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. 2016 Aug 26;6:32300. doi: 10.1038/srep32300

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Copyright © 2016, The Author(s)

This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

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(a) Schematic of acoustic meta-surface consisting of array of Helmholtz resonators with varying coiled path lengths, p (Sample 1, number of resonators on each side, N = 8). The subwavelength width, s, subwavelength separation, d, gap, g, and total length, D, are fixed to 15, 20, 2 and 317.5 mm, respectively, while p is adjusted to 1, 5.5, 9, 12.5, 16.5, 24, 31, and 36 mm. The structure is invariant in the z direction. (b) Series LC circuit model for resonators comprising the meta-surface, which have minimum impedance for the reflection phase, Φ(x) = π, at the resonance frequency. (c) Calculated Φ(x) for resonators having varying p, which comprise the meta-surface. (d) Calculated Φ(x) profile for meta-surface at various incident sound frequencies. (e) Calculated parabolic profile of Φ(x) at 1490 Hz. The profile follows the relationship, where λ is the wavelength and f is the focal length. (f–h) Sound pressure level profiles for normally, 15° obliquely, and 30° obliquely incident plane waves at 1490 Hz resulting in focal line at approximately (0, 30) and defocused lines at approximately (−30, 30) and (−60, 30), respectively. (All positions are in millimetres).

Inline graphic — (a) Schematic of acoustic meta-surface consisting of array of Helmholtz resonators with varying coiled path lengths, p (Sample 1, number of resonators on each side, N = 8). The subwavelength width, s, subwavelength separation, d, gap, g, and total length, D, are fixed to 15, 20, 2 and 317.5 mm, respectively, while p is adjusted to 1, 5.5, 9, 12.5, 16.5, 24, 31, and 36 mm. The structure is invariant in the z direction. (b) Series LC circuit model for resonators comprising the meta-surface, which have minimum impedance for the reflection phase, Φ(x) = π, at the resonance frequency. (c) Calculated Φ(x) for resonators having varying p, which comprise the meta-surface. (d) Calculated Φ(x) profile for meta-surface at various incident sound frequencies. (e) Calculated parabolic profile of Φ(x) at 1490 Hz. The profile follows the relationship, where λ is the wavelength and f is the focal length. (f–h) Sound pressure level profiles for normally, 15° obliquely, and 30° obliquely incident plane waves at 1490 Hz resulting in focal line at approximately (0, 30) and defocused lines at approximately (−30, 30) and (−60, 30), respectively. (All positions are in millimetres).