Tunable Phononic Crystals and Metamaterials

  • O. Bou Matar
  • J. O. Vasseur
  • Pierre A. Deymier
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 173)


The objective of this chapter is to show how it would be possible to introduce a certain degree of tunability of the properties of phononic crystals. The main concepts underlying the conception of tunable phononic crystals are first introduced with simple models: the one-dimensional harmonic crystal with varying parameter and two coupled one-dimensional harmonic crystals. An overview of the literature on tunable phononic crystals is given. Three of the tuning methods proposed in the literature are described in some details. We also illustrate the new or enhanced functionalities open by the tuning of the phononic crystal properties. These applications include reconfigurable waveguides and tunable superlenses.


Band Structure External Magnetic Field Epoxy Matrix Negative Refraction Filling Fraction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    E.A. Turov, V.G. Shavrov, Broken symmetry and magnetoacoustic effects in ferro- and antiferromagnetics. Sov. Phys. Usp. 26, 593–611 (1983)CrossRefGoogle Scholar
  2. 2.
    C. Goffaux, J.P. Vigneron, Theoretical study of a tunable phononic band gap system. Phys. Rev. B 64, 075118 (2001)CrossRefGoogle Scholar
  3. 3.
    X. Li, F. Wu, H. Hu, S. Zhong, Y. Liu, Large acoustic band gaps created by rotating square rods in two-dimensional periodic composites. J. Phys. D Appl. Phys. 36, L15–L17 (2003)CrossRefGoogle Scholar
  4. 4.
    L. Feng, X.-P. Liu, M.-H. Lu, Y.-B. Chen, Y.-W. Mao, J. Zi, Y.-Y. Zhu, S.-N. Zhu, N.-B. Ming, Refraction control of acoustic waves in a square rod-constructed tunable sonic crystal. Phys. Rev. B 73, 193101 (2006)CrossRefGoogle Scholar
  5. 5.
    S.-C.S. Lin, T.J. Huang, Tunable phononic crystals with anisotropic inclusions. Phys. Rev. B 83, 174303 (2011)Google Scholar
  6. 6.
    K. Bertoldi, M.C. Boyce, Mechanically triggered transformations of phononic band gaps in periodic elastomeric structures. Phys. Rev. B 77, 052105 (2008)CrossRefGoogle Scholar
  7. 7.
    J.-H. Jang, C.Y. Koh, K. Bertoldi, M.C. Boyce, E.L. Thomas, Combining pattern instability and shape-memory hysteresis for phononic switching. Nano Lett. 9(5), 2113–2119 (2009)CrossRefGoogle Scholar
  8. 8.
    J.-H. Jang, C.K. Ullal, T. Gorishnyy, V.V. Tsukruk, E.L. Thomas, Mechanically tunable three-dimensional elastomeric network/air structures via interference lithography. Nano Lett. 6(4), 740–743 (2006)CrossRefGoogle Scholar
  9. 9.
    W.-P. Yang, L.-W. Chen, The tunable acoustic band gaps of two-dimensional phononic crystals with a dielectric elastomer cylindrical actuator. Smart Mater. Struct. 17, 015011 (2008)CrossRefGoogle Scholar
  10. 10.
    W.-P. Yang, L.-Y. Wu, L.-W. Chen, Refractive and focusing behaviours of tunable sonic crystals with dielectric elastomer cylindrical actuators. J. Phys. D Appl. Phys. 41, 135408 (2008)CrossRefGoogle Scholar
  11. 11.
    L.-Y. Wu, M.-L. Wu, L.-W. Chen, The narrow pass band filter of tunable 1D phononic crystals with a dielectric elastomer layer. Smart Mater. Struct. 18, 015011 (2009)CrossRefGoogle Scholar
  12. 12.
    Z. Hou, F. Wu, Y. Liu, Phononic crystals containing piezoelectric material. Solid State Commun. 130(11), 745–749 (2004)CrossRefGoogle Scholar
  13. 13.
    Y.-Z. Wang, F.-M. Li, Y.-S. Wang, K. Kishimoto, W.-H. Huang, Tuning of band gaps for a two-dimensional piezoelectric phononic crystal with a rectangular lattice. Acta Mech. Sin. 25, 65–71 (2009)CrossRefGoogle Scholar
  14. 14.
    X.-Y. Zou, Q. Chen, B. Liang, J.-C. Cheng, Control of the elastic wave bandgaps in two-dimensional piezoelectric periodic structures. Smart Mater. Struct. 17, 015008 (2008)CrossRefGoogle Scholar
  15. 15.
    C.J. Rupp, M.L. Dunn, K. Maute, Switchable phononic wave filtering, guiding, harvesting, and actuating in polarization-patterned piezoelectric solids. Appl. Phys. Lett. 96, 111902 (2010)CrossRefGoogle Scholar
  16. 16.
    Y.-Z. Wang, F.-M. Li, W.-H. Huang, X. Jiang, Y.-S. Wang, K. Kishimoto, Wave band gaps in two-dimensional piezoelectric/piezomagnetic phononic crystals. Int. J. Solids Struct. 45(14–15), 4203–4210 (2008)CrossRefGoogle Scholar
  17. 17.
    O. Bou Matar, J.F. Robillard, J. Vasseur, A.-C. Hladky-Hennion, P.A. Deymier, P. Pernod, V. Preobrazhensky, Band gap tunability of magneto-elastic phononic crystal. J. Appl. Phys. 111, 054901 (2012)CrossRefGoogle Scholar
  18. 18.
    J.-F. Robillard, O. Bou Matar, J.O. Vasseur, P.A. Deymier, M. Stippinger, A.-C. Hladky-Hennion, Y. Pennec, B. Djafari-Rouhani, Tunable magnetoelastic phononic crystals. Appl. Phys. Lett. 95, 124104 (2009)CrossRefGoogle Scholar
