2D–3D Phononic Crystals

  • A. Sukhovich
  • J. H. Page
  • J. O. Vasseur
  • J. F. Robillard
  • N. Swinteck
  • Pierre A. Deymier
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 173)


This chapter presents a comprehensive description of the properties of phononic crystals ranging from spectral properties (e.g., band gaps) to wave vector properties (refraction) and phase properties. These properties are characterized by experiments and numerical simulations.


Evanescent Wave Finite Difference Time Domain Negative Refraction Phononic Crystal Super Resolution 
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  1. 1.
    Z. Liu, X. Zhang, Y. Mao, Y.Y. Zhu, Z. Yang, C.T. Chan, P. Sheng, Locally resonant sonic materials. Science 289, 1734 (2000)CrossRefGoogle Scholar
  2. 2.
    P. Sheng, X. Zhang, Z. Liu, C.T. Chan, Locally resonant sonic materials. Physica B 338, 201 (2003)CrossRefGoogle Scholar
  3. 3.
    J.H. Page, S. Yang, M.L. Cowan, Z. Liu, C.T. Chan, P. Sheng, 3D phononic crystals, in Wave Scattering in Complex Media: From Theory to Applications, (Kluwer Academic Publishers: NATO Science Series, Amsterdam, 2003) pp. 283–307Google Scholar
  4. 4.
    A. Sukhovich, J.H. Page, B. van Tiggelen, Z. Liu. Resonant tunneling of ultrasound in three-dimensional phononic crystals. Physics in Canada 60(4), 245 (2004)Google Scholar
  5. 5.
    A. Sukhovich, L. Jing, J.H. Page, Negative refraction and focusing of ultrasound in two-dimensional phononic crystals. Phys. Rev. B 77, 014301 (2008)CrossRefGoogle Scholar
  6. 6.
    S. Yang, J.H. Page, Z. Liu, M.L. Cowan, C.T. Chan, P. Sheng, Ultrasound tunnelling through 3D phononic crystals. Phys. Rev. Lett. 88, 104301 (2002)CrossRefGoogle Scholar
  7. 7.
    S. Yang, J.H. Page, Z. Liu, M.L. Cowan, C.T. Chan, P. Sheng, Focusing of sound in a 3D phononic crystal. Phys. Rev. Lett. 93, 024301 (2004)CrossRefGoogle Scholar
  8. 8.
    F. Van Der Biest, A. Sukhovich, A. Tourin, J.H. Page, B.A. van Tiggelen, Z. Liu, M. Fink, Resonant tunneling of acoustic waves through a double barrier consisting of two phononic crystals. Europhys. Lett. 71(1), 63–69 (2005)CrossRefGoogle Scholar
  9. 9.
    J.H. Page, A. Sukhovich, S. Yang, M.L. Cowan, F. Van Der Biest, A. Tourin, M. Fink, Z. Liu, C.T. Chan, P. Sheng, Phononic crystals. Phys. Stat. Sol. (b) 241(15), 3454 (2004)Google Scholar
  10. 10.
    J.H. Page, P. Sheng, H.P. Schriemer, I. Jones, X. Jing, D.A. Weitz, Group velocity in strongly scattering media. Science 271, 634 (1996)CrossRefGoogle Scholar
  11. 11.
    A. Sukhovich, B. Merheb, K. Muralidharan, J.O. Vasseur, Y. Pennec, P.A. Deymier, J.H. Page, Experimental and theoretical evidence for subwavelength imaging in phononic crystals. Phys. Rev. Lett. 102, 154301 (2009)CrossRefGoogle Scholar
  12. 12.
    Zeitschrift fur Kristallographie, vol, 220, issues 9–10, ed. by I.E. Psarobas, pp. 757–911 (2005)Google Scholar
  13. 13.
    T.E. Hartman, Tunneling of a wave packet. J. Appl. Phys. 33, 3427 (1962)CrossRefGoogle Scholar
  14. 14.
    J.H. Page, S. Yang, Z. Liu, M.L. Cowan, C.T. Chan, P. Sheng, Tunneling and dispersion in 3D phononic crystals. Z. Kristallogr. 220, 859–870 (2005)CrossRefGoogle Scholar
  15. 15.
