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Negative birefraction of acoustic waves in a sonic crystal

Nature Materials volume 6, pages 744–748 (2007)Cite this article

Abstract

Optical birefringence and dichroism are classical and important effects originating from two independent polarizations of optical waves in anisotropic crystals1. Furthermore, the distinct dispersion relations of transverse electric and transverse magnetic polarized electromagnetic waves in photonic crystals can lead to birefringence more easily2,3,4,5,6. However, it is impossible for acoustic waves in the fluid to show such a birefringence because only the longitudinal mode exists. The emergence of an artificial sonic crystal (SC) has significantly broadened the range of acoustic materials in nature7,8,9,10,11,12,13,14,15,16,17,18 that can give rise to acoustic bandgaps and be used to control the propagation of acoustic waves. Recently, negative refraction has attracted a lot of attention and has been demonstrated in both left-handed materials and photonic crystals19,20,21,22,23,24,25,26. Similar to left-handed materials and photonic crystals, negative refractions have also been found in SCs14,15,16,17,18. Here we report, for the first time, the acoustic negative-birefraction phenomenon in a two-dimensional SC, even with the same frequency and the same ‘polarization’ state. By means of this feature, double focusing images of a point source have been realized. This birefraction concept may be extended to other periodic systems corresponding to other forms of waves, showing great impacts on both fundamental physics and device applications.

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Figure 1: The theoretical analysis and experimental results of the birefraction of an acoustic wave in the SC with triangular lattices.
Figure 2: The simulation and experimental results of the point imaging with the SC at 73 kHz and 60 kHz.
Figure 3: The simulation and experimental results of the point imaging with the SC at 49 kHz.
Figure 4: The EFS and the corresponding relationships between the refractive angle and the incident angle of 49, 60 and 73 kHz.

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References

  1. Born, M. & Wolf, E. Principles of Optics (Pergamon, Oxford, 1975).

    Google Scholar 

  2. Netti, M. C. et al. Optical trirefringence in photonic crystal waveguides. Phys. Rev. Lett. 86, 1526–1529 (2001).

    Article  CAS  Google Scholar 

  3. Elliott, J., Smolyaninov, I., Zheludev, N. & Zayats, A. Wavelength dependent birefringence of surface plasmon polaritonic crystals. Phys. Rev. B 70, 233403 (2004).

    Article  Google Scholar 

  4. Zharov, A. A., Zharova, N. A., Noskov, R. E., Shadrivov, I. V. & Kivshar, Y. S. Birefingent left-handed metamaterials and perfect lenses for vectorial fields. New J. Phys. 7, 220–228 (2005).

    Article  Google Scholar 

  5. Kosaka, H. et al. Superprism phenomena in photonic crystals. Phys. Rev. B 58, R10096–R10099 (1998).

    Article  CAS  Google Scholar 

  6. Gajić, R., Meisels, R., Kuchar, F. & Hingerl, K. Refraction and rightness in photonic crystals. Opt. Express 13, 8596–8605 (2005).

    Article  Google Scholar 

  7. Kushwaha, M. S., Halevi, P., Dobrzynski, L. & Djafari-Rouhani, B. Acoustic band structure of periodic elastic composites. Phys. Rev. Lett. 71, 2022–2025 (1993).

    Article  CAS  Google Scholar 

  8. Montero de Espinosa, F. R., Jimenez, E. & Torres, M. Ultrasonic band gap in a periodic two-dimensional composite. Phys. Rev. Lett. 80, 1208–1211 (1998).

    Article  CAS  Google Scholar 

  9. Liu, Z. et al. Locally resonant sonic materials. Science 289, 1734–1736 (2000).

    Article  CAS  Google Scholar 

  10. Sánchez-Pérez, J. V. et al. Sound attenuation by a two-dimensional array of rigid cylinders. Phys. Rev. Lett. 80, 5325–5328 (1998).

    Article  Google Scholar 

  11. Gorishnyy, T., Ullal, C. K., Maldovan, M., Fytas, G. & Thomas, E. L. Hypersonic phononic crystals. Phys. Rev. Lett. 94, 115501 (2005).

    Article  CAS  Google Scholar 

  12. Cheng, W., Wang, J. J., Jonas, U., Fytas, G. & Stefanou, N. Observation and tuning of hypersonic bandgaps in colloidal crystals. Nature Mater. 5, 830–836 (2006).