  19. 19.
    J.R. Cullen, S. Rinaldi, G.V. Blessing, Elastic versus magnetoelastic anisotropy in rare earth-iron alloys. J. Appl. Phys. 49(3), 1960–1965 (1978)CrossRefGoogle Scholar
  20. 20.
    J. Baumgartl, M. Zvyagolskaya, C. Bechinger, Tailoring of phononic band structures in colloidal crystals. Phys. Rev. Lett. 99, 205503 (2007)CrossRefGoogle Scholar
  21. 21.
    Z.-G. Huang, T.-T. Wu, Temperature effect on the bandgaps of surface and bulk acoustic waves in two-dimensional phononic crystals. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 52(3), 365–370 (2005)CrossRefGoogle Scholar
  22. 22.
    L.-Y. Wu, W.-P. Yang, L.-W. Chen, The termal effects on the negative refraction of sonic crystals. Phys. Lett. A 372, 2701–2705 (2008)CrossRefGoogle Scholar
  23. 23.
    K.L. Jim, C.W. Leung, S.T. Lau, S.H. Choy, H.L.W. Chan, Thermal tuning of phononic bandstructure in ferroelectric ceramic/epoxy phononic crystal. Appl. Phys. Lett. 94, 193501 (2009)CrossRefGoogle Scholar
  24. 24.
    A. Sato, Y. Pennec, N. Shingne, T. Thurn-Albrecht, W. Knoll, M. Steinhart, B. Djafari-Rouhani, G. Fytas, Tuning and switching the hypersonic phononic properties of elastic impedance contrast nanocomposites. ACS Nano 4(6), 3471–3481 (2010)CrossRefGoogle Scholar
  25. 25.
    J.-Y. Yeh, Control analysis of the tunable phononic crystal with electrorheological material. Physica B 400, 137–144 (2007)CrossRefGoogle Scholar
  26. 26.
    B. Wu, R. Wei, C. He, H. Zhao, Research on two-dimensional phononic crystal with magnetorheological material. IEEE Int. Ultrason. Symp. Proc. 1484–1486 (2008)Google Scholar
  27. 27.
    A. Evgrafov, C.J. Rupp, M.L. Dunn, K. Maute, Optimal synthesis of tunable elastic wave-guides. Comput. Methods Appl. Mech. Eng. 198, 292–301 (2008)CrossRefGoogle Scholar
  28. 28.
    M. Gei, A.B.. Movchan, D. Bigoni. Band-gap shift and defect-induced annihilation in prestressed elastic structures. J. Appl. Phys. 105, 063507 (2009)Google Scholar
  29. 29.
    F. Wu, Z. Liu, Y. Liu, Acoustic band gaps created by rotating square rods in a 2D lattice. Phys. Rev. B 66, 046628 (2002)CrossRefGoogle Scholar
  30. 30.
    Y. Cheng, X.J. Liu, D.J. Wu, Temperature effects on the band gaps of Lamb waves in a one-dimensional phononic-crystal plate. J. Acoust. Soc. Am. 129(3), 1157–1160 (2011)CrossRefGoogle Scholar
  31. 31.
    M. Wilm, S. Ballandras, V. Laude, T. Pastureaud, A full 3D plane wave-expansion model for 1-3 piezoelectric composite structures. J. Acoust. Soc. Am. 112(3), 943–952 (2002)CrossRefGoogle Scholar
  32. 32.
    A. Khelif, B. Djafari-Rouhani, J.O. Vasseur, P.A. Deymier, P. Lambin, L. Dobrzynski, Transmittivity through straight and stublike waveguides in a two-dimensional phononic crystal. Phys. Rev. B 65(17), 174308 (2002)CrossRefGoogle Scholar
  33. 33.
    T. Miyashita, C. Inoue. Numerical investigations of transmission and waveguide properties of sonic crystals by finite-difference time-domain method. Jpn. J. Appl. Phys., Part 1, 40(Part 1, No. 5B), 3488–3492 (2001)Google Scholar
  34. 34.
    Y. Pennec, B. Djafari-Rouhani, J.O. Vasseur, A. Khelif, P.A. Deymier. Tunable filtering and demultiplexing in phononic crystals with hollow cylinders. Phys. Rev. E 69(4), 046608 (2004)Google Scholar
  35. 35.
    S. Mohammadi, A.A. Eftekhar, W.D. Hunt, A. Adibi. High-Q micromechanical resonators in a two-dimensional phononic crystal slab. Appl. Phys. Lett. 94(5), 051906 (2009)Google Scholar
  36. 36.
    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(15), 154301 (2009)CrossRefGoogle Scholar
  37. 37.
    I. Perez-Arjona, V.J. Sanchez-Morcillo, J. Redondo, V. Espinosa, K. Staliunas, Theoretical prediction of the nondiffractive propagation of sonic waves through periodic acoustic media. Phys. Rev. B 75(1), 014304 (2007)CrossRefGoogle Scholar
  38. 38.
    C. Luo, S.G. Johnson, J.D. Joannopoulos, J.B. Pendry, All-angle negative refraction without negative effective index. Phys. Rev. B 65, 201104 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • O. Bou Matar
    • 1
  • J. O. Vasseur
    • 2
  • Pierre A. Deymier
    • 3
  1. 1.International Associated Laboratory LEMAC: IEMN, UMR CNRS 8520PRES Lille Nord de France, EC LilleVilleneuve d’AscqFrance
  2. 2.Institut d’Electronique, de Micro-electronique et de Nanotechnologie (IEMN, UMR CNRS 8520)PRES Lille Nord de FranceVilleneuve d’AscqFrance
  3. 3.Department of Materials Science and EngineeringUniversity of ArizonaTucsonUSA

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