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Numerical Determination of Permittivity and Permeability Tensors of a Dielectric Metamaterial Composed of an Infinite Number of Split Ring Resonators

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Abstract

In this paper, the determination of electric permittivity and magnetic permeability of a dielectric metamaterial composed of an infinite number of conductors (split ring resonators) using the quasi-static Lorentz theory is investigated. The induced currents on the conductors are calculated with the method of moments. Negative values of the real parts of the permittivity and permeability are obtained within a given frequency band. Various modifications to the original configuration are made and their effects on the behavior of both permittivity and permeability are discussed. The obtained results are in good satisfactory with the theory predicting the possibility to have negative values of the considered parameters as well as the numerous reported works.

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References

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

    Article  Google Scholar 

  2. Pendry, J. B., Holden, A. J., Stewart, W. J., et al. (1996). Extremely low frequency plasmons in metallic mesostructures. Phys Rev Lett, 76, 4773–4776.

    Article  Google Scholar 

  3. Pendry, J. B., Holden, A. J., Obbins, D. J., et al. (1999). Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans Microw Theory Tech, 47, 2075–2084.

    Article  Google Scholar 

  4. Smith, D. R., & Liu, R. (2010). Metamaterials: theory, design and applications. New York: Springer.

    Google Scholar 

  5. Ishimaru, A. (2003). Generalized constitutive relations for metamaterials based on the quasi-static Lorentz theory. IEEE Trans Antennas Propag, 51(10), 2550–2557.

    Article  Google Scholar 

  6. Orfanidis, S. J. (2010). Electromagnetic waves and antennas. Piscataway: Rutgers University.

    Google Scholar 

  7. Collin, R. E. (1990). Field theory of guided waves. New York: Wiley-IEEE Press.

    Book  Google Scholar 

  8. Harrington, R. F. (1967). Matrix methods for field problems. Proc IEEE, 55(2), 136–149.

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Ecole Nationale Polytechnique (ENP), El-Harrach, Algeria

    Bedri Semmar, Rabia Aksas & Mohamed Trabelsi

  2. Signals and Systems Laboratory, Department of Electronics, IGEE, University of Boumerdes, Boumerdes, Algeria

    Mouloud Challal & Arab Azrar

Authors
  1. Bedri Semmar
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  2. Rabia Aksas
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  3. Mouloud Challal
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  4. Arab Azrar
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  5. Mohamed Trabelsi
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Correspondence to Mouloud Challal.

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Semmar, B., Aksas, R., Challal, M. et al. Numerical Determination of Permittivity and Permeability Tensors of a Dielectric Metamaterial Composed of an Infinite Number of Split Ring Resonators. Wireless Pers Commun 83, 2925–2947 (2015). https://doi.org/10.1007/s11277-015-2574-0

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  • DOI: https://doi.org/10.1007/s11277-015-2574-0

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