Isolated small particles with a dielectric nucleus and metal shell are characterized by more complex behavior under effect of electromagnetic radiation upon them, than solid metal particles. Therefore, the composite medium, containing a big number of such particles, will have more interesting optical properties compared to a composite with solid metal inclusions. On condition of small sizes of the inclusions compared to the electromagnetic radiation wave length the optical characteristics of non-homogeneous medium can be estimated using the effective dielectric permeability of the given medium. Based on the generalized approach of the effective field the formula for calculating the effective dielectric characteristics of the matrix composite with the spherical inclusions with the shell has been derived. The given formula can be considered as a generalization of the classical Maxwell-Garnet formula for a case of the matrix medium with non-homogeneous spherical inclusions, consisting of an anisotropic nucleus and an isotropic shell. Using this formula in the range of wave length 0.282-0.855 μm the frequency dependencies of real and imaginary parts of effective dielectric permeability of the composite, consisting of alpha-quartz as a matrix and spherical nanoinclusions with a nucleus from alpha-quartz and silver shell, at various relative volume parts in the composite have been calculated. In the indicated range of the wave lengths, also, the frequency dependencies of the refraction coefficients and extinction of the given composite and the transmission and refraction coefficients of the composite film have been calculated. It has been shown that presence in the composite of the inclusions with a metal shell results in appearance of an additional plasmon resonance compared to the composite with the whole metal inclusions. For the given composite an additional plasmon resonance becomes apparent in the ultra-violet region at the wave length of 0.33-0.34 μm and from the point of intensity is much weaker than the main plasmon resonance. The availability of an additional plasmon resonance leads to appearance of a narrow band of very weak transmission of the composite film in the ultra-violet region. At the fixed volume part of inclusions in the composite and increase of the nuclei volume parts in the inclusions results in the shift of the main Plasmon resonance to the side of big lengths of waves and in its intensity decrease.

- Key words: composite, effective permittivity tensor, coated inclusion, Plasmon resonan, Maxwell-Garnett approximation; generalized effective field approximation
- Published in: fundamental researches
- Bibliography link: Lavrov I.V. Forecasting of optical properties of matrix composites with spherical inclusions with a metal shell // Proc. of Universities. Electronics. – 2018. – Vol. 23. – № 2. – P. 113–123. DOI: 10.24151/1561-5405-2018-23-2-113-123

Igor V. Lavrov

National Research University of Electronic Technology, Moscow, Russia

National Research University of Electronic Technology, Moscow, Russia

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15. Ivanov E.N., Lavrov I.V. Teoriya dielektricheskoy pronitsaemosti kompositsionnyh materialov s teksturoy. Chast’ 1 [Theory of permittivity of composites with texture]. Oboronnyj kompleks - naucno-tehniceskomu progressu Rossii – Defense Industry Achievements – Russian Scientific and Technical Progress, 2007, no.1, pp. 73–78. (in Russian).

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18. Zolotaryov V.M., Morozov V.N., Smirnova E.V. Opticheskie postoyannyie prirodnyh i tekhnicheskih sred. Spravochnik [Optical constants of nature and technical media. Handbook]. Leningrad, Khimia Publ., 1984. 216 p. (in Russian).

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21. Moroz A. Electron mean-free path in metal-coated nanowires. J. Opt. Soc. Am. B, 2011, vol. 28, no. 5, pp. 1130–1138.

2. Lerman L.B. Vozniknoveniye dopolnitel’nyh plazmonnyh resonansov v malyh chastitsah s obolochkoy [Emergence of the additional plasmon resonances in small particles with a cover]. Khimiya, fizika i tekhnologiya poverhnosti – Chemistry, physics and technology of surface, 2008, no. 14, pp. 91–100. (in Russian).

3. Guzatov D.V., Oraevskij A.A., Oraevskij A.N. Plazmonnyj rezonans v ellipsoidal'nyh nanochasticah s obolochkoj [Plasmon resonance in ellipsoidal nanoparticles with shells]. Kvantovaya elektronika – Quantum electronics, 2003, vol. 33, no. 9, pp. 817–822. (in Russian).

4. Garnett J.C.M., Colours in metal glasses and in metallic films. Phil. Trans. R. Soc., 1904, vol. 203, pp. 385–420.

5. Kolesnikov V.I., Bardushkin V.V., Lavrov I.V., Sychyov A.P., Yakovlev V.B. Obobshchennoe priblizhenie effektivnogo polya dlya neodnorodnoj sredy s vklyucheniyami v obolochke [A generalized effective-field approximation for an inhomogeneous medium with coated inclusions]. Doklady Akademii Nauk, 2017, vol. 62, no. 9, pp. 415–419. (in Russian).

