Design of a resonant Luneburg lens for surface acoustic waves

Fuentes-Dom�nguez, Rafael; Yao, Mengting; Colombi, Andrea; Dryburgh, Paul; Pieris, Don; Jackson-Crisp, Alexander; Colquitt, Daniel; Clare, Adam; Smith, Richard J.; Clark, Matt

Abstract

© 2020 In this work we employ additive manufacturing to print a circular array of micropillars on an aluminium slab turning its top surface into a graded index metasurface for surface acoustic waves (SAW). The graded metasurface reproduces a Luneburg lens capable of focusing plane SAWs to a point. The graded index profile is obtained by exploiting the dispersion properties of the metasurface arising from the well-known resonant coupling between the micropillars (0.5 mm diameter and variable length ∼3 mm) and the surface waves propagating in the substrate. From the analytical formulation of the metasurface's dispersion curves, a slow phase velocity mode is shown to arise from the hybridisation of the surface wave with the pillar resonance. This is used to compute the radial height profile corresponding to the refractive index given by Luneburg's equation. An initial validation of the lens design, achieved through ray theory, shows that ray trajectories have a strong frequency dependence, meaning that the lens will only work on a narrow band. An ultrasonic experiment at 500 kHz where plane SAWs are generated with a piezoelectric transducer and a laser scanner measures the out of plane displacement on the metasurface, validates the actual lens performance and the manufacturing technique. Finally, comparison between the ray analysis and experimental results offers insight into the behaviour of this type of metasurface especially in the proximity of the acoustic bandgaps and highlights the possibility for acoustic shielding.

• Journal Article Type: Article
• Acceptance Date: Nov 14, 2020
• Online Publication Date: Nov 24, 2020
• Publication Date: Mar 1, 2021
• Deposit Date: Dec 9, 2020
• Publicly Available Date: Dec 9, 2020
• Journal: Ultrasonics
• Print ISSN: 0041-624X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 111
• Article Number: 106306
• DOI: https://doi.org/10.1016/j.ultras.2020.106306
• Keywords: Acoustics and Ultrasonics
• Public URL: https://nottingham-repository.worktribe.com/output/5122433
• Publisher URL: https://www.sciencedirect.com/science/article/pii/S0041624X20302419?via%3Dihub
• Additional Information: This article is maintained by: Elsevier; Article Title: Design of a resonant Luneburg lens for surface acoustic waves; Journal Title: Ultrasonics; CrossRef DOI link to publisher maintained version: https://doi.org/10.1016/j.ultras.2020.106306; Content Type: article; Copyright: © 2020 Published by Elsevier B.V.