Phenomenological Versus Multipole Models

  • Arkadi ChipoulineEmail author
  • Franko Küppers
Part of the Springer Series in Optical Sciences book series (SSOS, volume 211)


In order to further develop the homogenization procedure, we should find an analytical form for the functions \( \vec {P} \) and \( \vec {M} \) in case of “C” representation, \( \vec {P} \) in case of “L&L” representation, or \( \vec {M} \) in case of “T” representation.


  1. 1.
    A. Chipouline, C. Simovski, S. Tretyakov, Basics of averaging of the Maxwell equations for bulk materials. Metamaterials 6, 77 (2012)CrossRefGoogle Scholar
  2. 2.
    A. Miroshnichenko, A. Evlyukhin, Y.F. Yu, R. Bakker, A. Chipouline, A. Kuznetsov, B. Luk’yanchuk, B. Chichkov, Y. Kivshar, Observation of an anapole with dielectric nanoparticles. Nat. Commun. 6, 8069 (2015)CrossRefGoogle Scholar
  3. 3.
    A. Serdyukov, I. Semchenko, S. Tretyakov, A. Sihvola, Electromagnetics of Bi-Anisotropic Materials—Theory and Applications (Gordon and Breach, Amsterdam, 2001)Google Scholar
  4. 4.
    S. Pekar, Crystal Optics and Additional Light Waves (Naukova Dumka, Kiev, 1982)Google Scholar
  5. 5.
    V. Agranovich, V. Ginzburg, Kristallooptika s Uchetom Prostranstvennoi Dispersii i Teoriya Eksitonov (Crystal Optics with Spatial Dispersion, and Excitons) (Nauka, Moscow, 1965) [Translated into English (Springer, Berlin, 1984)]Google Scholar
  6. 6.
    J.D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 1999)Google Scholar
  7. 7.
    L.D. Landau, E.L. Lifshitz, Electrodynamics of Continuous Media, 2nd edn. (Pergamon Press, New York, 1960) (Chapter IX)Google Scholar
  8. 8.
    A. Vinogradov, Electrodynamics of Compound Media (Scientific and Educational Literature Publisher, Russian Federation, 2001). ISBN 5-8360-0283-5 (in Russian)Google Scholar
  9. 9.
    E. Turov, Material Equations of Electrodynamics (Nauka, 1983) (in Russian)Google Scholar
  10. 10.
    A. Vinogradov, A. Aivazyan, Scaling theory of homogenization of the Maxwell equations. Phys. Rev. E 60, 987 (1999)CrossRefGoogle Scholar
  11. 11.
    G. Bosi, F. Girouard, V. Truong, J. Appl. Phys. 53, 648 (1982)CrossRefGoogle Scholar
  12. 12.
    E. Graham, R. Raab, JOSA 6, 1239 (1996)CrossRefGoogle Scholar
  13. 13.
    E. Raab, J. Cloete, JEWA 8, 1073 (1994)Google Scholar
  14. 14.
    C. Simovski, S. Tretyakov, On effective electromagnetic parameters of artificial nanostructured magnetic materials. Photonics Nanostruct. Fundam. Appl. 8, 254 (2010)CrossRefGoogle Scholar
  15. 15.
    C. Simovski, Weak spatial dispersion in composite media Polytechnika (St. Petersburg, 2003) (in Russian)Google Scholar
  16. 16.
    S. Tretyakov, A. Sihvola, A. Sochava, C. Simovski, Magnetoelectric interactions in bi-anisotropic media. J. Electromagn. Wave Appl. 12, 481 (1998)CrossRefGoogle Scholar
  17. 17.
    C. Kriegler, M. Rill, S. Linden, M. Wegener, Bianisotropic photonic metamaterials. IEEE J. Sel. Top. Quantum Electron. 16, 367–375 (2010)CrossRefGoogle Scholar
  18. 18.
    I. Lindell, A. Sihvola, S. Tretyakov, A. Vitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, Boston; London, 1994)Google Scholar
  19. 19.
    B. Tellegen, The gyrator: a newelectric network element. Philips Res. Rep. 3, 81 (1948)Google Scholar
  20. 20.