6. Fokin A.G. Dielektricheskaya pronicaemost' smesej [Permittivity of mixtures]. Zhurnal Tekhnicheskoi Fiziki – Technical Physics,1971, vol. 41, iss. 6, pp. 1073–1079. (in Russian).

7. Fokin A.G. Makroskopicheskaya provodimost' sluchajno-neodnorodnyh sred. Metody rascheta [Macroscopic conductivity of random inhomogeneous media. Calculation methods]. Physics-Uspekhi –Advances in Physical Sciences, 1996, vol. 166, no.10, pp. 1009–1032. (in Russian).

8. Yakovlev V.V., Bardushkin V.V., Lavrov I.V., Yakovleva E.N. Simulation of the Frequency Dispersion of Effective Dielectric Characteristics of Composite Materials. Semiconductors, 2014, vol.48, no. 13, pp. 1710–1715.

9. Kolesnikov V.I., YAkovlev V.B., Bardushkin V.V., Lavrov I.V., Sychev A.P., Yakovleva E.N. Ob ob"edinenii metodov ocenki effektivnyh dielektricheskih harakteristik geterogennyh sred na osnove obobshchennogo singulyarnogo priblizheniya. Doklady Akademii nauk, 2013, vol. 452, no. 1, pp. 27–31. (in Russian).

10. De Groot S.R., Suttorp L.G. Foundations of Electrodynamics. Amsterdam, North-Holland Publishing Company, 1972. 535 p. (Russ. ed.: De Groot S.R., Sattorp L.G. Elektrodinamika. Moscow, Nauka Publ., 1982. 560 p.).

11. Bragg W.L., Pippard A.B. The Form Birefringence of Macromolecules. Acta Cryst., 1953, vol. 6, no. 11–12, pp. 865–867.

12. Levy O., Stroud D. Maxwell Garnett theory for mixtures of anisotropic inclusions: Applica-tion to conducting polymers. Phys. Rev. B, 1997, vol.56, no. 13, pp. 8035–8046.

13. Giordano S. Order and disorder in heterogeneous material microstructure: Electric and elastic characterization of dispersions of pseudo-oriented spheroids. Int. J. Eng. Sci., 2005, vol.43, pp. 1033–1058.

14. Giordano S. Equivalent permittivity tensor in anisotropic random media. J. Electrost., 2006, vol.64, pp. 655–663.

15. Ivanov E.N., Lavrov I.V. Teoriya dielektricheskoy pronitsaemosti kompositsionnyh materialov s teksturoy. Chast’ 1 [Theory of permittivity of composites with texture]. Oboronnyj kompleks - naucno-tehniceskomu progressu Rossii – Defense Industry Achievements – Russian Scientific and Technical Progress, 2007, no.1, pp. 73–78. (in Russian).

16. Zavgorodnyaya M I., Lavrov I.V., Fokin A.G. Analytical Approach to Calculating the Effec-tive Dielectric Characteristics of Heterogeneous Textured Materials with Randomly Shaped In-clusions. Semiconductors, 2015, vol.49, no13, pp. 1718–1726.

17. Zavgorodnyaya M.I., Lavrov I.V. Methods of Accounting for Inclusion-Shape Randomness in Calculating the Effective Dielectric Characteristics of Heterogeneous Textured Materials. Semiconductors, 2016, vol. 50, no.13, pp. 1708–1715.

18. Zolotaryov V.M., Morozov V.N., Smirnova E.V. Opticheskie postoyannyie prirodnyh i tekhnicheskih sred. Spravochnik [Optical constants of nature and technical media. Handbook]. Leningrad, Khimia Publ., 1984. 216 p. (in Russian).

19. Palik E.D. Handbook of Optical Constants of Solids. Orlando, Acad. Press, 1985.

20. Hlebcov N.G. Optika i biofotonika nanochastic s plazmonnym rezonansom [Optics and biophotonics of nanoparticles with a plasmon resonance]. Kvantovaya elektronika – Quantum electronics, 2008, vol. 38, no. 6, pp. 504–529. (in Russian).

21. Moroz A. Electron mean-free path in metal-coated nanowires. J. Opt. Soc. Am. B, 2011, vol. 28, no. 5, pp. 1130–1138.

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