- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Applied

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Elasticity-induced quasi–bound states in the continuum in compact acoustic resonators

Iman Madkhali1, Mohamed Farhat2,*, and Ying Wu1,2,†

  • *Contact author: mohamed.farhat@kaust.edu.sa
  • †Contact author: ying.wu@kaust.edu.sa
PDF

Phys. Rev. Applied 25, 054002 – Published 1 May, 2026

DOI: https://doi.org/10.1103/rgcx-zwv3

Abstract

This paper is a contribution to the Physical Review Applied collection titled Phononics and Metamaterials.

Quasi–bound states in the continuum (QBIC) have attracted considerable attention due to their exceptionally high Q factors. In this work, we reveal the critical role of elastic (shear) waves in the formation of acoustoelastic Friedrich-Wintgen QBIC in a simple and compact elastodynamic resonator consisting of a silicon frame enclosing an airborne acoustic cavity. Full-wave numerical simulations support the theoretical predictions based on temporal coupled mode theory, allowing for precise prediction of the near-field coupling. Of note, we demonstrate the emergence of a shear hybrid mode in conjunction with the classical coupled modes, which enhances the coupling strength between the cavity’s eigenmodes. We further analyze how material properties and frame thickness influence the characteristics of the elastic mode. Owing to its structural simplicity and ease of fabrication, the proposed resonator offers promising potential for applications in acoustic sensing, filtering, and beyond.

View figure in article

Physics Subject Headings (PhySH)

Collections

This article appears in the following collection:

Phononics and Metamaterials

Physical Review Applied is pleased to present a Collection on Phononics and Metamaterials, in which diverse developments in research on sound waves are gathered to offer a comprehensive view of both the state of the art and the challenges ahead. The Collection is dedicated to the memory of Dr. Sarah Benchabane (1980–2024), honoring her outstanding contributions to phononics and wave physics. Contributions to this Collection will be published beginning in 2025 and continuing into 2026. This Collection is being curated by Guest Editors Muamer Kadic, Daniel Torrent, and Abdelkrim Khelif.

Article Text

Supplemental Material

References (61)

