Advertisement

Acoustic Cloaking via Homogenization

  • José Sánchez-DehesaEmail author
  • Daniel Torrent
Chapter
  • 3.6k Downloads
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 166)

Abstract

Acoustic cloaking is the mechanism representing the ideal acoustic stealth. We introduce and discuss the acoustic cloak, a material shell that renders an object acoustically ‘invisible’ thanks to its presence surrounding the object. It has been shown that cloaking shells require very complex parameters to be realized. This complexity comes from the fact that their acoustic parameters must be anisotropic, inhomogeneous and divergent near the cloaked object. This chapter explains how to engineer artificial structures, which have been called acoustic metamaterials or metafluids, that respond dynamically as anisotropic and inhomogeneous materials. The metafluids are made from arrays of isotropic and homogeneous elastic cylinders or by metallic plates cylindrically corrugated. We also propose solutions to remove the divergences appearing in the design of cloaking shells. It is therefore predicted that, although difficult to realize, cloaking shells are not impossible by using metafluids based on the homogenization of periodic structures.

Keywords

Bulk Modulus Sound Speed Acoustic Parameter Filling Fraction Artificial Structure 
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.

Notes

Acknowledgements

The authors thank partial financial support by the US Office of Naval Research (Grant N000140910554) and by the Spanish Ministerio de Ciencia e Innovación (Grants TEC2010-19751 and CSD2009-0066 (CONSOLIDER program). D.T. also acknowledges the contract provided by the program Campus de Excelencia Internacional 2010 UPV.

