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Journal of the Optical Society of America B

Journal of the Optical Society of America B

| OPTICAL PHYSICS

  • Editor: Henry van Driel
  • Vol. 27, Iss. 5 — May. 1, 2010
  • pp: 1016–1021

On the signs of the imaginary parts of the effective permittivity and permeability in metamaterials

J. Woodley and M. Mojahedi  »View Author Affiliations


JOSA B, Vol. 27, Issue 5, pp. 1016-1021 (2010)
http://dx.doi.org/10.1364/JOSAB.27.001016


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Abstract

The signs of the imaginary parts of the permittivity and permeability in metamaterials such as split ring resonators and strip wires are investigated. It is shown that the Lorentzian model often used to describe the effective parameters (i.e., the permittivity and permeability) of these metamaterials does not physically allow their imaginary parts to be negative. Moreover, a popular technique used to retrieve the effective parameters of a structure from its S-parameters is also investigated. By comparing the effective parameters for an array of dielectric spheres obtained both from S-parameter simulations and analytical calculations, it is shown that an often observed negative imaginary permittivity obtained from the S-parameters is a result of numerical error in the simulations. This is shown both for the finite element method and finite-difference time-domain simulations.

© 2010 Optical Society of America

OCIS Codes
(160.0160) Materials : Materials
(350.5500) Other areas of optics : Propagation
(260.2065) Physical optics : Effective medium theory
(160.3918) Materials : Metamaterials

ToC Category:
Materials

History
Original Manuscript: December 9, 2009
Manuscript Accepted: January 29, 2010
Published: April 27, 2010

Citation
J. Woodley and M. Mojahedi, "On the signs of the imaginary parts of the effective permittivity and permeability in metamaterials," J. Opt. Soc. Am. B 27, 1016-1021 (2010)
http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-27-5-1016


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References

  1. V. G. Veselago, “The electrodynamics of substances with simultaneous negative values of ϵ and μ,” Sov. Phys. Usp. 10, 509–514 (1968). [CrossRef]
  2. J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, “Extremely low frequency plasmons in metallic mesostructures,” Phys. Rev. Lett. 76, 4773 (1996). [CrossRef] [PubMed]
  3. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999). [CrossRef]
  4. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permittivity and permittivity,” Phys. Rev. Lett. 84, 4184 (2000). [CrossRef] [PubMed]
  5. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of negative index of refraction,” Science 292, 77–79 (2001). [CrossRef] [PubMed]
  6. M. Bayindir, K. Aydin, and E. Ozbay, “Transmission properties of composite metamaterials in free space,” Appl. Phys. Lett. 81, 120 (2002). [CrossRef]
  7. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, “Experimental verification and simulation of negative index of refraction using Snell’s law,” Phys. Rev. Lett. 90, 107401 (2003). [CrossRef] [PubMed]
  8. J. F. Woodley and M. Mojahedi, “Negative group velocity and group delay in left-handed media,” Phys. Rev. E 70 (2004). [CrossRef]
  9. P. V. Parimi, W. T. Lu, P. Vodo, J. Sokoloff, J. S. Derov, and S. Sridhar, “Negative refraction and left-handed electromagnetism in microwave photonic crystals,” Phys. Rev. Lett. 92, 127401 (2004). [CrossRef] [PubMed]
  10. P. Markos and C. M. Soukoulis, “Transmission properties and effective electromagnetic parameters of double negative metamaterials,” Opt. Express 11, 649–661 (2003). [CrossRef] [PubMed]
  11. D. Seetharamdoo, R. Sauleau, K. Mahdjoubi, and A. C. Tarot, “Effective parameters of resonant negative refractive index metamaterials: interpretation and validity,” J. Appl. Phys. 98, 063505 (2005). [CrossRef]
  12. U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, “Negative index metameterials combining magnetic resonators with metal films,” Opt. Express 14, 7872–7877 (2006). [CrossRef] [PubMed]
  13. T. Koschny, P. Markos, D. R. Smith, and C. M. Soukoulis, “Resonant and antiresonant frequency dependence of the effective parameters of metamaterials,” Phys. Rev. E 68, 065602 (2003). [CrossRef]
  14. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65, 195104 (2002). [CrossRef]
  15. L. D. Landau, E. M. Lifshitz, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinemann, 2002).
  16. J. D. Jackson, Classical Electrodynamics (Wiley, 1999).
  17. R. Y. Chiao, “Superluminal (but causal) propagation of wave packets in transparent media with inverted atomic populations,” Phys. Rev. A 48, R34–R37 (1993). [CrossRef] [PubMed]
  18. P. W. Milonni and J. H. Eberly, Lasers (Wiley-Interscience, 1988).
  19. J.-M. Lerat, N. Mallejac, and O. Acher, “Determination of the effective parameters of a metamaterial by field summation method,” J. Appl. Phys. 100, 084908 (2006). [CrossRef]
  20. M. S. Wheeler, J. S. Aitchison, and M. Mojahedi, “Three dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies,” Phys. Rev. B 72, 193103 (2005). [CrossRef]

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