  1. C. W. Hsu, B. Zhen, A. D. Stone, J. D. Joannopoulos, and M. Soljačić, Bound states in the continuum, Nat. Rev. Mater. 1, 1 (2016).
  2. F. Monticone and A. Alu, Embedded photonic eigenvalues in 3D nanostructures, Phys. Rev. Lett. 112, 213903 (2014).
  3. D. Marinica, A. Borisov, and S. Shabanov, Bound states in the continuum in photonics, Phys. Rev. Lett. 100, 183902 (2008).
  4. E. Wigner and J. Von Neumann, Uber das verhalten von eigenwerten bei adiabatischen prozessen, Phys. Zeit. 30, 467 (1929).
  5. J. von Neumann and E. P. Wigner, Über merkwürdige diskrete eigenwerte, in The Collected Works of Eugene Paul Wigner, edited by A. S. Wightman, vol A/1 (Springer, Berlin, Heidelberg, 1993).
  6. Y.-X. Xiao, G. Ma, Z.-Q. Zhang, and C. T. Chan, Topological subspace-induced bound state in the continuum, Phys. Rev. Lett. 118, 166803 (2017).
  7. K. Koshelev, Y. Kivshar, and A. Bogdanov, Engineering with bound states in the continuum, Opt. Photonics News 31, 38 (2020).
  8. L. Huang, Y. K. Chiang, S. Huang, C. Shen, F. Deng, Y. Cheng, B. Jia, Y. Li, D. A. Powell, and A. E. Miroshnichenko, Sound trapping in an open resonator, Nat. Commun. 12, 4819 (2021).
  9. A. Lyapina, D. Maksimov, A. Pilipchuk, and A. Sadreev, Bound states in the continuum in open acoustic resonators, J. Fluid Mech. 780, 370 (2015).
  10. Y. Plotnik, O. Peleg, F. Dreisow, M. Heinrich, S. Nolte, A. Szameit, and M. Segev, Experimental observation of optical bound states in the continuum, Phys. Rev. Lett. 107, 183901 (2011).
  11. L. Huang, B. Jia, A. S. Pilipchuk, Y. Chiang, S. Huang, J. Li, C. Shen, E. N. Bulgakov, F. Deng, D. A. Powell et al., General framework of bound states in the continuum in an open acoustic resonator, Phys. Rev. Appl. 18, 054021 (2022).
  12. Y. Yin, Q. Duan, S. Zhu, J. Li, Z. Xie, C.-W. Qiu, and H. Chen, Accidental bound states in the continuum in acoustic resonators with rotating obstacles, Phys. Rev. B 110, 054201 (2024).
  13. M. Martí-Sabaté, J. Li, B. Djafari-Rouhani, S. A. Cummer, and D. Torrent, Observation of two-dimensional acoustic bound states in the continuum, Commun. Phys. 7, 122 (2024).
  14. L. Huang, B. Jia, Y. K. Chiang, S. Huang, C. Shen, F. Deng, T. Yang, D. A. Powell, Y. Li, and A. E. Miroshnichenko, Topological supercavity resonances in the finite system, Adv. Sci. 9, 2200257 (2022).
  15. S. Hein, W. Koch, and L. Nannen, Trapped modes and Fano resonances in two-dimensional acoustical duct–cavity systems, J. Fluid Mech. 692, 257 (2012).
  16. C. W. Hsu, B. Zhen, J. Lee, S.-L. Chua, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, Observation of trapped light within the radiation continuum, Nature 499, 188 (2013).
  17. H. Friedrich and D. Wintgen, Interfering resonances and bound states in the continuum, Phys. Rev. A 32, 3231 (1985).
  18. S. T. Ha, Y. H. Fu, N. K. Emani, Z. Pan, R. M. Bakker, R. Paniagua-Domínguez, and A. I. Kuznetsov, Directional lasing in resonant semiconductor nanoantenna arrays, Nat. Nanotechnol. 13, 1042 (2018).
  19. C. Huang, C. Zhang, S. Xiao, Y. Wang, Y. Fan, Y. Liu, N. Zhang, G. Qu, H. Ji, J. Han et al., Ultrafast control of vortex microlasers, Science 367, 1018 (2020).
  20. A. Kodigala, T. Lepetit, Q. Gu, B. Bahari, Y. Fainman, and B. Kanté, Lasing action from photonic bound states in continuum, Nature 541, 196 (2017).
  21. M. Rybin and Y. Kivshar, Supercavity lasing, Nature 541, 164 (2017).
  22. S. Romano, G. Zito, S. Torino, G. Calafiore, E. Penzo, G. Coppola, S. Cabrini, I. Rendina, and V. Mocella, Label-free sensing of ultralow-weight molecules with all-dielectric metasurfaces supporting bound states in the continuum, Photonics Res. 6, 726 (2018).
