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Transformation Acoustics

  • Steven A. CummerEmail author
Chapter
Part of the Springer Series in Materials Science book series (SSMATERIALS, volume 166)

Abstract

In this chapter we review the development of the concept of transformation acoustics, through which sound fields can be arbitrarily manipulated by complex acoustic materials. We describe the theory and the design equations in several different forms, and we present several explicit design examples using transformation acoustics. After briefly describing some theoretical offshoots from the original idea, we conclude with a summary of approaches for engineering composite materials with the smoothly inhomogeneous and anisotropic properties needed for many transformation acoustics devices.

Keywords

Bulk Modulus Coordinate Transformation Sound Field Acoustic Beam Acoustic Equation 
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.

References

  1. 1.
    Andkjaer, J., Sigmund, O.: Topology optimized low-contrast all-dielectric optical cloak. Appl. Phys. Lett. 98, 021112 (2011) CrossRefGoogle Scholar
  2. 2.
    Cai, W., et al.: Designs for optical cloaking with high-order transformations. Opt. Express 16(8), 5444–5452 (2008) CrossRefGoogle Scholar
  3. 3.
    Chen, H., Chan, C.T.: Acoustic cloaking in three dimensions using acoustic metamaterials. Appl. Phys. Lett. 91, 183518 (2007) CrossRefGoogle Scholar
  4. 4.
    Chen, H., Chan, C.T.: Acoustic cloaking and transformation acoustics. J. Phys. D 43, 113001 (2010) CrossRefGoogle Scholar
  5. 5.
    Cheng, Y., et al.: A multilayer structured acoustic cloak with homogeneous isotropic materials. Appl. Phys. Lett. 92, 151913 (2008) CrossRefGoogle Scholar
  6. 6.
    Climente, A., et al.: Sound focusing by gradient index sonic lenses. Appl. Phys. Lett. 97, 104103 (2010) CrossRefGoogle Scholar
  7. 7.
    Cummer, S.A., et al.: A rigorous and nonsingular two dimensional cloaking coordinate transformation. J. Appl. Phys. 105, 056102 (2009) CrossRefGoogle Scholar
  8. 8.
    Cummer, S.A., et al.: Full-wave simulations of electromagnetic cloaking structures. Phys. Rev. E 74(3), 036621 (2006) CrossRefGoogle Scholar
  9. 9.
    Cummer, S.A., et al.: Material parameters and vector scaling in transformation acoustics. New J. Phys. 10, 115025 (2008) CrossRefGoogle Scholar
  10. 10.
    Cummer, S.A., Schurig, D.: One path to acoustic cloaking. New J. Phys. 9, 45 (2007) CrossRefGoogle Scholar
  11. 11.
    Fang, N., et al.: Ultrasonic metamaterials with negative modulus. Nat. Mater. 5, 452–456 (2006) CrossRefGoogle Scholar
  12. 12.
    Farhat, M., et al.: Broadband cylindrical acoustic cloak for linear surface waves in a fluid. Phys. Rev. Lett. 101, 134501 (2008) CrossRefGoogle Scholar
  13. 13.
    Farhat, M., et al.: Ultrabroadband elastic cloaking in thin plates. Phys. Rev. Lett. 103, 024301 (2009) CrossRefGoogle Scholar
  14. 14.
    Greenleaf, A., et al.: Anisotropic conductivities that cannot be detected by EIT. Physiol. Meas. 24, 413–419 (2003) CrossRefGoogle Scholar
  15. 15.
    Knupp, P., Steinberg, S.: Fundamentals of Grid Generation. CRC Press, Boca Raton (1994) Google Scholar
  16. 16.
    Lai, Y., et al.: Illusion optics: the optical transformation of an object into another object. Phys. Rev. Lett. 102, 253902 (2009) CrossRefGoogle Scholar
  17. 17.
    Lee, S.H., et al.: Acoustic metamaterial with negative density. Phys. Lett. A 373, 4464–4469 (2009) CrossRefGoogle Scholar
  18. 18.
    Lee, S.H., et al.: Acoustic metamaterial with negative modulus. J. Phys. Condens. Matter 21, 175704 (2009) CrossRefGoogle Scholar
  19. 19.
    Li, J., Chan, C.T.: Double-negative acoustic metamaterial. Phys. Rev. E 70(5), 055602 (2004) CrossRefGoogle Scholar
  20. 20.