    Article  CAS  Google Scholar 

  13. Cervera, F. et al. Refractive acoustic devices for airborne sound. Phys. Rev. Lett. 88, 023902 (2001).

    Article  Google Scholar 

  14. Hu, X. H., Shen, Y. F., Liu, X. H., Fu, R. T. & Zi, J. Superlensing effect in liquid surface waves. Phys. Rev. E 69, 030201(R) (2004).

    Article  Google Scholar 

  15. Zhang, X. & Liu, Z. Negative refraction of acoustic waves in two-dimensional phononic crystals. Appl. Phys. Lett. 85, 341–343 (2004).

    Article  CAS  Google Scholar 

  16. Yang, S. et al. Focusing of sound in a 3D phononic crystal. Phys. Rev. Lett. 93, 024301 (2004).

    Article  Google Scholar 

  17. Feng, L. et al. Acoustic backward-wave negative refractions in the second band of a sonic crystal. Phys. Rev. Lett. 96, 014301 (2006).

    Article  Google Scholar 

  18. Ke, M. et al. Negative-refraction imaging with two-dimensional phononic crystals. Phys. Rev. B 72, 064306 (2005).

    Article  Google Scholar 

  19. Veselago, V. G. The electrodynamics of substances with simultaneously negative values of ɛ and μ. Sov. Phys. Usp. 10, 509–514 (1968).

    Article  Google Scholar 

  20. Pendry, J. B., Holden, A. J., Robbins, D. J. & Stewart, W. J. Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).

    Article  Google Scholar 

  21. Smith, D. R., Padilla, W. J., Vier, D. C., Nasser-Nemat, S. C. & Schultz, S. Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84, 4184–4187 (2000).

    Article  CAS  Google Scholar 

  22. Shelby, R. A., Smith, D. R. & Schultz, S. Experimental verification of a negative index of refraction. Science 292, 77–79 (2001).

    CAS  Google Scholar 

  23. Luo, C., Johnson, S. G., Joannopoulos, J. D. & Pendry, J. B. All-angle negative refraction without negative effective index. Phys. Rev. B 65, 201104(R) (2002).

    Article  Google Scholar 

  24. Cubukcu, E., Aydin, K., Ozbay, E., Foteinopoulou, S. & Soukoulis, C. M. Negative refraction by photonic crystals. Nature 423, 604–605 (2003).

    Article  CAS  Google Scholar 

  25. Foteinopoulou, S. & Soukoulis, C. M. Negative refraction and left-handed behavior in two dimensional photonic crystals. Phys. Rev. B 67, 235107 (2003).

    Article  Google Scholar 

  26. Berrier, A. et al. Negative refraction at infrared wavelengths in a two-dimensional photonic crystal. Phys. Rev. Lett. 93, 073902 (2004).

    Article  CAS  Google Scholar 

  27. Foteinopoulou, S. & Soukoulis, C. M. Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects. Phys. Rev. B 72, 165112 (2005).

    Article  Google Scholar 

  28. Ozbay, E. Plasmonics: Merging photonics and electronics at nanoscale dimensions. Science 311, 189–193 (2006).

    Article  CAS  Google Scholar 

  29. Hänsch, T. W. & Walther, H. Laser spectroscopy and quantum optics. Rev. Mod. Phys. 71, S242–S252 (1999).

    Article  Google Scholar 

Download references

Acknowledgements

The work was jointly supported by the National Basic Research Programme of China (973 Programme, grant no. 2007CB613202) and the National Nature Science Foundation of China (grant no. 50632030). We also acknowledge support from the Changjiang Scholars and Innovative Research Team in the university (PCSIRT).

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Author notes

  1. Liang Feng

    Present address: Present address: Department of Electrical and Computer Engineering, University of California, San Diego, California 92093, USA,

Authors and Affiliations

  1. National Laboratory of Solid State Microstructures and Department of Materials Science and Engineering, Nanjing University, Nanjing 210093, People’s Republic of China

    Ming-Hui Lu, Chao Zhang, Liang Feng, Jun Zhao, Yan-Feng Chen, Yong-Yuan Zhu, Shi-Ning Zhu & Nai-Ben Ming

  2. Institute of Acoustics, Nanjing University, Nanjing 210093, People’s Republic of China

    Yi-Wei Mao

  3. National Laboratory of Surface Physics, Fudan University, Shanghai 200433, People’s Republic of China

    Jian Zi

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Correspondence to Yan-Feng Chen.

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Lu, MH., Zhang, C., Feng, L. et al. Negative birefraction of acoustic waves in a sonic crystal. Nature Mater 6, 744–748 (2007). https://doi.org/10.1038/nmat1987

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