Applied Physics A

, 123:2 | Cite as

Permeability tensor for a metamaterial adjacent to a metal

  • Olga V. Porvatkina
  • Alexey A. Tishchenko
  • Mikhail N. Strikhanov
Part of the following topical collections:
  1. Advanced Metamaterials and Nanophotonics


In our work, we investigate magnetic properties of metamaterial–metal interface with the help of the local field theory combined with the method of images. Proceeding from microscopic description of the substance and calculating its macroscopic properties, for the first time the modified Clausius–Mossotti relation has been obtained for permeability of the metamaterial bordering a metal.


Local Field Radial Distribution Function Magnetic Polarizability Permeability Tensor Local Magnetic Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported by the Ministry of Education and Science of the Russian Federation, the Project 3.1110.2014/K, and by the Competitiveness Growth Program of National Research Nuclear University “MEPhI”.


  1. 1.
    J.B. Pendry, Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    V.M. Shalaev, Optical negative-index metamaterials. Nat. Photon. 1, 41–48 (2007)ADSCrossRefGoogle Scholar
  3. 3.
    O.V. Porvatkina, A.A. Tishchenko, M.I. Ryazanov, M.N. Strikhanov, Local field effects and metamaterials based on colloidal quantum dots. IOP Conf. Ser. 643, 012074 (2015)CrossRefGoogle Scholar
  4. 4.
    M. LoCascio, S.M. Yang, Nanostructured layers, methods of making nanostructured layers, and application thereof. Patent US 8368048 B2 (2013)Google Scholar
  5. 5.
    H. Lirong, S. Rong, Composite structure based on metamaterials and semiconductor low dimension quantum materials and application thereof. Patent CN103135151 A (2013)Google Scholar
  6. 6.
    W. Cai, V.M. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, New York, 2010)CrossRefGoogle Scholar
  7. 7.
    S. Kim, E.F. Kuester, C.L. Holloway, A.D. Scher, J. Baker-Jarvis, Boundary Effects on the Determination of Metamaterial Parameters from Normal Incidence Reflection and Transmission Measurements. IEEE Trans. Antennas Propag. 59(6), 2226–2240 (2011)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    I.V. Lindell, A.H. Sihvola, Electromagnetic boundary and its realization with anisotropic metamaterial. Phys. Rev. E 79, 026604 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    M.I. Ryazanov, The effect of the natural variation in the polarization of a near-surface layer on electromagnetic surface waves. JETP 110, 959–965 (1996)Google Scholar
  10. 10.
    W.L. Mochan, R.G. Barrera, Intrinsic surface-induced optical anisotropics of cubic crystals: local-field effect. Phys. Rev. Lett. 55, 1192–1195 (1985)ADSCrossRefGoogle Scholar
  11. 11.
    O.V. Porvatkina, A.A. Tishchenko, M.N. Strikhanov, Permittivity and permeability of semi-infinite metamaterial. IOP Conf. Ser. 740, 012011 (2016)CrossRefGoogle Scholar
  12. 12.
    R.A. Diaz, W.J. Herrera, J.V. Niño, Electrostatic internal energy using the method of images. Eur. J. Phys. 27, 1391–1398 (2006)CrossRefMATHGoogle Scholar
  13. 13.
    D.J. Griffiths, Introduction to Electrodynamics (Prentice Hall, New Jersey, 1999)Google Scholar
  14. 14.
    M.T. de Oliveira, C.J.B. Pagan, The Method of Images applied to the grounded sphere: the problem of the ground wire. J. Electrostat. 70, 292–299 (2012)CrossRefGoogle Scholar
  15. 15.
    M.I. Ryazanov, A.A. Tishchenko, Clausius–Mossotti-type relation for planar monolayers. JETP 103, 539–545 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    O.V. Porvatkina, A.A. Tishchenko, M.I. Ryazanov, M.N. Strikhanov, Local field effects in anisotropic metamaterials. IOP Conf. Ser. 541, 012024 (2014)CrossRefGoogle Scholar
  17. 17.
    O.V. Porvatkina, A.A. Tishchenko, M.N. Strikhanov, Local field effects in periodic metamaterials. IOP Conf. Ser. 741, 012128 (2016)CrossRefGoogle Scholar
  18. 18.
    M.N. Anokhin, A.A. Tishchenko, M.I. Ryazanov, M.N. Strikhanov, Dielectric permittivity of artificial periodic structure and local field effects. J. Phys: Conf. Ser. 643, 012066 (2015)Google Scholar
  19. 19.
    M.I. Ryazanov, Electrodynamics of Condensed Matter (Nauka, Moscow, 1984). (in Russian) Google Scholar
  20. 20.
    P. Hammond, Electric and magnetic images. Proc. IEE Part C Monogr. 107, 306–313 (1960)MathSciNetCrossRefGoogle Scholar
  21. 21.
    M.I. Ryazanov, M.N. Strikhanov, A.A. Tishchenko, Diffraction radiation from an inhomogeneous dielectric film on the surface of a perfect conductor. JETP 99, 311–319 (2004)ADSCrossRefGoogle Scholar
  22. 22.
    H. Touba, G.A. Mansoori, An analytic expression for the first shell of the radial distribution function. Int. J. Thermophys. 18, 1217–1235 (1997)ADSCrossRefGoogle Scholar
  23. 23.
    A. Sarkar, P. Barat, P. Mukherjee, Molecular dynamics simulation of rapid solidification of aluminum under pressure. Int. J. Mod. Phys. B 22, 2781–2785 (2008)ADSCrossRefGoogle Scholar
  24. 24.
    J.D. Li, Y.G. Li, J.F. Lu, T. Teng, A new analytic formula for molecular radial distribution function in fluid and fluid mixtures. Fluid Phase Equilib. 55, 75–85 (1990)CrossRefGoogle Scholar
  25. 25.
    J.L. Lebowitz, Exact solution of generalized Percus–Yevick equation for a mixture of hard spheres. Phys. Rev. 133, 895–899 (1964)ADSMathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    A.K. Soper, Joint structure refinement of x-ray and neutron diffraction data on disordered materials: application to liquid water. J. Phys.: Condens. Matter 19, 335206 (2007)Google Scholar
  27. 27.
    D.E. Aspnes, Local-field effects and effective-medium theory: a microscopic perspective. Am. J. Phys. 50, 704–709 (1982)ADSCrossRefGoogle Scholar
  28. 28.
    M.N. Anokhin, A.A. Tishchenko, M.I. Ryazanov, M.N. Strikhanov, Permittivity of anisotropic dielectric near surface with local field effects. J. Phys: Conf. Ser. 541, 012023 (2014)Google Scholar
  29. 29.
    M.I. Ryazanov, M.N. Strikhanov, A.A. Tishchenko, Local field effect in diffraction radiation from a periodical system of dielectric spheres. Nucl. Instrum. Methods B 266, 3811–3815 (2008)ADSCrossRefGoogle Scholar
  30. 30.
    I.D. Morokhov, V.I. Petinov, L.I. Trusov, V.F. Petrunin, Structure and properties of fine metallic particles. Sov. Phys. Usp. 24, 295–317 (1981)ADSCrossRefGoogle Scholar
  31. 31.
    J. Kästel, M. Fleischhauer, Local-field effects in magnetodielectric media: negative refraction and absorption reduction. Phys. Rev. A 76, 062509 (2007)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.National Research Nuclear University MEPhIMoscowRussia

Personalised recommendations