  23. S. Romano, A. Lamberti, M. Masullo, E. Penzo, S. Cabrini, I. Rendina, and V. Mocella, Optical biosensors based on photonic crystals supporting bound states in the continuum, Materials 11, 526 (2018).
  24. A. Tittl, A. Leitis, M. Liu, F. Yesilkoy, D.-Y. Choi, D. N. Neshev, Y. S. Kivshar, and H. Altug, Imaging-based molecular barcoding with pixelated dielectric metasurfaces, Science 360, 1105 (2018).
  25. B. Wang, W. Liu, M. Zhao, J. Wang, Y. Zhang, A. Chen, F. Guan, X. Liu, L. Shi, and J. Zi, Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum, Nat. Photonics 14, 623 (2020).
  26. J. M. Foley, S. M. Young, and J. D. Phillips, Symmetry-protected mode coupling near normal incidence for narrow-band transmission filtering in a dielectric grating, Phys. Rev. B 89, 165111 (2014).
  27. J. M. Foley and J. D. Phillips, Normal incidence narrowband transmission filtering capabilities using symmetry-protected modes of a subwavelength, dielectric grating, Opt. Lett. 40, 2637 (2015).
  28. A. A. Bogdanov, K. L. Koshelev, P. V. Kapitanova, M. V. Rybin, S. A. Gladyshev, Z. F. Sadrieva, K. B. Samusev, Y. S. Kivshar, and M. F. Limonov, Bound states in the continuum and Fano resonances in the strong mode coupling regime, Adv. Photonics 1, 016001 (2019).
  29. N. Solodovchenko, K. Samusev, D. Bochek, and M. Limonov, Bound states in the continuum in strong-coupling and weak-coupling regimes under the cylinder–ring transition, Nanophotonics 10, 4347 (2021).
  30. X. Zong, L. Li, and Y. Liu, Bound states in the continuum enabling ultra-narrowband perfect absorption, New J. Phys. 25, 023020 (2023).
  31. Z. Sadrieva, K. Frizyuk, M. Petrov, Y. Kivshar, and A. Bogdanov, Multipolar origin of bound states in the continuum, Phys. Rev. B 100, 115303 (2019).
  32. S. V. Nabol, P. S. Pankin, D. N. Maksimov, and I. V. Timofeev, Fabry-Perot bound states in the continuum in an anisotropic photonic crystal, Phys. Rev. B 106, 245403 (2022).
  33. F. Kronowetter, M. Maeder, Y. K. Chiang, L. Huang, J. D. Schmid, S. Oberst, D. A. Powell, and S. Marburg, Realistic prediction and engineering of high-Q modes to implement stable fano resonances in acoustic devices, Nat. Commun. 14, 6847 (2023).
  34. S. Huang, T. Liu, Z. Zhou, X. Wang, J. Zhu, and Y. Li, Extreme sound confinement from quasibound states in the continuum, Phys. Rev. Appl. 14, 021001(R) (2020).
  35. Y. Yu, X. Xi, and X. Sun, Observation of mechanical bound states in the continuum in an optomechanical microresonator, Light: Sci. Appl. 11, 328 (2022).
  36. Y. Chen, Z. Shen, X. Xiong, C.-H. Dong, C.-L. Zou, and G.-C. Guo, Mechanical bound state in the continuum for optomechanical microresonators, New J. Phys. 18, 063031 (2016).
  37. M. Zhao and K. Fang, Mechanical bound states in the continuum for macroscopic optomechanics, Opt. Express 27, 10138 (2019).
  38. L. Cao, Y. Zhu, Y. Xu, S.-W. Fan, Z. Yang, and B. Assouar, Elastic bound state in the continuum with perfect mode conversion, J. Mech. Phys. Solids 154, 104502 (2021).
  39. M. Amrani, I. Quotane, C. Ghouila-Houri, E. H. El Boudouti, L. Krutyansky, B. Piwakowski, P. Pernod, A. Talbi, and B. Djafari-Rouhani, Experimental evidence of the existence of bound states in the continuum and Fano resonances in solid-liquid layered media, Phys. Rev. Appl. 15, 054046 (2021).
  40. F. Ursell, in Mathematical Proceedings of the Cambridge Philosophical Society (Cambridge University Press, Cambridge, UK, 1951), Vol. 47, pp. 347–358.
