Homogenization of Harmonic Maxwell Equations with Allowance for Interfacial Surface Currents: Layered Structure
The Maxwell equations for a composite two-component laminated material with a periodic structure in the field of a time-harmonic source acting along the layers are considered. Two-scale homogenization of the equations is performed with allowance for complex conductivity of interfacial 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 interfacial 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 dielectric permittivity, magnetic permeability, and electrical conductivities. Conditions at which the effective parameters depend on interfacial currents are described. It is found that the effective dielectric permittivity can be negative at specially chosen parameters of interfacial layers if it is determined on the basis of the effective wave number.
KeywordsMaxwell equation interfacial currents homogenization two-scale convergence
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