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Journal of Applied Mechanics and Technical Physics

2019 year, number 4

Homogenization of Harmonic Maxwell Equations with Allowance for Interphase Surface Currents: Layered Structure

Y. Amirat1, V. V. Shelukhin2,3
1University of Auvergne, Clermont-Ferrand, France
2Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
3Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: уравнения Максвелла, межфазные токи, гомогенизация, двух-масштабная сходимость, Maxwell equation, interphase currents, homogenization, two-scale convergence


The Maxwell equations for a composite two-component layered material with a periodic structure in the field of a time-harmonic source acting along the layer are considered. Two-scale homogenization of the equations is performed with allowance for complex conductivity of interphase layers and their thickness. The boundary-value problem for systems of differential equations with boundary conditions is reduced to a problem in a weakly variational formulation. Unique solvability of the problem is established. The case of low frequencies of interphase surface currents of different intensities with allowance for the frequency-dependent wave length and skin layer length is analyzed. Macro-equations are derived, and effective material constants are determined, such as the magnetic and dielectric permeabilities and electrical conductivity. Conditions at which the effective parameters depend on interphase currents are described. It is found that the effective dielectric permeability can be negative at specially chosen parameters of interphase layers, if the effective dielectric permeability is determined on the basis of the effective wave number.