Electromagnetic metamaterials are artificial materials exhibiting simultaneously negative permeability and permittivity, and the “double negativity” gives rise to many interesting phenomena such as negative refraction, backward waves and superlensing effects. We will see that the concept can be extended to acoustic waves. We will show the existence of acoustic metamaterial, in which both the effective density and bulk modulus are simultaneously negative at some particular frequency range, in the sense of an effective medium. Such a double negative acoustic system is an acoustic analog of Veselogo’s medium in electromagnetism, and shares many novel consequences such as negative refractive index, flat slab focusing and super-resolution. The double negativity in acoustics is derived from low frequency resonances, as in the case of electromagnetism, but the negative density and modulus can come from a single resonance structure, as distinct from electromagnetism in which the negative permeability and negative permittivity originates from different resonance mechanisms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
V.C. Veselago, Sov. Phys. Usp. 10, 509 (1968).
D.R. Smith, J.B. Pendry, M.C.K. Wiltshire, Science 305, 788 (2004).
J.B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
4. J.B. Pendry, A.J. Holden, D.J. Robins, W.J. Stewart, IEEE Trans. Microw. Theory Tech. 47, 2075 (1999).
R.A. Shelby, D.R. Smith, S. Schultz, Science 292, 77 (2001).
J. Li, C.T. Chan, Phys. Rev. E 70, 055602 (2004).
Z. Hashin, S. Shtrikman, J. Appl. Phys. 33, 3125 (1962).
J.G. Berryman, J. Acoust. Soc. Am. 68, 1809 (1980).
G. Mie, Ann. Phys. (Leipzig) 25, 377 (1908).
J.H. Page, A. Sukhovich, S. Yang, M.L. Cowan, F. Van Der Biest, A. Tourin, M. Fing, Z. Liu, C.T. Chan, P. Sheng, Phys. Status Solidi B 241, 3454 (2004).
For an introduction to photonic crystal, see, e.g., J.D. Joannopoulos, R.D. Meade, J.N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University Press, Princeton, 1995).
S. Yang, J.H. Page, Z.Y. Liu, M.L. Cowan, C.T. Chan, P. Sheng, Phys. Rev. Lett. 93, 024301 (2004).
X. Zhang, Z.Y. Liu, Appl. Phys. Lett. 85, 341 (2004).
L. Feng, X.P. Liu, M.H. Lu, Y.B. Chen, Y.F. Chen, Y.W. Mao, J. Zi, Y.Y. Zhu, S.N. Zhu, N.B. Ming, Phys. Rev. Lett. 96, 14301 (2006).
See, e.g., C. Luo, S.G. Johnson, J.D. Joannopoulos, J.B. Pendry, Phys. Rev. B. 65,201104(R) (2002).
See, e.g., N.W. Ashcroft, N.D. Mermin, Solid State Physics(Saunders, Philadelphia, 1976).
Z.Y. Liu, X.X. Zhang, Y. Mao, Y.Y. Zhu, Z. Yang, C.T. Chan, P. Sheng, Science. 289, 1641( 2000).
Z.Y. Liu, C.T. Chan, P. Sheng, A.L. Goertzen, J.H. Page, Phys. Rev. B 62, 2446(2000).
Z.Y. Liu, C.T. Chan, P. Sheng, Phys. Rev. B 65, 165116 (2002).
K.H. Fung, Z.Y. Liu, C.T. Chan, Zeitschrift Fur Kristallographie 220, 871. (2005).
See, e.g., A.L. Fetter, J.D. Walecka, Theoretical Mechanics of Particles and Continua (McGraw-Hill, New York, 1980).
J.E. Sipe, J. Van Kranendonk, Phys. Rev. A 9, 1806 (1974).
S. Tretyakov, Analytical Modeling in Applied Electromagnetics (Artech House, Boston, 2003).
L. Tsang, J.A. Kong, K.-H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, New York, 2000).
M. Kafeski, E.N. Economou, Phys. Rev. B 60, 1 (1993).
E. Psarobas, A. Modinos, R. Sainidou, N. Stefanou, Phys. Rev. B 65, 064307. (2002).
D.R. Smith, D. Schurig, M. Rosenbluth, S. Schultz, S.A. Ramakrishna, J.B. Pendry, Appl. Phys. Lett. 82, 1506 (2003).
L. Zhou, C.T. Chan, Appl. Phys. Lett. 86, 101104 (2005).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Li, J., Fung, K.H., Liu, Z.Y., Sheng, P., Chan, C.T. (2007). Generalizing the Concept of Negative Medium to Acoustic Waves. In: Krowne, C.M., Zhang, Y. (eds) Physics of Negative Refraction and Negative Index Materials. Springer Series in Materials Science, vol 98. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72132-1_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-72132-1_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72131-4
Online ISBN: 978-3-540-72132-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)