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  • Open Access

Bound states to the continuum: Time-varying spoof acoustic surface waves

E. Paul*, G. J. Chaplain, J. Li, T. A. Starkey, and S. A. R. Horsley

  • Centre for Metamaterial Research and Innovation, Department of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, United Kingdom

  • *Contact author: ep564@exeter.ac.uk
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Phys. Rev. B 113, 224317 – Published 23 June, 2026

DOI: https://doi.org/10.1103/shc3-btj7

Abstract

We develop a theoretical framework for time-modulated acoustic metasurfaces comprising a line array of modulated cavities, and show that bound acoustic surface waves can undergo temporal diffraction from bound states localized at an interface into bulk waves. The dispersion relation is derived via an operator formalism that captures the spatiotemporal coupling between Floquet sidebands. We show that under periodic modulation of the cavity length sidebands spaced by the modulation frequency are produced (diffraction in time), enabling the coupling of bound surface acoustic waves with bulk radiation, i.e., from a bound state to the continuum. We observe the negative-frequency spectra as spatial reflections along the array via time-domain finite element simulations. Spectral k-gaps are observed at band crossings, with the width of the gap proportional to the modulation amplitude. The modulation enters solely through a time-dependent reflection phase, such that the framework applies generally to metasurfaces with programmable boundary conditions, beyond purely mechanical modulation.

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Phys. Rev. B 113, 224317– Published 23 June, 2026
  • Received 19 December 2025
  • Revised 10 April 2026
  • Accepted 26 May 2026
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