Ultrasonic metamaterials with negative modulus (original) (raw)
- Letter
- Published: 30 April 2006
- Dongjuan Xi1,
- Jianyi Xu1,
- Muralidhar Ambati1,
- Werayut Srituravanich1,
- Cheng Sun1 &
- …
- Xiang Zhang1
Nature Materials volume 5, pages 452–456 (2006) Cite this article
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Abstract
The emergence of artificially designed subwavelength electromagnetic materials, denoted metamaterials1,2,3,4,5,6,7,8,9,10, has significantly broadened the range of material responses found in nature. However, the acoustic analogue to electromagnetic metamaterials has, so far, not been investigated. We report a new class of ultrasonic metamaterials consisting of an array of subwavelength Helmholtz resonators with designed acoustic inductance and capacitance. These materials have an effective dynamic modulus with negative values near the resonance frequency. As a result, these ultrasonic metamaterials can convey acoustic waves with a group velocity antiparallel to phase velocity, as observed experimentally. On the basis of homogenized-media theory, we calculated the dispersion and transmission, which agrees well with experiments near 30 kHz. As the negative dynamic modulus leads to a richness of surface states with very large wavevectors, this new class of acoustic metamaterials may offer interesting applications, such as acoustic negative refraction and superlensing below the diffraction limit.
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Figure 1: A new class of ultrasonic metamaterials consisting of arrays of subwavelength Helmholtz resonators.

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Figure 2: Ultrasonic experiments demonstrating the negative dynamic modulus of the acoustic metamaterials near 32 kHz.

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Figure 3: Measured and calculated transmission (amplitude ratio) as a function of frequency between upstream and downstream detectors.

