Effective transmission conditions for an array of locally resonant inclusions

We study the scattering of waves by a single row of resonant inclusions, of the Mie type. An effective model based on matched asymptotic analyzed is used to account for the small thickness of the array. Hence, instead of the effective bulk parameters (permittivity and permeabilty), we end up with interface parameters entering in jump conditions for the electromagnetic fields; among these parameters, one is frequency dependent and encapsulates the resonant behavior of the inclusions. Our effective model is validated by comparison with results of full wave calculations.