    J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, T. Pertsch, Multipole approach to metamaterials. Phys. Rev. B 78, 043811 (2008)CrossRefGoogle Scholar
  21. 21.
    P. Mazur, B. Nijboer, On the statistical mechanics of matter in an electromagnetic field. I. Physica XIX, 971 (1953)CrossRefGoogle Scholar
  22. 22.
    G. Rusakoff, A derivation of the macroscopic Maxwell equations. Am. J. Phys. 38(10), 1188 (1970)CrossRefGoogle Scholar
  23. 23.
    R. Raab, O. De Lange, Multipole Theory in Electromagnetism (Clarendon, Oxford, 2005)Google Scholar
  24. 24.
    T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, P.A. Wolff, Nature (London) 391, 667 (1998)CrossRefGoogle Scholar
  25. 25.
    E. Pshenay-Severin, U. Hübner, C. Menzel, C. Helgert, A. Chipouline, C. Rockstuhl, A. Tünnermann, F. Lederer, T. Pertsch, Double-element metamaterial with negative index at near-infrared wavelengths. Opt. Lett. 34, 1678 (2009)CrossRefGoogle Scholar
  26. 26.
    A. Chipouline, J. Petschulat, A. Tuennermann, T. Pertsch, C. Menzel, C. Rockstuhl, F. Lederer, Multipole approach in electrodynamics of metamaterials. Appl. Phys. A 103, 899–904 (2011)CrossRefGoogle Scholar
  27. 27.
    J. Petschulat, A. Chipouline, A. Tünnermann, T. Pertsch, C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, Simple and versatile analytical approach for planar metamaterials. Phys. Rev. B 82, 075102 (2010)CrossRefGoogle Scholar
  28. 28.
    E. Pshenay-Severin, A. Chipouline, J. Petschulat, U. Huebner, A. Tuennermann, T. Pertsch, Optical properties of metamaterials based on asymmetric double-wire structures. Opt. Express 19, 6269 (2011)CrossRefGoogle Scholar
  29. 29.
    J. Petschulat, A. Chipouline, A. Tüunnermann, T. Pertsch, C. Menzel, C. Rockstuhl, F. Lederer, Phys. Rev. A 80, 063828 (2009)CrossRefGoogle Scholar
  30. 30.
    L.D. Landau, E.L. Lifshitz, Field Theory, 2nd edn. (Pergamon Press, New York, 1960)Google Scholar
  31. 31.
    V. Dubovik, V. Tugushev, Toroid moments in electrodynamics and solid-state physics. Phys. Rep. 187(4), 145 (1990)CrossRefGoogle Scholar
  32. 32.
    P. Grahn, A. Shevchenko, M. Kaivola, Electromagnetic multipole theory for optical nanomaterials. New J. Phys. 14, 093033 (2012)CrossRefGoogle Scholar
  33. 33.
    I.B. Zeldovich, Electromagnetic interaction with parity violation. JETP 33, 1531 (1957)Google Scholar
  34. 34.
    G. Afanasiev, Simplest source of electromagnetic fields as a tool for testing the reciprocity-like theorems. J. Phys. D: Appl. Phys. 34, 539 (2001)CrossRefGoogle Scholar
  35. 35.
    G. Afanasiev, Vector solutions of the Laplace equation and the influence of helicity on Aharonov-Bohm scattering. J. Phys. A: Math. Gen. 27, 2143 (1994)CrossRefGoogle Scholar
  36. 36.
    G.N. Afanasiev, Y.P. Stepanovsky, J. Phys. A: Math. Gen. 8, 4565 (1995)CrossRefGoogle Scholar
  37. 37.
    V. Dubovik, L. Tosunyan, V. Tugushev, Axial toroidal moments in electrodynamics and solid-state physics. Zh. Eksp. Teor. Fiz. 90, 590 (1986)Google Scholar
  38. 38.
    T. Kaelberer, V.A. Fedotov, N. Papasimakis, D.P. Tsai, N.I. Zheludev, Science 330, 1510 (2010)CrossRefGoogle Scholar
  39. 39.