  41. C. M. Linton and P. McIver, Embedded trapped modes in water waves and acoustics, Wave Motion 45, 16 (2007).
  42. L. Huang, S. Huang, C. Shen, S. Yves, A. S. Pilipchuk, X. Ni, S. Kim, Y. K. Chiang, D. A. Powell, J. Zhu et al., Acoustic resonances in non-Hermitian open systems, Nat. Rev. Phys. 6, 11 (2024).
  43. I. Deriy, I. Toftul, M. Petrov, and A. Bogdanov, Bound states in the continuum in compact acoustic resonators, Phys. Rev. Lett. 128, 084301 (2022).
  44. M. Farhat, Y. Achaoui, J. A. I. Martínez, M. Addouche, Y. Wu, and A. Khelif, Observation of ultra-high-Q resonators in the ultrasound via bound states in the continuum, Adv. Sci. 11, 2402917 (2024).
  45. S. Mizuno, Fano resonances and bound states in the continuum in a simple phononic system, Appl. Phys. Exp. 12, 035504 (2019).
  46. B. Assouar, B. Liang, Y. Wu, Y. Li, J.-C. Cheng, and Y. Jing, Acoustic metasurfaces, Nat. Rev. Mater. 3, 460 (2018).
  47. K. F. Graff, Wave Motion in Elastic Solids (Dover Publications, New York, 1991).
  48. L. D. Landau and E. M. Lifshitz, Theory of Elasticity, 3rd Edition (Butterworth-Heinemann, Oxford, 1986), Vol. 7.
  49. J. J. Faran, Jr., Sound scattering by solid cylinders and spheres, J. Acoust. Soc. Am. 23, 405 (1951).
  50. See Supplemental Material at http://link.aps.org/supplemental/10.1103/rgcx-zwv3 for complete derivation of the eigenfrequencies of the two-level system, effect of varying the shear-wave velocity and geometry of the frame, as well as energy considerations.
  51. P. Lalanne, W. Yan, K. Vynck, C. Sauvan, and J.-P. Hugonin, Light interaction with photonic and plasmonic resonances, Laser Photonics Rev. 12, 1700113 (2018).
  52. M. Farhat, P.-Y. Chen, S. Guenneau, S. Enoch, and A. Alu, Frequency-selective surface acoustic invisibility for three-dimensional immersed objects, Phys. Rev. B 86, 174303 (2012).
  53. COMSOL Multiphysics, V6.2 (build: 415). https://www.comsol.com.
  54. S. Fan, W. Suh, and J. D. Joannopoulos, Temporal coupled-mode theory for the Fano resonance in optical resonators, J. Opt. Soc. Am. A 20, 569 (2003).
  55. W. Suh, Z. Wang, and S. Fan, Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities, IEEE. J. Quantum Electron. 40, 1511 (2004).
  56. L. Verslegers, Z. Yu, Z. Ruan, P. B. Catrysse, and S. Fan, From electromagnetically induced transparency to superscattering with a single structure: A coupled-mode theory for doubly resonant structures, Phys. Rev. Lett. 108, 083902 (2012).
  57. Z. Hayran and F. Monticone, Capturing broadband light in a compact bound state in the continuum, ACS Photonics 8, 813 (2021).
  58. Z. Ruan and S. Fan, Temporal coupled-mode theory for Fano resonance in light scattering by a single obstacle, J. Phys. Chem. C 114, 7324 (2010).
  59. M. Le Bellac, Quantum Physics (Cambridge University Press, Cambridge, UK, 2011).
  60. S. Liu, S. Huang, Z. Zhou, P. Qian, B. Jia, H. Ding, N. Wang, Y. Li, and J. Chen, Observation of acoustic Friedrich-Wintgen bound state in the continuum with bridging near-field coupling, Phys. Rev. Appl. 20, 044075 (2023).
  61. M. Krasikova, F. Kronowetter, S. Krasikov, M. Kuzmin, M. Maeder, T. Yang, A. Melnikov, S. Marburg, and A. Bogdanov, Acoustic bound states in the continuum in coupled Helmholtz resonators, Phys. Rev. Appl. 22, 024045 (2024).

Outline

Information

Phys. Rev. Applied 25, 054002– Published 1 May, 2026
  • Received 17 October 2025
  • Revised 12 February 2026
  • Accepted 18 February 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by King Abdullah University of Science and Technology (KAUST).

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation