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Material parameters of metamaterials (a Review)

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Abstract

A theory of the homogenization of a certain class of metamaterials is stated. These metamaterials are volume lattices of electric and magnetic dipoles that are resonant with frequencies that are considerably lower than that of the first Bragg resonance of the lattice. It was shown that, for plates of a metamaterial, which are described by bulk material parameters, transition layers play an important role, and the known Drude notion of transition layers is significantly revised. The paper also discusses a more widespread method of determining the material parameters of metamaterials based on the extraction of the refractive index and the characteristic impedance from the scattering matrix of the plate of the metamaterial. The physical meaning of the material parameters obtained in this way is clarified, and the concept of Bloch lattices related to it is discussed. It is shown that the bulk material parameters and the parameters of transition layers can also be extracted from components of the scattering matrix of plates.

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References

  1. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 8: Electrodynamics of Continuous Media, 2nd ed. (Nauka, Moscow, 1982; Pergamon, Oxford, 1984).

    Google Scholar 

  2. V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, 2nd ed. (Nauka, Moscow, 1979; Springer-Verlag, New York, 1984).

    Google Scholar 

  3. Artificial Materials Handbook, Vol. 1: Theory and Phenomena of Artificial Materials and Vol. 2: Applications of Artificial Materials, Ed. by F. Capolino (CRC Pr I Llc Publishers, New York, 2009).

    Google Scholar 

  4. A. K. Sarychev and V. A. Shalaev, Electrodynamics of Metamaterials (World Sci., Singapore, 2007).

    MATH  Google Scholar 

  5. G. Eleftheriades and K. G. Balmain, Negative-Refraction Metamaterials: Fundamental Principles and Applications (Wiley, New York, 2006).

    Google Scholar 

  6. C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications (Wiley, New York, 2006).

    Google Scholar 

  7. M. Born and K. Huang, Dynamical Theory of Crystal Lattices (Clarendon Press, Oxford, 1954; Inostrannaya Literatura, Moscow, 1958).

    MATH  Google Scholar 

  8. J. C. Slater, Insulators, Semiconductors, and Metals (McGraw-Hill, New York, 1967; Mir, Moscow, 1969).

    Google Scholar 

  9. A. P. Vinogradov, Electrodynamics of Composite Materials (Izd-vo URSS, Moscow, 2001) [in Russian].

    Google Scholar 

  10. S. L. Adler, Phys. Rev. 126, 413 (1962).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1969; Nauka, Moscow 1973).

    Google Scholar 

  12. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1998).

    Google Scholar 

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

    Google Scholar 

  14. S. M. Rytov, Zh. éksp. Teor. Fiz. 29, 605 (1955).

    Google Scholar 

  15. M. R. Phipott, J. Chem. Phys. 65, 3599 (1976).

    Article  ADS  Google Scholar 

  16. A. P. Vinogradov, A. V. Dorofeenko, and S. Zukhdi, Usp. Fiz. Nauk 178, 510 (2008).

    Google Scholar 

  17. J. Sipe and J. V. Kranendonk, Phys. Rev. A 9, 1806 (1974).

    Article  ADS  Google Scholar 

  18. X. Chen, T. Grzegorczyk, B.-E. Wu, et al., Phys. Rev. E 70, 16608 (2004).

    Article  ADS  Google Scholar 

  19. C. R. Simovski and S. A. Tretyakov, Phys. Rev. B 75, 195111 (2007).

    Article  ADS  Google Scholar 

  20. C. R. Simovski, Metamaterials 1, 62 (2007).

    Article  ADS  Google Scholar 

  21. C. R. Simovski, Metamaterials 2, 342 (2008).

    Article  Google Scholar 

  22. G. S. Agarwal, D. N. Pattanayak, and E. Wolf, Phys. Rev. B 10, 1447 (1974).

    Article  MathSciNet  ADS  Google Scholar 

  23. K. Sakoda, Optical Properties of Photonic Crystals (Springer, Heidelberg, 2005).

    Google Scholar 

  24. N. Nilius, N. Ernst, and H.-J. Freund, Phys. Rev. Lett. 84, 3994 (2000).

    Article  ADS  Google Scholar 

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

    Google Scholar 

  26. P. Ewald, ZS f. Kristallen 54, 129 (1921).

    Google Scholar 

  27. D. V. Sivukhin, Zh. Éksp. Teor. Fiz. 26, 269 (1956).

    Google Scholar 

  28. D. V. Sivukhin, Zh. Éksp. Teor. Fiz. 18, 976 (1948).

    Google Scholar 

  29. D. V. Sivukhin, Zh. Éksp. Teor. Fiz. 21, 267 (1951).

    Google Scholar 

  30. G. Mahan and G. Obermair, Phys. Rev. 183, 834 (1969).

    Article  ADS  Google Scholar 

  31. I. E. Tamm, The Principles of Electricity Theory, 10th ed. (Nauka, Moscow, 1989) [in Russian].

    Google Scholar 

  32. F. Bloch, Z. Phys. 52, 555 (1929).

    Article  ADS  Google Scholar 

  33. G. Korn and T. Korn, Mathematical Handbook for Scientists and Engineers, 2nd ed. (McGraw-Hill, New York, 1968; Nauka, Moscow, 1978).