    K. Marinov, A.D. Boardman, V.A. Fedotov, N. Zheludev, Toroidal metamaterial. New J. Phys. 9, 324 (2007)CrossRefGoogle Scholar
  40. 40.
    V.A. Fedotov, A. Rogacheva, V. Savinov, D. Tsai, N.I. Zheludev, Resonant transparency and non-trivial non-radiating excitations in toroidal metamaterials. Sci. Rep. 3, 2967 (2013)CrossRefGoogle Scholar
  41. 41.
    B. Ögüt, N. Talebi, R. Vogelgesang, W. Sigle, P.A. van Aken, Toroidal plasmonic eigenmodes in oligomer nanocavities for the visible. Nano Lett. 12, 5239 (2012)CrossRefGoogle Scholar
  42. 42.
    A.M. Zagoskin, A. Chipouline, E. Il’ichev, J.R. Johansson, F. Nori, Toroidal qubits: naturally decoupled quiet artificial atoms. Sci. Rep. 5, 16934 (2015). Scholar
  43. 43.
    V. Dubovik, M.A. Martsenyuk, B. Saha, Material equations for electromagnetism with toroidal polarizations. Phys. Rev. E 61(6), 7087 (2000)CrossRefGoogle Scholar
  44. 44.
    D. Singleton, Am. J. Phys. 64, 452 (1996)CrossRefGoogle Scholar
  45. 45.
    C. Menzel, C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, Retrieving effective parameters for metamaterials at oblique incidence. Phys. Rev. B 77, 195328 (2008)CrossRefGoogle Scholar
  46. 46.
    C. Simovski, On electromagnetic characterization and homogenization of nanostructured metamaterials. J. Opt. 13, 013001 (2011)CrossRefGoogle Scholar
  47. 47.
    C. Menzel, R. Alaee, E. Pshenay-Severin, C. Helgert, A. Chipouline, C. Rockstuhl, T. Pertsch, F. Lederer, Genuine effectively biaxial left-handed metamaterials due to extreme coupling. Opt. Lett. 37, 596 (2012)CrossRefGoogle Scholar
  48. 48.
    A. Vinogradov, A. Ignatov, A. Merzlikin, S. Tretyakov, C. Simovski, Additional effective medium parameters for composite materials (excess surface current). Opt. Express 19, 6699 (2011)CrossRefGoogle Scholar
  49. 49.
    D. Morits, C. Simovski, Electromagnetic characterization of planar and bulk metamaterials: a theoretical study. Phys. Rev. B 82, 165114 (2010)CrossRefGoogle Scholar
  50. 50.
    M. Albooyeh, D. Morits, C. Simovski, Electromagnetic characterization of substrated metasurfaces. Metamaterials 5, 178 (2011)CrossRefGoogle Scholar
  51. 51.
    W.B. Weir, Proc. IEEE 62, 33 (1974)CrossRefGoogle Scholar
  52. 52.
    A.M. Nicholson, G.F. Ross, IEEE Trans. Instrum. Meas. IM-19, 377 (1970)CrossRefGoogle Scholar
  53. 53.
    D. Smith, S. Schultz, P. Markos, C. Soukoulis, Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients. Phys. Rev. B 65, 195104 (2002)CrossRefGoogle Scholar
  54. 54.
    D.R. Smith, D.C. Vier, T. Koschny, C.M. Soukoulis, Electromagnetic parameter retrieval from inhomogeneous metamaterials. Phys. Rev. E 71, 036617 (2005)CrossRefGoogle Scholar
  55. 55.
    M. Silveirinha, Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters. Phys. Rev. B 75, 115104 (2007)CrossRefGoogle Scholar
  56. 56.
    X. Chen, B.-I. Wu, J. Kong, T. Grzegorczyk, Retrieval of the effective constitutive parameters of bianisotropic metamaterials. Phys. Rev. E 71, 046610 (2005)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Microwave Engineering and PhotonicsTechnical University of DarmstadtDarmstadtGermany
  2. 2.Department of Electrical Engineering and Information TechnologiesTechnical University of DarmstadtDarmstadtGermany

Personalised recommendations