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Gauge Invariance Approach to Acoustic Fields pp 95–124Cite as

Negative Refraction, Acoustical Metamaterials and Acoustical Cloaking

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Abstract

An introduction is given. Then, there is an explanation of the limitation of Veselago’s theory with the following coverage: introduction, gauge invariance of homogeneous electromagnetic wave equation, gauge invariance of acoustic field equation, acoustical cloaking, gauge invariance of nonlinear homogeneous acoustic wave equation; the discovery of negative refraction is a special case of coordinate transformations or a unified theory for negative refraction and cloaking, conclusions. This is followed by the multiple scattering approach to perfect acoustic lens. Acoustical cloaking is described with introduction, derivation of transformation acoustics and application to a specific example. Acoustic metamaterial and simultaneous negative mass density and negative bulk modulus is described. Then, there is acoustical cloaking based on nonlinear coordinate transformations. Acoustical cloaking of underwater objects and extension of double negativity to nonlinear acoustics are also provided.

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References

  1. Veselago, V.G.: The electrodynamics of substances with simultaneous negative values of ε and μ. Sov. Phys. Usp. 10(4), 509–514 (1968)

    Article  Google Scholar 

  2. Mandel’stam, L.I.: JETP 15, 475 (1945)

    Google Scholar 

  3. Pendry, J.B., Holden, A.J., Robbins, D.J., Stewart, W.J.: Magnetism from conductors and enhanced non-linear phenomena. IEEE Trans. Microwave Theory Technol. 47(11), 2075–2984 (1999)

    Article  Google Scholar 

  4. Shelby, R.A., Smith, D.R., Schultz, S.: Experimental evidence of a negative index of refraction. Science 292(5514), 77 (2001)

    Article  Google Scholar 

  5. Gan, W.S.: Gauge invariance approach to acoustic fields. In: Akiyama, I. (ed) Acoustical Imaging, vol. 29, pp. 389–314. Springer (2007)

    Google Scholar 

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

    Article  Google Scholar 

  7. Korringa,J.: Physica (Amsterdam) XIII, 392 (1947)

    Google Scholar 

  8. Kohn, W., Rostoker, N.: Phys. Rev. 94, 1111 (1951)

    Article  Google Scholar 

  9. Liu, Z., Chan, C.T., Sheng, P., Goertzen, A.L., Page, J.H.: Elastic wave scattering by periodic structures of spherical objects: theory and experiment. Phys. Rev. B 62(4), 2446–2457 (2000)

    Article  Google Scholar 

  10. Sigalas,M.M., Economou, E.N. J. Sound Vib. 158, 377 (1992)

    Google Scholar 

  11. Kushwaha, M.S., Halevi, P., Dobrzynski, L., Djafrari-Rouhani, B.: Phys. Rev. Lett. 71, 2022 (1993)

    Article  Google Scholar 

  12. Sanchez-Perez, J.V., Caballero, D., Martinez-Sala, R., Rubio, C., Sanchez-Dehesa, J., Meseguer, F.: Phys. Rev. Lett. 80, 5325 (1998)

    Google Scholar 

  13. Kafesaki, M., Economou, E.N.: Phys. Rev. B 52, 13317 (1995)

    Article  Google Scholar 

  14. Yang, S., et al.: Phys. Rev. Lett. 88, 104301 (2002)

    Google Scholar 

  15. Wolfe, J.P.: Imaging Phonons: Acoustic Wave Propagation in Solids. Cambridge University Press, Cambridge, England (1998)

    Book  Google Scholar 

  16. Liu, Z., et al.: Phys. Rev. B 62, 2446 (2000)

    Article  Google Scholar 

  17. Zhang, X., Liu, Z.: Negative refraction of acoustic waves in two-dimensional phononic crystals. Appl. Phys. Lett. 85(2), 341–343 (2004)