    Google Scholar 

  34. D. R. Smith and D. Shurig, Phys. Rev. Lett. 90, 77405 (2003).

    Article  ADS  Google Scholar 

  35. P. A. Belov and C. R. Simovski, Phys. Rev. E 72, 26615 (2005).

    Article  ADS  Google Scholar 

  36. J. B. Pendry, A. J. Holden, D. J. Robins, and W. J. Stewart, IEEE Trans. MTT 47, 2075 (1999).

    Article  Google Scholar 

  37. J. B. Pendry and D. R. Smith, Phys. Today 57, 37 (2004).

    Article  Google Scholar 

  38. B. Sauviac, C. Simovski, and S. Tretyakov, Electromagnetics 24, 317 (2004).

    Article  Google Scholar 

  39. R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).

    Article  ADS  Google Scholar 

  40. C. Simovski, P. A. Belov, and S. He, IEEE Trans. Antennas Propag. 51, 2582 (2003).

    Article  ADS  Google Scholar 

  41. C. Simovski and B. Sauviac, Phys. Rev. E 70, 46607 (2004).

    Article  ADS  Google Scholar 

  42. H. A. Lorentz, The Theory of Electrons and Its Applications to the Phenomena of Light and Radiant Heat (Dover Publications, New York, 1952).

    Google Scholar 

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

    Google Scholar 

  44. I. I. Sobel’man, Usp. Fiz. Nauk 172, 85 (2002).

    Article  Google Scholar 

  45. F. Reiche, Ann. Phys. 70, 7 (1916).

    Google Scholar 

  46. H. Faxen, Z. Phys. 2, 218 (1920).

    Article  ADS  Google Scholar 

  47. G. Darwin, Trans. Cambridge Soc. 23, 137 (1924).

    Google Scholar 

  48. B. A. Sotskiĭ and F. I. Fedorov, Opt. Spektrosk. 4(2), 365 (1958).

    Google Scholar 

  49. K. R. Simovskiĭ, Weak Spatial Dispersion in Composite Media (Politekhnika, St. Petersburg, 2003) [in Russian].

    Google Scholar 

  50. K. R. Simovskiĭ, Radiotekh. Elektron. (Moscow) 52, 1031 (2007).

    Google Scholar 

  51. P. Drude, Wied. Ann. 43, 146 (1891).

    Google Scholar 

  52. C. Maclaurin, Proc. Roy. Soc. (London), Ser. A 76, 149 (1905).

    Google Scholar 

  53. P. K. L. Drude, Theory of Optics (Longmans, London, 1902; ONTI, Moscow, 1935).

    Google Scholar 

  54. C. Strachan, Proc. Camb. Phil. Soc. 29, 116 (1933).

    Article  Google Scholar 

  55. D. W. Rayleigh, Phil. Mag. 33, 1 (1892).

    Google Scholar 

  56. C. V. Raman and L. A. Ramdas, Philos. Mag. 3, 220 (1927).

    Google Scholar 

  57. C. V. Raman and L. A. Ramdas, Proc. Roy. Soc. (London), Ser. A 108, 561 (1925).

    Article  ADS  Google Scholar 

  58. O. S. Heavens, Optical Properties of Thin Solid Films (Dover Publications, New York, 1991).

    Google Scholar 

  59. I. E. Tamm, Z. Phys. 76, 849 (1932).

    Article  ADS  Google Scholar 

  60. W. Shockley, Phys. Rev. 56, 317 (1939).

    Article  MATH  ADS  Google Scholar 

  61. C. R. Simovski, S. He, and M. Popov, Phys. Rev. B 62, 13718 (2000).

    Article  ADS  Google Scholar 

  62. C. R. Simovski and B. Sauviac, Eur. Phys. J. 17, 11 (2002).

    Google Scholar 

  63. A. N. Serdyukov, I. V. Semchenko, S. A. Tretyakov, and A. Sihvola, Electromagnetics of Bianisotropic Materials: Theory and Applications (Gordon and Breach Publishers, Amsterdam, 2003).

