Explicit Modeling and Optimization of Acoustic Metalenses for Baffled Sources
Résumé
The steering and the focusing of acoustic beams are of increasing interest for personalized-sound-zone applications. Sound zones require the generation of a strong contrast in sound pressure level between different regions of the space. A way to do so is to control and steer the acoustic field radiated from a source with use of metamaterial-based acoustic lenses. Predictive models based on numerical approaches such as the finite-element method are commonly used, but they are generally cumbersome and time-consuming. In contrast, explicit models rely on Snell’s law of refraction and phase gratings but do not account for the couplings between the metamaterial atoms. In this work, a metamaterial-based acoustic lens is proposed as a solution to steer and focus acoustic sources, with use of slits loaded with periodic Helmholtz resonators. We control the radiation of a baffled duct by a metalens located at the output of the waveguide and excited at the other end by a loudspeaker. A fully explicit two-dimensional predictive model is developed on the basis of the mode-matching technique, accounting for thermoviscous losses, interslit evanescent coupling, and high-order modes in the baffled duct. The pressure radiated by the metalens outside the baffled duct is then explicitly derived. The semianalytical results show excellent agreement when compared with the solutions obtained by the finite-element method, both in the near field and in the far field over a wide frequency range. An optimization strategy is then proposed, and the beam steering and focusing are reported experimentally on a three-dimensionally-printed prototype.
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