On the Electromagnetic Modelling of Left-Handed Metamaterials

  • R. Marqués
  • F. Medina
  • F. Mesa
  • J. Martel
Part of the NATO Science Series book series (NAII, volume 89)


The electromagnetic modelling of discrete left-handed microwave metamaterials is discussed. A continuous-medium approach is proposed for the analysis of a wide class of left-handed and negative permeability media made by placing metallic inclusions in a host dielectric medium. This includes all artificial media made by the superposition of an artificial plasma and a negative magnetic permeability medium made of split ring resonators. The proposed model allows for the consideration of both edge- and broadsidecoupled split rings resonators. It also allows for the use of wires and/or metallic plates in the plasma simulation. Other related physical effects that can appear in these artificial media, such as bianisotropy, are also taken into account. The numerical computations provided by the model are compared with full-wave numerical simulations and experimental results, showing a good agreement. The advantages and disadvantages of the different left-handed metamaterial designs considered along the text are also discussed.


Artificial Medium Split Ring Resonator Metallic Plate Negative Refractive Index Artificial Plasma 
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  1. 1.
    Veselago, V.G. (1968) Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities, Soviet Phys. USPEKHI 10, pp. 509–514.CrossRefGoogle Scholar
  2. 2.
    Smith, D.R., Padilla, W.J., Vier, D.C., Nemat-Nasser, S.C and Schultz, S. (2000) Composite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett. 84, pp. 4184–4187.CrossRefGoogle Scholar
  3. 3.
    Rotman, W. (1962) Plasma simulation by artificial dielectrics and parallel-plate media, IRE Trans, on Antennas and Prop. AP-10, pp. 82–95.CrossRefGoogle Scholar
  4. 4.
    Pendry, J.B., Holden, A.J., Robbins, D.J. and Stewart, W.J. (1999) Magnetism from conductors and enhanced nonlinear phenomena, IEEE Trans, on Microwave Theory and Tech., MTT-47, pp. 2075–2084.CrossRefGoogle Scholar
  5. 5.
    Shelby, R.A., Smith, D.R., Nemat-Nasser, S.C. and Schultz, S. (2001) Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial, Applied Phys. Lett. 78, pp. 489–491.CrossRefGoogle Scholar
  6. 6.
    Koch, W.E. (1948) Metallic delay lenses, Bell Syst. Tech. J. 27, pp. 58–82.Google Scholar
  7. 7.
    Collin, R.E. (1991) Field theory of guided waves, IEEE Press, N.Y.Google Scholar
  8. 8.
    Lindell, I.V., Sihvola, A.H., Tretyakov, S.A. and Viitanen, A.J. (1994) Electromagnetic waves in chiral and bi-isotropic media. Artech House, Boston and London.Google Scholar
  9. 9.
    Saadoun, M.M.I, and Engheta, N. (1992) A reciprocal phase shifter using novel preudochiral or Ω medium, Microwave and Opt. Tech. Lett. 5, pp. 184–188.CrossRefGoogle Scholar
  10. 10.
    Mariotte, F., Tretyakov, S.A., Sauviac, B. (1994) Isotropic chiral composite modeling: comparison between analytical, numerical, and experimental results, Microwave and Opt. Tech. Lett 7, pp. 861–864.CrossRefGoogle Scholar
  11. 11.
    Bahr, A.J. and Clausing, K.R. (1994) An approximate model for artificial chiral material, IEEE Trans, on Antennas and Prop. AP-42, pp. 1592–1599.CrossRefGoogle Scholar
  12. 12.
    Tretyakov, S.A., Sochava, A.A., Simovski, C.R. (1996) Influence of chiral shapes of individual inclusions on the absorption in chiral composite materials, Electromagnetics 16, pp. 113–127.CrossRefGoogle Scholar
  13. 13.
    Marqués, R., Medina, F., Rafii-El-Idrissi, R. (2002) Role of bianisotropy in negative permeability and left-handed metamaterials, Phys. Rev. B 65 pp. 144440CrossRefGoogle Scholar
  14. 14.
    Sihvola, A.H. (1999) Electromagnetic mixing formulas and applications. IEE, London.CrossRefGoogle Scholar
  15. 15.
    Shelby, R.A., Smith, D.R., Schultz, S. (2001) Experimental verification of a negative index of refraction, Science 292, pp. 77–79.CrossRefGoogle Scholar
  16. 16.
    Marqués, R., Martel, J., Mesa, F. and Medina, F. (2002) A new 2-D isotropic lefthanded metamaterial design: theory and experiment, Microwave and Opt. Tech. Lett. (in press).Google Scholar
  17. 17.
    Marqués, R., Martel, J., Mesa, F. and Medina, F. (2002) Left-handed media simulation and transmission of EM waves in sub-wavelength SRR-loaded metallic waveguides, Phys. Rev. Lett. (accepted for publication).Google Scholar
  18. 18.
    Pendry, J.B., Holden, A.J., Stewart, W.J. and Youngs, I. (1996) Extremely low frequency plasmons in metallic mesostructures, Phys. Rev. Lett. 76, pp. 4773–4776.CrossRefGoogle Scholar
  19. 19.
    Pitarke, J.M., Garcia Vidal, F.J., Pendry, J.B. (1998) Effective electronic response of a system of metallic cilinders, Pys. Rev. B 57 pp. 15261–15266.CrossRefGoogle Scholar
  20. 20.
    Bahl, I., Bhartia, P. (1998) Microwave solid state circuit design, Wiley, N.Y.Google Scholar
  21. 21.
    Wheeler, H.A. (1965) Transmission lines properties of parallel strips separated by a dielectric sheet, IEEE Trans. Microwave Theory and Tech. MTT-13, pp. 172–185.CrossRefGoogle Scholar
  22. 22.
    Ghione, G., Naldi, C. (1984) Analytical formulas for coplanar lines and monolithic MICs, Electronic Lett., 20, pp. 179–181.CrossRefGoogle Scholar
  23. 23.
    Landau, L., Lifshitz, E. (1980) Statistical Phys., Pergamonn Press, Oxford.Google Scholar
  24. 24.
    Pendry, J.B. (2000) Negative refraction makes a perfect lens, Phys. Rev. Lett. 85, pp. 3966–3969.CrossRefGoogle Scholar
  25. 25.
    Smith, D.R., Padilla, W.J., Vier, D.C., Shelby, R., Nemat-Nasser, S.C., Kroll, N. and Schultz, S. (2001) Left-handed metamaterials, in Photonic crystals and light localization in the 21st century, Proceedings of the NATO-ASI Conference on Photonic Crystals and Light Localization. Crete, June pp. 18–30, 2000, ed. by Costas M. Sokoulis (Kluwer Academic, Dordrecht), p. 351.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • R. Marqués
    • 1
  • F. Medina
    • 1
  • F. Mesa
    • 2
  • J. Martel
    • 3
  1. 1.Departamento de Electricidad y ElectrónicaUniversidad de SevillaSevillaSpain
  2. 2.Departamento de Física Aplicada 1Universidad de SevillaSevillaSpain
  3. 3.Departamento de Física Aplicada 3Universidad de SevillaSevillaSpain

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