    Li, J., Pendry, J.B.: Hiding under the carpet: A new strategy for cloaking. Phys. Rev. Lett. 101, 203901 (2008) CrossRefGoogle Scholar
  21. 21.
    Liu, R., et al.: Broadband ground-plane cloak. Science 323, 366 (2009) CrossRefGoogle Scholar
  22. 22.
    Milton, G.W., et al.: On cloaking for elasticity and physical equations with a transformation invariant form. New J. Phys. 8, 248 (2006) CrossRefGoogle Scholar
  23. 23.
    Norris, A.N.: Acoustic cloaking theory. Proc. R. Soc. A 464, 2411–2434 (2008) CrossRefGoogle Scholar
  24. 24.
    Norris, A.N.: Acoustic metafluids. J. Acoust. Soc. Am. 464, 839–849 (2008) Google Scholar
  25. 25.
    Padilla, W.J., et al.: Negative refractive index metamaterials. Mater. Today 9, 28 (2006) CrossRefGoogle Scholar
  26. 26.
    Pendry, J.B., et al.: Controlling electromagnetic fields. Science 312, 1780–1782 (2006) CrossRefGoogle Scholar
  27. 27.
    Plebanski, J.: Electromagnetic waves in gravitational fields. Phys. Rev. 118, 1396–1408 (1960) CrossRefGoogle Scholar
  28. 28.
    Popa, B.-I., Cummer, S.A.: Cloaking with optimized homogeneous anisotropic layers. Phys. Rev. A 79, 023806 (2009) CrossRefGoogle Scholar
  29. 29.
    Popa, B.-I., Cummer, S.A.: Design and characterization of broadband acoustic composite metamaterials. Phys. Rev. B 80, 174303 (2009) CrossRefGoogle Scholar
  30. 30.
    Popa, B.-I., Cummer, S.A.: Homogeneous and compact acoustic ground cloaks. Phys. Rev. B. In review (2011) Google Scholar
  31. 31.
    Popa, B.-I., et al.: Experimental acoustic ground cloak in air. Phys. Rev. Lett. 106, 253901 (2011) CrossRefGoogle Scholar
  32. 32.
    Rahm, M., et al.: Optical design of reflectionless complex media by finite embedded coordinate transformations. Phys. Rev. Lett. 100, 063903 (2008) CrossRefGoogle Scholar
  33. 33.
    Rahm, M., et al.: Transformation-optical design of adaptive beam bends and beam expanders. Opt. Express 16, 11555 (2008) CrossRefGoogle Scholar
  34. 34.
    Rahm, M., et al.: Design of electromagnetic cloaks and concentrators using form-invariant coordinate transformations of Maxwell’s equations. Photonics Nanostruct. 6, 87–95 (2008) CrossRefGoogle Scholar
  35. 35.
    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
  36. 36.
    Schurig, D., et al.: Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977–980 (2006) CrossRefGoogle Scholar
  37. 37.
    Schurig, D., et al.: Calculation of material properties and ray tracing in transformation media. Opt. Express 14, 9794–9804 (2006) CrossRefGoogle Scholar
  38. 38.
    Tamm, I.Y.: Electrodynamics of an anisotropic medium and the special theory of relativity. J. Russ. Phys.-Chem. Soc. 56, 248 (1924) Google Scholar
  39. 39.
    Torrent, D., Sanchez-Dehesa, J.: Acoustic metamaterials for new two-dimensional sonic devices. New J. Phys. 9, 323 (2007) CrossRefGoogle Scholar
  40. 40.
    Torrent, D., Sanchez-Dehesa, J.: Acoustic cloaking in two dimensions: A feasible approach. New J. Phys. 10, 063015 (2008) CrossRefGoogle Scholar
  41. 41.
    Wood, A.B.: A Textbook of Sound. Macmillan, New York (1955) Google Scholar
  42. 42.
    Zhang, S., et al.: Cloaking of matter waves. Phys. Rev. Lett. 100, 123002 (2008) CrossRefGoogle Scholar
  43. 43.
    Zhang, S., et al.: Broadband acoustic cloak for ultrasound waves. Phys. Rev. Lett. 106, 024301 (2011) CrossRefGoogle Scholar
  44. 44.
    Zigoneanu, L., et al.: Design and measurements of a broadband 2D acoustic lens. Phys. Rev. B 84, 024305 (2011) CrossRefGoogle Scholar
  45. 45.
    Zigoneanu, L., et al.: Design and measurements of a broadband 2D acoustic metamaterial with anisotropic effective mass density. J. Appl. Phys. 109, 054906 (2011) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringDuke UniversityDurhamUSA

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