Fig. 3: Applications of acoustic resonances.
Fig. 4: Acoustic BICs.
Fig. 5: Applications of acoustic BICs.
Fig. 6: Active acoustic and phononic metamaterials.
Fig. 7: Non-Hermitian acoustics and phononics.

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Acknowledgements

L.H. and A.E.M. were supported by the Australian Research Council Discovery Project (DP200101353) and the UNSW Scientia Fellowship programme. S.H. and Y.L. were supported by the Shanghai Science and Technology Committee (grant nos. 21JC1405600). C.S. was supported by the US National Science Foundation under grant no. CMMI-2137749. S.Y., X.N., S.K. and A.A. were supported by the Air Force Office of Scientific Research and Simons Foundation. A.S.P and A.F.S acknowledge the state assignment of Kirensky Institute of Physics. Y.K.C. and D.A.P. were supported by the Australian Research Council Discovery Project (grant no. DP200101708).

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Author notes

  1. These authors contributed equally: Lujun Huang, Sibo Huang, Chen Shen, Simon Yves, Artem S. Pilipchuk.

Authors and Affiliations

  1. The Extreme Optoelectromechanics Laboratory (XXL), School of Physics and Electronic Sciences, East China Normal University, Shanghai, China

    Lujun Huang & Ya Cheng

  2. Institute of Acoustics, Tongji University, Shanghai, China

    Sibo Huang, Jie Zhu & Yong Li

  3. Department of Mechanical Engineering, Rowan University, Glassboro, NJ, USA

    Chen Shen

  4. Photonics Initiative, Advanced Science Research Center, City University of New York, New York, NY, USA

    Simon Yves, Xiang Ni, Seunghwi Kim & Andrea Alù

  5. L. V. Kirensky Institute of Physics, Krasnoyarsk, Russia

    Artem S. Pilipchuk & Almas F. Sadreev

  6. School of Engineering and Technology, University of New South Wales, Canberra, Australian Capital Territory, Australia

    Yan Kei Chiang, David A. Powell & Andrey E. Miroshnichenko

  7. Physics Program, Graduate Center, City University of New York, New York, NY, USA

    Andrea Alù

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Contributions

L.H., S.H., C.S., S.Y. and A.S.P. provided initial drafts of portions of the manuscript. All authors subsequently integrated, reviewed and revised the full manuscript.

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Correspondence to Lujun Huang, Yong Li, Almas F. Sadreev, Andrea Alù or Andrey E. Miroshnichenko.

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Supplementary information

Glossary

Acoustic Purcell factor

Acoustic Purcell factor is defined as the ratio of emitted acoustic power of an acoustic source in a structure and in free space (or in an empty tube for waveguide systems).

Active acoustic systems

Active acoustic systems involve tunable properties including non-passivity, nonlinearity and time-dependence.

Bound states in the continuum

Bound states in the continuum (BICs) are peculiar states with infinite quality factors (or lifetime) and forbidden radiation, despite residing in the radiation continuum.

Fabry–Perot resonances

Fabry–Perot resonances usually occur in a cavity made of two parallel reflecting surfaces. They appear only when the accumulated round-trip phase in the cavity equals an integer number of 2π.

Hermitian system

A Hermitian system is usually associated with a closed system with a Hermitian Hamiltonian satisfying H = H+, where + indicates the combination of complex conjugation and transposition of Hamiltonian. The Hermitian nature ensures real eigenvalues and orthogonal eigenvectors.

Non-Hermitian system

A non-Hermitian system has a Hamiltonian that is not equal to its conjugate transpose, H ≠ H+, giving rise to complex eigenvalues and non-orthogonal eigenvectors, manifested by an open system that involves interaction and energy exchange with the surrounding environment.

Passive acoustic systems

Passive acoustic systems rely on the natural propagation and reception of sound waves without any intentional modification or manipulation.

Q-factors

The Q-factor is defined as the ratio of the stored energy to the dissipated energy per radian of the oscillation. It is widely used to describe the resonance behaviour of an underdamped harmonic oscillator.

Quasi-bound states in the continuum

Quasi-bound states in the continuum correspond to the eigenstates with finite but high-quality factors by perturbing system from critical parameters.

Willis coupling

Willis coupling in acoustic materials defines the coupling strength between strains and momentum, analogous to bianisotropy in electromagnetics.

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Huang, L., Huang, S., Shen, C. et al. Acoustic resonances in non-Hermitian open systems. Nat Rev Phys 6, 11–27 (2024). https://doi.org/10.1038/s42254-023-00659-z

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