    Google Scholar 

  64. D. P. Makhnovskiy, L. V. Panina, and D. J. Mapps, Phys. Rev. B 64, 134205 (2002).

    Article  ADS  Google Scholar 

  65. I. El-Kady, M. M. Sigalas, R. Biswas, et al., Phys. Rev. B 62, 15299 (2000).

    Article  ADS  Google Scholar 

  66. D. R. Smith, S. Schultz, P. Markos, and C. Soukoulis, Phys. Rev. B 65, 195104 (2002).

    Article  ADS  Google Scholar 

  67. S. O’Brien and J. B. Pendry, J. Phys.: Condens. Matter 14, 6383 (2002).

    Article  ADS  Google Scholar 

  68. S. O’Brien and J. B. Pendry, J. Phys.: Condens. Matter 14, 4035 (2002).

    Article  ADS  Google Scholar 

  69. D. R. Smith, P. Kolinko, and D. Schuring, J. Opt. Soc. Am. B 21, 1032 (2004).

    Article  ADS  Google Scholar 

  70. K. C. Huang, M. L. Povinelli, and J. D. Joannopoulos, Appl. Phys. Lett. 85, 543 (2004).

    Article  ADS  Google Scholar 

  71. S. O’Brien, Artificial Magnetic Structures, PhD Thesis (Imperial College of Science, Technology and Medicine, 2002).

  72. T. Koschny, L. Zhang, and C. M. Soukoulis, Phys. Rev. B 71, 121103 (2005).

    Article  ADS  Google Scholar 

  73. T. Koschny, P. Markos, D. R. Smith, and C. M. Souloulis, Phys. Rev. E 68, 65602 (2003).

    Article  ADS  Google Scholar 

  74. N. Katsarakis, G. Konstantinidis, and A. Kostopoulos, Opt. Lett. 30, 1348 (2005).

    Article  ADS  Google Scholar 

  75. S. O’Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, Phys. Rev. B 69, 241101 (2004).

    Article  ADS  Google Scholar 

  76. N. Katsarakis, T. Koschny, M. Kafesaki, et al., Phys. Rev. B 70, 201101 (2004).

    Article  ADS  Google Scholar 

  77. T. Koschny, P. Markos, E. N. Economou, et al., Phys. Rev. B 71, 245105 (2005).

    Article  ADS  Google Scholar 

  78. G. Dolling, M. Wegener, C. Enkrich, et al., Opt. Lett. 30, 3198 (2005).

    Article  ADS  Google Scholar 

  79. N. Katsarakis, T. Koschny, M. Kafesaki, et al., Appl. Phys. Lett. 84, 2943 (2004).

    Article  ADS  Google Scholar 

  80. T. J. Yen, W. J. Padilla, N. Fang, et al., Science 303, 1494 (2004).

    Article  ADS  Google Scholar 

  81. P. A. Belov and C. R. Simovski, Phys. Rev. B 73, 45102 (2006).

    Article  ADS  Google Scholar 

  82. D. R. Smith and J. B. Pendry, J. Opt. Soc. Am. B 23, 391 (2006).

    Article  ADS  Google Scholar 

  83. A. M. Nicolson and G. F. Ross, IEEE Trans. Instrum. Meas. 17, 395 (1968).

    Article  Google Scholar 

  84. W. W. Weir, Proc. IEEE 62, 33 (1974).

    Article  Google Scholar 

  85. L. P. Ligthart, IEEE Trans. Microw. Theory Tech. 31, 249 (1983).

    Article  ADS  Google Scholar 

  86. J. Baker-Jarvis, E. J. Vanzura, and W. A. Kissick, IEEE Trans. Microw. Theory Tech. 38, 1096 (1990).

    Article  Google Scholar 

  87. S. A. Tretyakov, Analytical Modelling in Applied Electromagnetics (Artech House, Norwood, 2003).

    Google Scholar 

  88. G. Dolling, C. Enkrich, and M. Wegener, Science 312, 892 (2006).

    Article  ADS  Google Scholar 

  89. S. L. Prosvirnin and S. Zouhdi, J. Electromagn. Waves Appl. 20, 583 (2006).

    Article  Google Scholar 

  90. U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, Opt. Express 30, 7872 (2006).

    Article  ADS  Google Scholar 

  91. G. Dolling, M. Wegener, and S. Linden, Opt. Lett. 32, 551 (2007).

    Article  ADS  Google Scholar 

  92. V. M. Shalaev, W. Cai, U. K. Chettiar, et al., Opt. Lett. 30, 3356 (2005).

    Article  ADS  Google Scholar 

  93. G. Dolling, C. Enkrich, M. Wegener, et al., Opt. Lett. 31, 1800 (2006).

    Article  ADS  Google Scholar 

  94. G. Dolling, M. Wegener, C. Soukoulis, and S. Linden, Opt. Lett. 32, 53 (2007).

    Article  ADS  Google Scholar 

  95. J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. St. Petersburg State University of Information Technologies, Mechanics, and Optics, St. Petersburg, 197101, Russia

    C. R. Simovski

  2. Helsinki University of Technology, 02015, TKK, Helsinki, Finland

    C. R. Simovski

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  1. C. R. Simovski
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Correspondence to C. R. Simovski.

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Original Russian Text © C.R. Simovski, 2009, published in Optika i Spektroskopiya, 2009, Vol. 107, No. 5, pp. 766–793.

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Simovski, C.R. Material parameters of metamaterials (a Review). Opt. Spectrosc. 107, 726–753 (2009). https://doi.org/10.1134/S0030400X09110101

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