References

  1. 1.
    Bradley, C.E.: Time-harmonic acoustic Bloch wave-propagation in periodic wave-guides. 1. Theory. J. Acoust. Soc. Am. 96, 1844–1853 (1994) CrossRefGoogle Scholar
  2. 2.
    Brun, M., Guenneau, S., Movchan, A.B.: Achieving control of in-plane elastic waves. Appl. Phys. Lett. 94, 061903 (2009) CrossRefGoogle Scholar
  3. 3.
    Cai, L.W.: Multiple scattering in single scatterers. J. Acoust. Soc. Am. 115, 986–995 (2004) CrossRefGoogle Scholar
  4. 4.
    Cai, L.W., Sánchez-Dehesa, J.: Acoustical scattering by radially stratified scatterers. J. Acoust. Soc. Am. 124, 2715–2726 (2008) CrossRefGoogle Scholar
  5. 5.
    Cai, L.W., Sánchez-Dehesa, J.: Analysis of Cummer-Schurig acoustic cloaking. New J. Phys. 9, 450 (2007) CrossRefGoogle Scholar
  6. 6.
    Cervera, F., Sanchis, L., Sánchez-Pérez, J.V., Martínez-Sala, R., Rubio, C., Caballero, D., Sánchez-Dehesa, J.: Refractive acoustic devices for airborne sound. Phys. Rev. Lett. 88, 023902 (2002) CrossRefGoogle Scholar
  7. 7.
    Chen, H., Chan, C.T.: Acoustic cloaking and transformation acoustics. J. Phys. D, Appl. Phys. 43, 11301 (2010) Google Scholar
  8. 8.
    Chen, H., Chan, C.T.: Acoustic cloaking in three dimensions using acoustic metamaterials. Appl. Phys. Lett. 91, 183518 (2007) CrossRefGoogle Scholar
  9. 9.
    Cheng, Y., Yang, F., Xu, J.Y., Liu, X.J.: A multilayer structured acoustic cloak with homogeneous isotropic materials. Appl. Phys. Lett. 92, 151913 (2008) CrossRefGoogle Scholar
  10. 10.
    Climente, A., Torrent, D., Sánchez-Dehesa, J.: Acoustic metamaterials for new two-dimensional sonic devices. Appl. Phys. Lett. 9, 323 (2010) Google Scholar
  11. 11.
    Cummer, S.A., Schurig, D.: One path to acoustic cloaking. New J. Phys. 9, 45 (2007) CrossRefGoogle Scholar
  12. 12.
    Cummer, S.A., Popa, B.-I., Schurig, D., Smith, D.R., Pendry, J., Rahm, M., Starr, A.: Scattering theory derivation of a 3D acoustic cloaking shell. Phys. Rev. Lett. 100, 024301 (2008) CrossRefGoogle Scholar
  13. 13.
    Farhat, M., Guenneau, S., Enoch, S.: Ultrabroadband elastic cloaking in thin plates. Phys. Rev. Lett. 103, 024301 (2009) CrossRefGoogle Scholar
  14. 14.
    Farhat, M., Guenneau, S., Enoch, S., Movchan, A.B.: Cloaking bending waves propagating in thin elastic plates. Phys. Rev. B 79, 033102 (2009) CrossRefGoogle Scholar
  15. 15.
    Greenleaf, A., Lassas, M., Uhlmann, G.: On nonuniqueness for Calderon’s inverse problem. Math. Res. Lett. 10, 685–693 (2003) Google Scholar
  16. 16.
    Leonhard, U.: Optical conformal mapping. Science 312, 1777–1779 (2006) CrossRefGoogle Scholar
  17. 17.
    Krokhin, A.A., Arriaga, J., Gumen, L.: Speed of sound in periodic elastic composites. Phys. Rev. Lett. 91, 264302 (2003) CrossRefGoogle Scholar
  18. 18.
    Martin, T., Nicholas, M., Orris, G., Cai, L.W., Torrent, D., Sánchez-Dehesa, J.: Sonic gradient index lens for aqueous applications. Appl. Phys. Lett. 97, 113503 (2010) CrossRefGoogle Scholar
  19. 19.
    Mei, J., Liu, Z., Wen, W., Sheng, P.: Effective mass density of fluid-solid composites. Phys. Rev. Lett. 96, 024301 (2006) CrossRefGoogle Scholar
  20. 20.
    Milton, G.M., Briane, M., Willis, J.R.: On cloaking for elasticity and physical equations with a transformation invariant form. New J. Phys. 8, 248 (2006) CrossRefGoogle Scholar
  21. 21.
    Norris, A.N.: Acoustic metafluids. J. Acoust. Soc. Am. 125, 839–849 (2009) CrossRefGoogle Scholar
  22. 22.
    Pendry, J.B., Li, J.: An acoustic metafluid: Realizing a broadband acoustic cloak. New J. Phys. 10(11), 115032 (2008) CrossRefGoogle Scholar
  23. 23.
    Pendry, J.B., Schurig, D., Smith, D.R.: Controlling electromagnetic fields. Science 312, 1780–1782 (2006) CrossRefGoogle Scholar
  24. 24.
    Popa, B.I., Cummer, S.A.: Design and characterization of broadband acoustic composite metamaterials. Phys. Rev. B 80, 174303 (2009) CrossRefGoogle Scholar
  25. 25.
    Schoenberg, M., Sen, P.N.: Properties of a periodically stratified acoustic half-space and its relation to a Biot fluid. J. Acoust. Soc. Am. 73, 61–67 (1983) CrossRefGoogle Scholar
  26. 26.
    Schurig, D., Mock, J.J., Justice, B.J., Cummer, S.A., Pendry, J.B., Starr, A.F., Smith, D.R.: Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977–980 (2006) CrossRefGoogle Scholar
  27. 27.
    Torrent, D., Håkansson, A., Cervera, F., Sánchez-Dehesa, J.: Homogenization of two-dimensional clusters of rigid rods in air. Phys. Rev. Lett. 96, 204302 (2006) CrossRefGoogle Scholar
  28. 28.
    Torrent, D., Sánchez-Dehesa, J.: Anisotropic mass density by two-dimensional acoustic metamaterials. New J. Phys. 9, 023004 (2008) CrossRefGoogle Scholar
  29. 29.
    Torrent, D., Sánchez-Dehesa, J.: Acoustic cloaking in two dimensions: A feasible approach. New J. Phys. 10, 063015 (2008) CrossRefGoogle Scholar
  30. 30.
    Torrent, D., Sánchez-Dehesa, J.: Effective parameters of clusters of cylinders embedded in a non viscous fluid or gas. Phys. Rev. B 74, 224305 (2006) CrossRefGoogle Scholar
  31. 31.
    Torrent, D., Sánchez-Dehesa, J.: Acoustic metamaterials for new two-dimensional sonic devices. New J. Phys. 9, 323 (2007) CrossRefGoogle Scholar
  32. 32.
    Torrent, D., Sánchez-Dehesa, J.: Anisotropic mass density by radially periodic fluid structures. Phys. Rev. Lett. 105, 174301 (2010) CrossRefGoogle Scholar
  33. 33.
    Tretyakov, S.: Analytical Modeling in Applied Electromagnetism. Artech House, Norwood (2000) Google Scholar
  34. 34.
    Waterman, P.C.: New formulation of acoustic scattering. J. Acoust. Soc. Am. 45, 1417–1429 (1969) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Grupo de Fenómenos Ondulatorios, Departamento de Ingeniería ElectrónicaUniversidad Politécnica de ValenciaValenciaSpain

Personalised recommendations