    Article  Google Scholar 

  18. Luo, C., Johnson, S.G., Joannopuolos, J.D., Pendry, J.B.: Phys. Rev. B 65, 201104 (2002)

    Article  Google Scholar 

  19. Luo, C., Johnson, S.G., Joannopoulos, J.D.: Appl. Phys. Lett. 83, 2352 (2002)

    Article  Google Scholar 

  20. Lai, Y., Zhang, X., Zhang, Z.Q.: Appl. Phys. Lett. 79, 3224 (2001)

    Article  Google Scholar 

  21. Pendry, J.B.: Phys. Rev. Lett. 85, 3966 (2000)

    Article  Google Scholar 

  22. Pendry, J.B., Schurig, D., Smith, D.R.: Controlling electromagnetic fields. Science 312, 1780–1782 (2006)

    Article  MathSciNet  Google Scholar 

  23. 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)

    Article  Google Scholar 

  24. Milton, G.W., Briane, M., Willis, J.R.: On cloaking for elasticity and physical equations with a transformation invariant form. New J. Phys. 8, 248 (2006)

    Article  Google Scholar 

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

    Article  Google Scholar 

  26. Greenleaf, A., Kurylev, Y., Lassas, M., Uhlmann, G.: Comment on “Scattering Derivation of a 3D Acoustic Cloaking Shell” (2008)

    Google Scholar 

  27. Cummer, S.A., Raleigh, M., Schurig, D.: New J. Phys. 10, 115025–115034 (2008)

    Article  Google Scholar 

  28. Lee, S.H., Kim, C.K., Park, C.M., Seo, Y.M., Wang, Z.G.: Composite acoustic medium with simultaneously negative density and modulus. In: Proceedings of ICSV17 (2010)

    Google Scholar 

  29. Cheng, Y., Xu, J.Y., Liu, X.J.: One-dimensional structured ultrasonic metamaterials with simultaneously negative dynamic density and modulus. Phys. Rev. B 77, 045134 (2008)

    Article  Google Scholar 

  30. Cummer, S.A., Rahm, M., Schurig, D.: Material parameters and vector scaling in transformationacoustics. New J. Phys. 10, 115025 (2008)

    Article  Google Scholar 

  31. Greenleaf, A.et al.: Anistropic conductivities that cannot ne detected by EIT. Physiol. Meas. 24, 413–419 (2003)

    Article  Google Scholar 

  32. Cummer, S.A., et al.: Scattering theory derivation of a 3D acoustic cloaking shell. Phys. Rev. Lett. 100, 024301 (2008)

    Article  Google Scholar 

  33. Yang, S., Page, J.H., Liu, Z., Cowan, M.L., Chan, C.T., Sheng, P.: Focusing of sound in a 3D phononic crystal. Phys. Rev. Lett. 93(2), 024301-1–024301-4 (2004)

    Google Scholar 

  34. Hu, J., Zhou, X., Hu, G.: A numerical method for designing acoustic cloak with arbitrary shapes. Comput. Mater. Sci. (Elsevier) 46, 708–712 (2009)

    Article  Google Scholar 

  35. Akl, W., Elnady, T., Elsabbagh, A.: Improving acoustic cloak bandwidth using nonlinear coordinate transformations. In: Proceedings of ICSV17 (2010)

    Google Scholar 

  36. Fang, N., Zhang, S.: Phys. Rev. Lett. (2009)

    Google Scholar 

  37. Thurston, R.N., Shapiro, M.J.: J. Acoust. Soc. Am. 41, 1112 (1967)

    Article  Google Scholar 

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  1. Acoustical Technologies Singapore Pte Ltd., Singapore, Singapore

    Woon Siong Gan

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  1. Woon Siong Gan
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Correspondence to Woon Siong Gan .

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Gan, W.S. (2019). Negative Refraction, Acoustical Metamaterials and Acoustical Cloaking. In: Gauge Invariance Approach to Acoustic Fields. Springer, Singapore. https://doi.org/10.1007/978-981-13-8751-7_13

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  • DOI: https://doi.org/10.1007/978-981-13-8751-7_13

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-8750-0

  • Online ISBN: 978-981-13-8751-7

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