    M. Sigalas, M.S. Kushwaha, E.N. Economou, M. Kafesaki, I.E. Psarobas, W. Steurer, Classical vibrational modes in phononic lattices: theory and experiment. Z. Kristallogr. 220, 765–809 (2005)CrossRefGoogle Scholar
  16. 16.
    J. Liu, L. Ye, D.A. Weitz, P. Sheng, Phys. Rev. Lett. 65, 2602 (1990)CrossRefGoogle Scholar
  17. 17.
    X.D. Jing, P. Sheng, M.Y. Zhou, Phys. Rev. Lett. 66, 1240 (1991)CrossRefGoogle Scholar
  18. 18.
    R.S. Penciu, H. Kriegs, G. Petekidis, G. Fytas, E.N. Economou, J. Chem. Phys. 118, 5224 (2003)CrossRefGoogle Scholar
  19. 19.
    G. Tommaseo, G. Petekidis, W. Steffen, G. Fytas, A.B.. Schofield, N. Stefanou, J. Chem. Phys. 126, 014707 (2007)CrossRefGoogle Scholar
  20. 20.
    M.L. Cowan, J.H. Page, Ping Sheng, Phys. Rev. B 84, 094305 (2011)Google Scholar
  21. 21.
    J. Li, C.T. Chan, Double-negative acoustic metamaterial. Phys. Rev. E 70, 055602(R) (2004)Google Scholar
  22. 22.
    T. Still, W. Cheng, M. Retsch, R. Sainidou, J. Wang, U. Jonas, N. Stefanou, G. Fytas, Phys. Rev. Lett. 100, 194301 (2008)CrossRefGoogle Scholar
  23. 23.
    R. Sainidou, N. Stefanou, A. Modinos, Formation of absolute frequency gaps in three-dimensional solid phononic crystals. Phys. Rev. B 66, 212301 (2002)CrossRefGoogle Scholar
  24. 24.
    H. Zhao, Y. Liu, G. Wang, J. Wen, D. Yu, X. Han, X. Wen, Phys. Rev. B 72, 012301 (2005)CrossRefGoogle Scholar
  25. 25.
    V. Leroy, A. Bretagne, M. Fink, H. Willaime, P. Tabeling, A. Tourin, Appl. Phys. Lett. 95, 171904 (2009)CrossRefGoogle Scholar
  26. 26.
    C. Croënne, E.J.S. Lee, Hefei Hu, J.H. Page, Special Issue on Phononics, ed. by Ihab El Kady and Mahmoud I Hussein, in AIP Advances, 1(4), (2011)Google Scholar
  27. 27.
    A.V. Akimov et al., Phys. Rev. Lett. 101, 33902 (2008)CrossRefGoogle Scholar
  28. 28.
    J.A. Turner, M.E. Chambers, R.L. Weaver, Acustica 84, 628–631 (1998)Google Scholar
  29. 29.
    H. Hu, A. Strybulevych, J.H. Page, S.E. Skipetrov, B.A. van Tiggelen, Nature Phys. 4, 945–948 (2008)CrossRefGoogle Scholar
  30. 30.
    V.G. Veselago, The electrodynamics of substances with simultaneously negative values of ε and μ. Usp. Fiz. Nauk 92, 517 (1964)CrossRefGoogle Scholar
  31. 31.
    J.B. Pendry, Negative Refraction Makes a Perfect Lens. Phys. Rev. Lett. 85, 3966 (2000)CrossRefGoogle Scholar
  32. 32.
    P.A. Deymier, B. Merheb, J.O. Vasseur, A. Sukhovich, J.H. Page, Focusing of acoustic waves by flat lenses made from negatively refracting two-dimensional phononic crystals. Revista Mexicana De Fisica 54, 74 (2008)Google Scholar
  33. 33.
    J. Li, K.H. Fung, Z.Y. Liu, P. Sheng, C.T. Chan, in Physics of Negative Refraction and Negative Index Materials, Springer Series in Materials Science, vol. 98, Chap. 8 (Springer, Berlin, 2007)Google Scholar
  34. 34.
    P. Sheng, J. Mei, Z. Liu, W. Wen, Dynamic mass density and acoustic metamaterials. Physica B 394, 256 (2007)CrossRefGoogle Scholar
  35. 35.
    X. Zhang, Z. Liu, Negative refraction of acoustic waves in two-dimensional phononic crystals. Appl. Phys. Lett. 85, 341 (2004)CrossRefGoogle Scholar
  36. 36.
