The symmetric Bruggeman approximation, also known as the Effective Medium Approximation (EMA), is widely used in applications including the description of light scattering on inhomogeneous structures containing discrete inclusions. However, in the latter case, the natural asymmetry of the fillers topology, where discrete inclusions are mostly surrounded by the material of a simply connected matrix, is not taken into account. In this paper, two versions of asymmetric EMA are proposed for the case of a statistically isotropic medium containing discrete inclusions based on the difference in the structure of the fields inside and outside the inclusions. One of them does not differ too much from the usual EMA and leads to the same percolation threshold. For the second, the threshold value differs from the usual one even in the case of spherical particles. Expressions are given for the corresponding percolation thresholds in the model of randomly oriented elliptical particles. The proposed approximations are compared with the standard Maxwell Garnett and Bruggeman approximations for the case of silver particles in a dielectric matrix. 1. Apresyan L. A., Effective electrodynamic parameters of nano-composiote media and the homogenization theory.// Light & Engineering, 2019, Vol. 27, No. 1, pp. 4–14.
2. Stroud D., Generalized effective-medium approach to the conductivity of an inhomogeneous material.// Phys. Rev. 1975, B12, № 8, pp. 3368–3373. DOI:10.1103/ PhysRevB.12.3368.
3. Apresyan L.A., Vlasov D.V., Zadorin D.A. et al. On the effective medium model for particles with a complex structure// Tech. Phys. 2017, Vol. 62, pp. 6–13. DOI:10.1134/S1063784217010029
4. L. D. Landau, E.M. Lifshitz. Electrodynamics of Continuous Media. Vol. 8 (1st ed.). N.Y.: Pergamon Press, 1960, 417 p.
5. Bruggeman D.A.G. Calculation of various physics constants in heterogeneous substances. I. Dielectric constants and conductivity of mixed bodies from isotropic substances.//Ann.Phys. 1935, V.23, pp. 636–664. DOI: 10.1002/andp.19354160705
6. Milton G.W. The Theory of Composites. Cambridge Univ. Press, 2004, 749p.
7. Lynch D.W., Hunter W.R. In: Handbook of Optical Constants of Solids. Ed. Palik E.D. N..Y.: Academic Press, 1985, pp. 350–356.
8. Bohren C.F. Applicability of effective-medium theories to problems of scattering and absorption by nonhomogeneous atmospheric particles.// J. Atmosph. Sci, 1986, Vol. 43, pp. 468–475. doi: 10.1175/1520– 0469(1986)043 %3C0468: AOEMTT%3E2.0.CO;2
9. Mishchenko, M. I., Dlugach, J. M., & Liu, L. Applicability of the effective-medium approximation to heterogeneous aerosol particles.// Journal of Quantitative Spectroscopy and Radiative Transfer, 2016, Vol. 178, pp. 284–294. doi:10.1016/j.jqsrt.2015.12.028

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• effective parameters of randomly inhomogeneous media
• homogenization
• Bruggeman and Maxwell Garnett approximations
• percolation threshold