, Volume 52, Issue 15, pp 1919–1924 | Cite as

Predicting the Optical Properties of Matrix Composites Containing Spherical Inclusions with Metal Shells

  • I. V. LavrovEmail author


Individual small particles consisting of an insulating core and a metal shell exhibit more intricate behavior when exposed to electromagnetic radiation than continuous metal particles. A composite medium containing a large number of such particles is therefore bound to have new optical properties. If the inclusions are small relative to the wavelength of electromagnetic radiation, the optical characteristics of an inhomogeneous medium can be estimated from its effective permittivity. On the basis of the generalized effective field approximation, a formula is derived to calculate the effective dielectric characteristics of a matrix composite containing spherical inclusions with shells. The formula can be considered a generalization of the classical Maxwell–Garnett formula for a matrix medium with inhomogeneous inclusions consisting of anisotropic cores and isotropic shells. Using the formula, the frequency dependences of the real and imaginary parts of the effective permittivity in the 0.282–0.855 μm range of wavelengths are calculated for a composite consisting of an α-quartz matrix and spherical nanoinclusions with α-quartz cores and silver shells. The dependences are obtained for different relative volume fractions of cores in the inclusions and of inclusions in the composite. The frequency dependences of the refractive index, the extinction coefficient of the composite, and the transmittance and reflectance of a thin composite film are calculated for the range of wavelengths indicated above. It is shown that inclusions with metal shells in a matrix composite result in an additional plasmon resonance, compared to a composite containing all-metal inclusions. With a matrix composite, the additional plasmon resonance is observed at a wavelength of 0.33–0.34 μm in the ultraviolet range and is much less intense than the principal plasmon resonance. The additional plasmon resonance is responsible for the very low transmittance of a composite film in the ultraviolet region. At a constant volume fraction of inclusions in the composite, an increase in the volume fraction of the cores in them shifts the principal plasmon resonance to longer wavelengths and lowers its intensity.


composite effective permittivity tensor inclusion with a shell plasmon resonance Maxwell–Garnet approximation generalized effective field approximation 



This work was supported by the Russian Foundation for Basic Research, project no. 16-08-00262-a.


  1. 1.
    A. Sihvola, PIER 62, 317 (2006).CrossRefGoogle Scholar
  2. 2.
    L. B. Lerman, Khim. Fiz. Tekhnol. Poverkhn., No. 14, 91 (2008).Google Scholar
  3. 3.
    D. V. Guzatov, A. A. Oraevsky, and A. N. Oraevsky, Quantum Electron. 33, 817 (2003).ADSCrossRefGoogle Scholar
  4. 4.
    J. C. M. Garnett, Philos. Trans. R. Soc. 203, 385 (1904).ADSCrossRefGoogle Scholar
  5. 5.
    V. I. Kolesnikov, V. V. Bardushkin, I. V. Lavrov, A. P. Sychev, and V. B. Yakovlev, Dokl. Phys. 62, 415 (2017).ADSCrossRefGoogle Scholar
  6. 6.
    A. G. Fokin, Tech. Phys. 16, 849 (1971).Google Scholar
  7. 7.
    A. G. Fokin, Phys. Usp. 39, 1009 (1996).ADSCrossRefGoogle Scholar
  8. 8.
    V. V. Yakovlev, V. V. Bardushkin, I. V. Lavrov, and E. N. Yakovleva, Semiconductors 48, 1710 (2014).ADSCrossRefGoogle Scholar
  9. 9.
    V. I. Kolesnikov, V. B. Yakovlev, V. V. Bardushkin, I. V. Lavrov, A. P. Sychev, and E. N. Yakovleva, Dokl. Phys. 58, 379 (2013).ADSCrossRefGoogle Scholar
  10. 10.
    S. R. de Groot and L. G. Sattorp, Foundations of Electrodynamics (North-Holland, Amsterdam, 1972).Google Scholar
  11. 11.
    W. L. Bragg and A. B. Pippard, Acta Crystallogr. 6, 865 (1953).CrossRefGoogle Scholar
  12. 12.
    O. Levy and D. Stroud, Phys. Rev. B 56, 8035 (1997).ADSCrossRefGoogle Scholar
  13. 13.
    S. Giordano, Int. J. Eng. Sci. 43, 1033 (2005).CrossRefGoogle Scholar
  14. 14.
    S. Giordano, J. Electrost. 64, 655 (2006).CrossRefGoogle Scholar
  15. 15.
    E. N. Ivanov and I. V. Lavrov, Oboron. Kompleks Nauch.-Tekh. Progr. Ross., No. 1, 73 (2007) [in Russian].Google Scholar
  16. 16.
    M. I. Zavgorodnyaya, I. V. Lavrov, and A. G. Fokin, Semiconductors 49, 1718 (2015).ADSCrossRefGoogle Scholar
  17. 17.
    Zavgorodnyaya and I. V. Lavrov, Semiconductors 50, 1708 (2016).Google Scholar
  18. 18.
    V. M. Zolotarev, V. N. Morozov, and E. V. Smirnova, Optical Constants of Natural and Technical Media, The Handbook (Khimiya, Leningrad, 1984) [in Russian].Google Scholar
  19. 19.
    E. D. Palik, Handbook of Optical Constants of Solids (Academic, Orlando, 1985).Google Scholar
  20. 20.
    N. G. Khlebtsov, Quantum Electron. 38, 504 (2008).ADSCrossRefGoogle Scholar
  21. 21.
    A. Moroz, J. Opt. Soc. Am. B 28, 1130 (2011).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.National Research University of Electronic Technology (MIET)MoscowRussia

Personalised recommendations