  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.
