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Published March 3, 2022 | Submitted
Journal Article Open

Rayleigh wave propagation in nonlinear metasurfaces


We investigate the propagation of Rayleigh waves in a half-space coupled to a nonlinear metasurface. The metasurface consists of an array of nonlinear oscillators attached to the free surface of a homogeneous substrate. We describe, analytically and numerically, the effects of nonlinear interaction force and energy loss on the dispersion of Rayleigh waves. We develop closed-form expressions to predict the dispersive characteristics of nonlinear Rayleigh waves by adopting a leading-order effective medium description. In particular, we demonstrate how hardening nonlinearity reduces and eventually eliminates the linear filtering bandwidth of the metasurface. Softening nonlinearity, in contrast, induces lower and broader spectral gaps for weak to moderate strengths of nonlinearity, and narrows and eventually closes the gaps at high strengths of nonlinearity. We also observe the emergence of a spatial gap (in wavenumber) in the in-phase branch of the dispersion curves for softening nonlinearity. Finally, we investigate the interplay between nonlinearity and energy loss and discuss their combined effects on the dispersive properties of the metasurface. Our analytical results, supported by finite element simulations, demonstrate the mechanisms for achieving tunable dispersion characteristics in nonlinear metasurfaces.

Additional Information

© 2021 Elsevier Ltd. Received 14 July 2021, Revised 24 October 2021, Accepted 31 October 2021, Available online 11 November 2021. C.D. acknowledges support for this project from NSF EFRI award number 1741565. A.M. and A.P. acknowledge support for this project from European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska Curie grant agreement No 813424. CRediT authorship contribution statement: A. Palermo: Conceptualization, Investigation, Visualization, Software, Writing – original draft. B. Yousefzadeh: Conceptualization, Investigation, Visualization, Formal analysis, Writing – original draft. C. Daraio: Writing – review & editing, Conceptualization. A. Marzani: Writing – review & editing, Validation, Resources. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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August 22, 2023
October 23, 2023