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References
- Veselago, V. G. Electrodynamics of substances with simultaneously negative values of sigma and mu. Sov. Phys. Uspekhi-USSR 10, 509–514 (1968).
Article Google Scholar - Pendry, J. B., Holden, A. J., Stewart, W. J. & Youngs, I. Extremely low frequency plasmons in metallic mesostructures. Phys. Rev. Lett. 76, 4773–4776 (1996).
Article Google Scholar - Pendry, J. B., Holden, A. J., Robbins, D. J. & Stewart, W. J. Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999).
Article Google Scholar - Smith, D. R., Padilla, W. J., Vier, D. C., Nemat-Nasser, S. C. & Schultz, S. Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84, 4184–4187 (2000).
Article Google Scholar - Wiltshire, M. C. K. et al. Microstructured magnetic materials for RF flux guides in magnetic resonance imaging. Science 291, 849–851 (2001).
Article Google Scholar - Iyer, A. K., Kremer, P. C. & Eleftheriades, G. V. Experimental and theoretical verification of focusing in a large, periodically loaded transmission line negative refractive index metamaterial. Opt. Express 11, 696–708 (2003).
Article Google Scholar - Yen, T. J. et al. Terahertz magnetic response from artificial materials. Science 303, 1494–1496 (2004).
Article Google Scholar - Linden, S. et al. Magnetic response of metamaterials at 100 terahertz. Science 306, 1351–1353 (2004).
Article Google Scholar - Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000).
Article Google Scholar - Ziolkowski, R. W. & Heyman, E. Wave propagation in media having negative permittivity and permeability. Phys. Rev. E 64, 056625 (2001).
Article Google Scholar - Lakes, R. S., Lee, T., Bersie, A. & Wang, Y. C. Extreme damping in composite materials with negative-stiffness inclusions. Nature 410, 565–567 (2001).
Article Google Scholar - Liu, Z. Y. et al. Locally resonant sonic materials. Science 289, 1734–1736 (2000).
Article Google Scholar - Goffaux, C. et al. Evidence of Fano-like interference phenomena in locally resonant materials. Phys. Rev. Lett. 88, 225502 (2002).
Article Google Scholar - Li, J. & Chan, C. T. Double-negative acoustic metamaterial. Phys. Rev. E 70, 055602 (2004).
Article Google Scholar - Sigalas, M. M. et al. Classical vibrational modes in phononic lattices: theory and experiment. Z. Kristallogr. 220, 765–809 (2005).
Google Scholar - Yang, S. X. et al. Focusing of sound in a 3D phononic crystal. Phys. Rev. Lett. 93, 024301 (2004).
Article Google Scholar - Hu, X. H., Chan, C. T. & Zi, J. Two-dimensional sonic crystals with Helmholtz resonators. Phys. Rev. E 71, 055601R (2005).
Google Scholar - Kinsler, L. E. Fundamentals of Acoustics 3rd edn (Wiley, New York, 1982).
Google Scholar - Yang, S. X. et al. Ultrasound tunneling through 3D phononic crystals. Phys. Rev. Lett. 88, 104301 (2002).
Article Google Scholar - Halevi, P. in Electromagnetic Surface Modes (ed. Boardman, A. D.) Ch. 7 (Wiley, New York, 1982).
Google Scholar - Arakawa, E. T., Williams, M. W., Hamm, R. N. & Ritchie, R. H. Effect of damping on surface plasmon dispersion. Phys. Rev. Lett. 31, 1127–1129 (1973).
Article Google Scholar - Lee, H. T. & Poon, A. W. Fano resonances in prism-coupled square micropillars. Opt. Lett. 29, 5–7 (2004).
Article Google Scholar - Kushwaha, M. S., Halevi, P., Dobrzynski, L. & Djafarirouhani, B. Acoustic band-structure of periodic elastic composites. Phys. Rev. Lett. 71, 2022–2025 (1993).
Article Google Scholar - de Espinosa, F. R. M., Jimenez, E. & Torres, M. Ultrasonic band gap in a periodic two-dimensional composite. Phys. Rev. Lett. 80, 1208–1211 (1998).
Article Google Scholar - Martinez-Sala, R. et al. Sound-attenuation by sculpture. Nature 378, 241 (1995).
Article Google Scholar - Pendry, J. B., Martin-Moreno, L. & Garcia-Vidal, F. J. Mimicking surface plasmons with structured surfaces. Science 305, 847–848 (2004).
Article Google Scholar - Fang, N., Lee, H., Sun, C. & Zhang, X. Sub-diffraction-limited optical imaging with a silver superlens. Science 308, 534–537 (2005).
Article Google Scholar - Cubukcu, E., Aydin, K., Ozbay, E., Foteinopolou, S. & Soukoulis, C. M. Subwavelength resolution in a two-dimensional photonic-crystal-based superlens. Phys. Rev. Lett. 91, 207401 (2003).
Article Google Scholar - Sugimoto, N. & Horioka, T. Dispersion characteristics of sound-waves in a tunnel with an array of Helmholtz resonators. J. Acoust. Soc. Am. 97, 1446–1459 (1995).
Article Google Scholar
Acknowledgements
This research was supported by the ONR/DARPA Multidisciplinary University Research Initiative (MURI) (grant N00014-01-1-0803) and the NSF Nanoscale Science and Engineering Center (NSEC) (grant DMI-0327077). The authors also thank A. Mal at the University of California, Los Angeles for allowing us to use his ultrasonic measurement facilities.
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Authors and Affiliations
- Nano-scale Science and Engineering Center, 5130 Etcheverry Hall, University of California, Berkeley, California, 94720-1740, USA
Nicholas Fang, Dongjuan Xi, Jianyi Xu, Muralidhar Ambati, Werayut Srituravanich, Cheng Sun & Xiang Zhang
Authors
- Nicholas Fang
- Dongjuan Xi
- Jianyi Xu
- Muralidhar Ambati
- Werayut Srituravanich
- Cheng Sun
- Xiang Zhang
Corresponding author
Correspondence toXiang Zhang.
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The authors declare no competing financial interests.
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Fang, N., Xi, D., Xu, J. et al. Ultrasonic metamaterials with negative modulus.Nature Mater 5, 452–456 (2006). https://doi.org/10.1038/nmat1644
- Received: 09 January 2006
- Accepted: 08 March 2006
- Published: 30 April 2006
- Issue date: 01 June 2006
- DOI: https://doi.org/10.1038/nmat1644