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Homogenization of Maxwell Equations—Macroscopic and Microscopic Approaches

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Optical Metamaterials: Qualitative Models

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 211))

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Abstract

It is assumed that system (2.1) is strictly valid without any approximations. Actually, system (2.1) can be elaborated in the framework of the minimum action approach; nevertheless, one should remember that the minimum action principle does not give an unambiguous form of the MEs (2.1), but instead gives a set of different forms which satisfy the requirement of relativistic invariance. The “right” form can be chosen based on the evident requirement of correspondence of the results of the final system of equations to the observed physical effects.

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References

  1. L.D. Landau, E.L. Lifshitz, Electrodynamics of Continuous Media, 2nd edn. (Pergamon Press, New York, 1960) (Chapter IX)

    Google Scholar 

  2. V. Dubovik, S. Shabanov, in Essays on the Formal Aspects of Electromagnetic Theory, ed. by A. Lakhakia. The Gauge Invariance, Toroid Order Parameters and Radiation in Electromagnetic Theory, vol. 399 (World Scientific, Singapore, New Jersey, London, Hong-Kong, 1993)

    Google Scholar 

  3. J. Schwinger, L.L. De-Raad, K. Milton, W. Tsai, Classical Electrodynamics (Perseus Books, Reading, MA, 1998)

    Google Scholar 

  4. P. Mazur, B. Nijboer, On the statistical mechanics of matter in an electromagnetic field. I. Physica XIX, 971 (1953)

    Article  Google Scholar 

  5. G. Rusakoff, A derivation of the macroscopic Maxwell equations. Am. J. Phys. 38(10), 1188 (1970)

    Article  Google Scholar 

  6. A. Maradudin, D.L. Mills, Phys. Rev. B 7, 2787 (1973)

    Article  CAS  Google Scholar 

  7. J.D. Jackson, Classical Electrodynamics, 3rd edn. (Wiley, New York, 1999)

    Google Scholar 

  8. S. Maslovsky, Electrodynamics of composite materials with pronounced spatial dispersion. Ph.D. thesis (St. Petersburg Polytechnic University, Russia, 2004)

    Google Scholar 

  9. A. Vinogradov, A. Aivazyan, Scaling theory of homogenization of the Maxwell equations. Phys. Rev. E 60, 987 (1999)

    Article  CAS  Google Scholar 

  10. C. Simovski, Weak spatial dispersion in composite media. Polytechnika (St. Petersburg, 2003) (in Russian)

    Google Scholar 

  11. Y. Svirko, N. Zheludev, M. Osipov, Layered chiral metallic microstructures with inductive coupling. APL 78, 498 (2001)

    CAS  Google Scholar 

  12. N. Zheludev, The road ahead for metamaterials. Science 328, 582 (2010)

    Article  CAS  Google Scholar 

  13. N. Papasimakis, V. Fedotov, K. Marinov, N. Zheludev, Gyrotropy of a metamolecule: wire on a torus. PRL 103, 093901 (2009)

    Article  CAS  Google Scholar 

  14. A.N. Grigorenko, A.K. Geim, H.F. Gleeson, Y. Zhang, A.A. Firsov, I.Y. Khrushchev, J. Petrovic, Nanofabricated media with negative permeability at visible frequencies. Nature 438, 335–338 (2005)

    Article  CAS  Google Scholar 

  15. V. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. Sarychev, V. Drachev, A. Kildishev, Negative index of refraction in optical metamaterials. Opt. Lett. 30, 3356 (2005)

    Article  Google Scholar 

  16. A. Vinogradov, Electrodynamics of Compound Media (Scientific and Educational Literature Publisher, Russian Federation, 2001). ISBN 5-8360-0283-5 (in Russian)

