Effect of transition layers on the electromagnetic properties of   composites containing conducting fibres
  The approach to calculating the effective dielectric and magnetic response in bounded composite materials is developed. The method is essentially based on the renormalisation of the dielectric matrix parameters to account for the surface polarisation and the displacement currents at the interfaces. This makes it possible the use of the effective medium theory developed for unbounded materials, where the spatially-dependent local dielectric constant and magnetic permeability are introduced. A detailed mathematical analysis is given for a dielectric layer having conducting fibres with in-plane positions. The surface effects are most essential at microwave frequencies in correspondence to the resonance excitation of fibres. In thin layers (having a thickness of the transition layer), the effective dielectric constant has a dispersion region at much higher frequencies compared to those for unbounded materials, exhibiting a strong dependence on the layer thickness. For the geometry considered, the effective magnetic permeability differs slightly from unity and corresponds to the renormalised matrix parameter. The magnetic effect is due entirely to the existence of the surface displacement currents. 
D.P. Makhnovskiy, L.V. Panina, D.J. Mapps, and A.K. Sarychev