Two-scale homogenization to determine effective parameters of thin metallic-structured films

We present a homogenization method based on matched asymptotic expansion technique to derive effective transmission conditions of thin structured films. The method leads unambiguously to effective parameters of the interface which define jump conditions or boundary conditions at an equivalent zero thickness interface. The homogenized interface model is presented in the context of electromagnetic waves for metallic inclusions associated with Neumann or Dirichlet boundary conditions for transverse electric or transverse magnetic wave polarization. By comparison with full-wave simulations, the model is shown to be valid for thin interfaces up to thicknesses close to the wavelength. We also compare our effective conditions with the two-sided impedance conditions obtained in transmission line theory and to the so-called generalized sheet transition conditions.