Electrodynamic Calculation of Effective Electromagnetic Parameters of a Dielectric Medium with Metallic Nanoparticles of a Given Size
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The frequency dependence of the effective complex permittivity and effective complex permeability of a heterostructure based on a dielectric medium containing metallic nanoparticles of spherical shape is calculated by an original method. In contrast to the Bruggeman  and the Maxwell Garnett  approaches, which use the quasi-static approximation in calculations, a nonuniform distribution of electromagnetic fields inside metallic particles is calculated, which allows the analysis of the electromagnetic parameters of the heterostructure not only as a function of frequency but also as a function of the nanoparticle size. It is shown that the plasmon resonant frequency decreases with increasing both the size and the concentration of particles in the heterostructure. It is also shown that a dielectric medium containing nonmagnetic metallic nanoparticles exhibits diamagnetic properties. In this case, the position of the maximum on the frequency dependence of the imaginary part of the magnetic susceptibility coincides with the relaxation frequency of charge carriers. The calculated spectra of the real and imaginary components of the permittivity of the heterostructure with a size of metallic particles less than 10 nm are in good agreement with Bruggeman calculations; however, the agreement with Maxwell Garnett calculations is observed only at nanoparticle concentrations lower than 10–6.
This work was supported by the Ministry of Education and Science of the Russian Federation (contract no. 14.575.21.0142; unique identifier of the project is RFMEFI57517X0142).
- 1.M. Mishra and P. Chauhan, J. Nanomed. Res. 2, 00039 (2015).Google Scholar
- 7.S. J. Oldenburg, https://www.sigmaaldrich.com/technical-documents/articles/materials-science/nanomaterials/silver-nanoparticles.html (2017).Google Scholar
- 12.T. C. Choy, Effective Medium Theory: Principles and Applications (Oxford Univ. Press, Oxford, 2016).Google Scholar
- 16.M. Sancho and G. Martinez, J. Electrostat. 22, 319 (1989).Google Scholar
- 18.A. Sihvola, J. Electromag. Waves Appl. 15, 715 (2001).Google Scholar
- 20.M. Scheller, C. Jansen, and M. Koch, in RecentOptical and Photonic Technologies, Ed. by K. Y. Kim (Intech, Croatia, Vukovar, 2010), p. 231.Google Scholar
- 21.D. A. G. Bruggeman, Ann. Phys., Ser. 5 24, 636 (1935).Google Scholar
- 24.A. Lakhtakia, Optik 91, 134 (1992).Google Scholar
- 28.C. F. Bohren, J. Atmosph. Sci. 43, 468 (1986).Google Scholar
- 31.I. V. Timofeev, Extended Abstract of Doctoral (Phys. Math.) Dissertation (Inst. Phys. Siberian Branch of RAS, Krasnoyarsk, 2017). http://kirensky.ru/zdoc/ ref_timofeev.pdf.Google Scholar