    K. Imamura, S. Tamura, Negative refraction of phonons and acoustic lensing effect of a crystalline slab. Physical Review B 70, 174308 (2004)CrossRefGoogle Scholar
  37. 37.
    J.-F. Robillard, J. Bucay, P.A. Deymier, A. Shelke, K. Muralidharan, B. Merheb, J.O. Vasseur, A. Sukhovich, J.H. Page, Resolution limit of a phononic crystal superlens. Physical Review B 83, 224301 (2011)CrossRefGoogle Scholar
  38. 38.
    Z. He, X. Li, J. Mei, Z. Liu, Improving imaging resolution of a phononic crystal lens by employing acoustic surface waves. Journal of Applied Physics 106, 026105 (2009)CrossRefGoogle Scholar
  39. 39.
    F. Liu, F. Cai, S. Peng, R. Hao, M. Ke, Z. Liu, Parallel acoustic near-field microscope: A steel slab with a periodic array of slits. Physical Review E 80, 026603 (2009)CrossRefGoogle Scholar
  40. 40.
    P. Sheng, Metamaterials: Acoustic lenses to shout about. Nature Materials 8, 928 (2009)CrossRefGoogle Scholar
  41. 41.
    C. Luo, S.G. Johnson, J.D. Joannopoulos, J.B. Pendry, Subwavelength imaging in photonic crystals. Phys. Rev. B 68, 045115 (2003)CrossRefGoogle Scholar
  42. 42.
    V. Fokin, M. Ambati, C. Sun, X. Zhang, Method for retrieving effective properties of locally resonant acoustic metamaterials. Physical Review B 76, 144302 (2007)CrossRefGoogle Scholar
  43. 43.
    J. Bucay, E. Roussel, J.O. Vasseur, P.A. Deymier, A.-C. Hladky-Hennion, Y. Pennec, K. Muralidharan, B. Djafari-Rouhani, B. Dubus, Positive, negative, zero refraction, and beam splitting in a solid/air phononic crystal: theoretical and experimental study. Phys. Rev. B 79, 214305 (2009)Google Scholar
  44. 44.
    G.P. Srivastava, The Physics of Phonons. (A. Hilger, 1990)Google Scholar
  45. 45.
    N. Swinteck, J.-F. Robillard, S. Bringuier, J. Bucay, K. Muralidharan, J.O. Vasseur, K. Runge, P.A. Deymier, Phase-controlling phononic crystal. Appl. Phys. Lett. 98, 103508 (2011)Google Scholar
  46. 46.
    N. Swinteck, S. Bringuier, J.-F. Robillard, J.O. Vasseur, A.C. Hladky-Hennion, K. Runge, P.A. Deymier, Phase-control in two-dimensional phononic crystals. J. Appl. Phys. 110, 074507 (2011)Google Scholar
  47. 47.
    S. Bringuier, N. Swinteck, J.O. Vasseur, J.-F. Robillard, K. Runge, K. Muralidharan, P.A. Deymier, Phase-controlling phononic crystals: Realization of acoustic Boolean logic gates. The Journal of the Acoustical Society of America 130, 1919 (2011)CrossRefGoogle Scholar
  48. 48.
    A.P. Godse, D.A. Godse, Digital Logic Circuits (Technical Publications Pune, Pune, India, 2010)Google Scholar
  49. 49.
    A.R. Selfridge, Approximate Material Properties in Isotropic Materials, Transactions on Sonics and Ultrasonics SU-32, 381 (1985)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • A. Sukhovich
    • 1
  • J. H. Page
    • 2
  • J. O. Vasseur
    • 3
  • J. F. Robillard
    • 3
  • N. Swinteck
    • 4
  • Pierre A. Deymier
    • 4
  1. 1.Laboratoire Domaines Océaniques, UMR CNRS 6538, UFR Sciences et TechniquesUniversité de Bretagne OccidentaleBrestFrance
  2. 2.Department of Physics and AstronomyUniversity of ManitobaWinnipegCanada
  3. 3.Institut d’Electronique, de Micro-électronique et de NanotechnologieUMR CNRS 8520Cité ScientifiqueFrance
  4. 4.Department of Materials Science and EngineeringUniversity of ArizonaTucsonUSA

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