    Google Scholar 

  17. C. Simovski, Material parameters of metamaterials (a review). Opt. Spectrosc. 107, 726 (2009)

    Article  CAS  Google Scholar 

  18. R. Clausius, Mechanische Warmetheorie, vol. 2, 2nd edn. (Braunschweig, 1878), p. 62

    Google Scholar 

  19. O. Mossotti, Mem. Soc. Sci. Modena 14, 49 (1850)

    Google Scholar 

  20. H. Lorentz, Proc. Acad. Sci. Amsterdam 13, 92 (1910)

    Google Scholar 

  21. P. Ewald, Ann. Phys. 64, 2943 (1921)

    Google Scholar 

  22. D. Bruggeman, Ann. Phys. Lpz. 24, 636 (1935)

    Article  CAS  Google Scholar 

  23. C. Simovski, Radiotekh. Elecktron. 52, 1031 (2007)

    Google Scholar 

  24. G. Shvets, Photonic approach to make a surface wave accelerator. AIP Conf. Proc. 647, 371 (2002)

    Article  CAS  Google Scholar 

  25. P. Belov, R. Marques, M. Silveirinha, I. Nefedov, C. Simovski, S. Trtyakov, Strong spatial dispersion in wire media in the very long wavelength limit. Phys. Rev. B 70, 113103 (2003)

    Article  Google Scholar 

  26. M. Silveirinha, Nonlocal homogenization model for a periodic array of epsilon-negative rods. Phys. Rev. E 73, 046612 (2006)

    Article  Google Scholar 

  27. 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)

    Article  CAS  Google Scholar 

  28. C. Simovski, On electromagnetic characterization and homogenization of nanostructured metamaterials. J. Opt. 13, 013001 (2011)

    Article  Google Scholar 

  29. A. Sarychev, V. Shalaev, Electrodynamics of Metamaterials (World Scientific, Singapore, 2007)

    Book  Google Scholar 

  30. D. Smith, D. Shurig, PRL 90, 077405 (2003)

    Article  CAS  Google Scholar 

  31. P. Belov, C. Simovski, Phys. Rev. E 72, 026615 (2005)

    Article  Google Scholar 

  32. J.D. Joannopoulos, R.D. Meade, J.N. Winn, Photonic Crystals: Molding the Flow of Light (1995). ISBN-13: 978-0-691-03744-8

    Google Scholar 

  33. C. Rockstuhl, T. Paul, F. Lederer, T. Pertsch, T. Zentgraf, T. Meyrath, H. Giessen, Phys. Rev. B 77, 035126 (2008)

    Article  Google Scholar 

  34. M. Born, K. Huang, Dynamic Theory of Crystal Lattices (Oxford University Press, Oxford, 1954)

    Google Scholar 

  35. M. Silveirinha, Time domain homogenization of metamaterials. Phys. Rev. B 77, 035126 (2011)

    Google Scholar 

  36. C. Menzel, T. Paul, C. Rockstuhl, T. Pertsch, S. Tretyakov, F. Lederer, Validity of effective material parameters for optical fishnet metamaterials. Phys. Rev. B 81, 035320 (2010)

    Article  Google Scholar 

  37. M. Bredov, V. Rumyantcev, I. Toptygin, Classical Electrodynamics (Nauka, 1985) (in Russian)

    Google Scholar 

  38. I.B. Zeldovich, Electromagnetic interaction with parity violation. JETP 33, 1531 (1957)

    CAS  Google Scholar 

  39. L. Mandelshtam, Full collection of publications. Publ. Acad. Sci. USSR 1, 162 (1957) (in Russian)

    Google Scholar 

  40. T. Kaelberer, V.A. Fedotov, N. Papasimakis, D.P. Tsai, N.I. Zheludev, Science 330, 1510 (2010)

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Center for Photonics and Quantum Materials, Skolkovo Institute of Science and Technology, Moscow, Russia

    Arkadi Chipouline & Franko Küppers

  2. Institute for Microwave Engineering and Photonics, Darmstadt University of Technology, Darmstadt, Germany

    Arkadi Chipouline & Franko Küppers

Authors
  1. Arkadi Chipouline
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  2. Franko Küppers
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Correspondence to Arkadi Chipouline .

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Chipouline, A., Küppers, F. (2018). Homogenization of Maxwell Equations—Macroscopic and Microscopic Approaches. In: Optical Metamaterials: Qualitative Models. Springer Series in Optical Sciences, vol 211. Springer, Cham. https://doi.org/10.1007/978-3-319-77520-3_2

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