Applied Physics A

, 125:153 | Cite as

Revised homogenization for two-component metamaterial with non-magnetic metallic cylindrical inclusions

  • Oleg RybinEmail author
  • Sergey Shulga


Electromagnetic response of the 2-D metamaterial as the regular lattice of infinitely long circular non-magnetic metallic inclusions periodically embedded in a host dielectric material was carried out in the frequency range up to THz frequencies. It has been shown that such a metamaterial behaves like an ultra-low index homogenous material in some frequency range containing the frequencies at which the electric and magnetic resonances are excited. The resonances give rise to the electric and magnetic dipole moments. Averaging of these dipole moments over the volumes of unit cell of the metamaterial enables to derive the expressions of complex effective relative permittivity and permeability of the metamaterial. In some partial cases, the derived expressions are rather very close to microwave approximations of the effective parameters obtained earlier by other authors for the frequencies up to GHz frequencies. Numerical validation of the derived effective parameters is also preformed by making the full-wave simulation using a finite-difference time-domain software.



The authors would like to acknowledge Dr. Georgios Zouganelis for his encouragement and advice during the research that underlies this study. The authors would also like to acknowledge Ms. Julia Rybin for her help in preparing the manuscript.


  1. 1.
    G. Zouganelis, O. Rybin, Two layer magnetodielectric metamaterial with enhanced dielectric constant as a new ferrite like material. Jpn. J. Appl. Phys. 45, part 2, LL.1175–LL.1178 (2006)Google Scholar
  2. 2.
    O. Rybin, S. Shulga, An advanced microwave effective medium theory for two-component non-magnetic metamaterials: fundamentals and antenna substrate application. J. Comput. Electron. 16, 369–381 (2017)CrossRefGoogle Scholar
  3. 3.
    VYu. Reshetnyak, I.P. Pinkevych, T.J. Sluckin, A.M. Urbas, D.R. Evans, Effective medium theory for anisotropic media with plasmonic core-shell nanoparticle inclusions. Eur. Phys. J. Plus 133, 373 (2018)CrossRefGoogle Scholar
  4. 4.
    A.V. Tyukhtin, E.G. Doilnitsina, Effective permittivity of a metamaterial from coated wires. J. Phys. D Appl. Phys. 44, 265401 (2011)ADSCrossRefGoogle Scholar
  5. 5.
    O. Rybin, S. Shulga, M. Raza, O. Bagatska, V. Sukhov, Effective electromagnetic Response of the Infinite Chain of Dielectric Coated Circular Metal Cylinders. In: Proceedings of 9th International Conference on Ultrawideband and Ultrashort Impulse Signals (UWBUSIS’2018), September 4–7, Odessa, Ukraine, pp. 214–217 (2018)Google Scholar
  6. 6.
    S.R. Simovski, P.A. Belov, A.V. Atrashchenko, YuS Kivshar, Wire metamaterials: physics and applications. Adv. Mater. 24, 4229–4248 (2012)CrossRefGoogle Scholar
  7. 7.
    I.B. Vendik, O.G. Vendik, M.S. Gashinova, Artificial dielectric medium possessing simultaneously negative permittivity and magnetic permeability. Tech. Phys. Lett. 32, 429–433 (2006)ADSCrossRefGoogle Scholar
  8. 8.
    Cristophe Caloz, Tatsuo Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications. The Engineering Approach, vol. 2 (Wiley, Hoboken, 2006)Google Scholar
  9. 9.
    J.B. Pendry, A.J. Holden, D.J. Robbins, W.J. Stewart, Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microw. Theory Tech. 47, 2075–2084 (1999)ADSCrossRefGoogle Scholar
  10. 10.
    V. Yannopapas, Artificial magnetism and negative refractive index in three-dimensional metamaterials of spherical particles at near-infrared and visible frequencies. Appl. Phys. A Mater. Sci. Process. 87, 259–264 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    I.A. Deryugin, M.A. Sigal, Frequency dependence of the magnetic permeability and dielectric susceptibility of artificial dielectrics between 500 and 35000 Mcs. Tech. Physics 6, 72–77 (1961)Google Scholar
  12. 12.
    Ch. Kittel, Introduction to Solid State Physics, vol. 381, 7th edn. (Wiley, New York, 1996)zbMATHGoogle Scholar
  13. 13.
    E.A. Velichko, A.P. Nikolaenko, Modelling of plane electromagnetic wave scattering by a metallic cylinder. Telecommun. Radio Eng. 69, 1319–1332 (2010)CrossRefGoogle Scholar
  14. 14.
    Tom G. Mackay, Lewin’s homogenization formula revised for nanocomposite materials. J. Nanophoton. 2, 029503 (2008)CrossRefGoogle Scholar
  15. 15.
    S.I. Maslovski, S.A. Tretykov, P.A. Belov, Wire media with negative effective permittivity. Microw. Opt. Technol. Lett. 35, 47–51 (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.V.N. Kharkiv Karazin National UniversityKharkivUkraine

Personalised recommendations