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Transformation Acoustics

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Acoustic Metamaterials

Part of the book series: Springer Series in Materials Science ((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.

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References

  1. Andkjaer, J., Sigmund, O.: Topology optimized low-contrast all-dielectric optical cloak. Appl. Phys. Lett. 98, 021112 (2011)

    Article  Google Scholar 

  2. Cai, W., et al.: Designs for optical cloaking with high-order transformations. Opt. Express 16(8), 5444–5452 (2008)

    Article  Google Scholar 

  3. Chen, H., Chan, C.T.: Acoustic cloaking in three dimensions using acoustic metamaterials. Appl. Phys. Lett. 91, 183518 (2007)

    Article  Google Scholar 

  4. Chen, H., Chan, C.T.: Acoustic cloaking and transformation acoustics. J. Phys. D 43, 113001 (2010)

    Article  Google Scholar 

  5. Cheng, Y., et al.: A multilayer structured acoustic cloak with homogeneous isotropic materials. Appl. Phys. Lett. 92, 151913 (2008)

    Article  Google Scholar 

  6. Climente, A., et al.: Sound focusing by gradient index sonic lenses. Appl. Phys. Lett. 97, 104103 (2010)

    Article  Google Scholar 

  7. Cummer, S.A., et al.: A rigorous and nonsingular two dimensional cloaking coordinate transformation. J. Appl. Phys. 105, 056102 (2009)

    Article  Google Scholar 

  8. Cummer, S.A., et al.: Full-wave simulations of electromagnetic cloaking structures. Phys. Rev. E 74(3), 036621 (2006)

    Article  Google Scholar 

  9. Cummer, S.A., et al.: Material parameters and vector scaling in transformation acoustics. New J. Phys. 10, 115025 (2008)

    Article  Google Scholar 

  10. Cummer, S.A., Schurig, D.: One path to acoustic cloaking. New J. Phys. 9, 45 (2007)

    Article  Google Scholar 

  11. Fang, N., et al.: Ultrasonic metamaterials with negative modulus. Nat. Mater. 5, 452–456 (2006)

    Article  CAS  Google Scholar 

  12. Farhat, M., et al.: Broadband cylindrical acoustic cloak for linear surface waves in a fluid. Phys. Rev. Lett. 101, 134501 (2008)

    Article  CAS  Google Scholar 

  13. Farhat, M., et al.: Ultrabroadband elastic cloaking in thin plates. Phys. Rev. Lett. 103, 024301 (2009)

    Article  Google Scholar 

  14. Greenleaf, A., et al.: Anisotropic conductivities that cannot be detected by EIT. Physiol. Meas. 24, 413–419 (2003)

    Article  Google Scholar 

  15. Knupp, P., Steinberg, S.: Fundamentals of Grid Generation. CRC Press, Boca Raton (1994)

    Google Scholar 

  16. Lai, Y., et al.: Illusion optics: the optical transformation of an object into another object. Phys. Rev. Lett. 102, 253902 (2009)

    Article  Google Scholar 

  17. Lee, S.H., et al.: Acoustic metamaterial with negative density. Phys. Lett. A 373, 4464–4469 (2009)

    Article  CAS  Google Scholar 

  18. Lee, S.H., et al.: Acoustic metamaterial with negative modulus. J. Phys. Condens. Matter 21, 175704 (2009)

    Article  Google Scholar 

  19. Li, J., Chan, C.T.: Double-negative acoustic metamaterial. Phys. Rev. E 70(5), 055602 (2004)

    Article  Google Scholar 

  20. Li, J., Pendry, J.B.: Hiding under the carpet: A new strategy for cloaking. Phys. Rev. Lett. 101, 203901 (2008)

    Article  Google Scholar 

  21. Liu, R., et al.: Broadband ground-plane cloak. Science 323, 366 (2009)

    Article  CAS  Google Scholar 

  22. Milton, G.W., et al.: On cloaking for elasticity and physical equations with a transformation invariant form. New J. Phys. 8, 248 (2006)

    Article  Google Scholar 

  23. Norris, A.N.: Acoustic cloaking theory. Proc. R. Soc. A 464, 2411–2434 (2008)

    Article  CAS  Google Scholar 

  24. Norris, A.N.: Acoustic metafluids. J. Acoust. Soc. Am. 464, 839–849 (2008)

    Google Scholar 

  25. Padilla, W.J., et al.: Negative refractive index metamaterials. Mater. Today 9, 28 (2006)

    Article  CAS  Google Scholar 

  26. Pendry, J.B., et al.: Controlling electromagnetic fields. Science 312, 1780–1782 (2006)

    Article  CAS  Google Scholar 

  27. Plebanski, J.: Electromagnetic waves in gravitational fields. Phys. Rev. 118, 1396–1408 (1960)

    Article  Google Scholar 

  28. Popa, B.-I., Cummer, S.A.: Cloaking with optimized homogeneous anisotropic layers. Phys. Rev. A 79, 023806 (2009)

    Article  Google Scholar 

  29. Popa, B.-I., Cummer, S.A.: Design and characterization of broadband acoustic composite metamaterials. Phys. Rev. B 80, 174303 (2009)

    Article  Google Scholar 

  30. Popa, B.-I., Cummer, S.A.: Homogeneous and compact acoustic ground cloaks. Phys. Rev. B. In review (2011)

    Google Scholar 

  31. Popa, B.-I., et al.: Experimental acoustic ground cloak in air. Phys. Rev. Lett. 106, 253901 (2011)

    Article  Google Scholar 

  32. Rahm, M., et al.: Optical design of reflectionless complex media by finite embedded coordinate transformations. Phys. Rev. Lett. 100, 063903 (2008)

    Article  Google Scholar 

  33. Rahm, M., et al.: Transformation-optical design of adaptive beam bends and beam expanders. Opt. Express 16, 11555 (2008)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  36. Schurig, D., et al.: Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977–980 (2006)

    Article  CAS  Google Scholar 

  37. Schurig, D., et al.: Calculation of material properties and ray tracing in transformation media. Opt. Express 14, 9794–9804 (2006)

    Article  CAS  Google Scholar 

  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. Torrent, D., Sanchez-Dehesa, J.: Acoustic metamaterials for new two-dimensional sonic devices. New J. Phys. 9, 323 (2007)

    Article  Google Scholar 

  40. Torrent, D., Sanchez-Dehesa, J.: Acoustic cloaking in two dimensions: A feasible approach. New J. Phys. 10, 063015 (2008)

    Article  Google Scholar 

  41. Wood, A.B.: A Textbook of Sound. Macmillan, New York (1955)

    Google Scholar 

  42. Zhang, S., et al.: Cloaking of matter waves. Phys. Rev. Lett. 100, 123002 (2008)

    Article  Google Scholar 

  43. Zhang, S., et al.: Broadband acoustic cloak for ultrasound waves. Phys. Rev. Lett. 106, 024301 (2011)

    Article  Google Scholar 

  44. Zigoneanu, L., et al.: Design and measurements of a broadband 2D acoustic lens. Phys. Rev. B 84, 024305 (2011)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

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Correspondence to Steven A. Cummer .

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Cummer, S.A. (2013). Transformation Acoustics. In: Craster, R., Guenneau, S. (eds) Acoustic Metamaterials. Springer Series in Materials Science, vol 166. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4813-2_8

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