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The response of a thin, high-contrast, finely layered structure with dielectric and conductive properties to an incident, pulsed, electromagnetic field is investigated theoretically. The fine layering causes the standard spatial discretization techniques to solve Maxwell's equations numerically to be practically inapplicable. To overcome this difficulty, an approximate method is proposed that models the interaction of the layer with an incident electromagnetic field via a boundary condition that expresses the in-plane conduction and contrast electric polarization currents in terms of the exciting incident field by relating the jump in the tangential component of the magnetic field strength across the layer in terms of the (continuous) tangential component of the electric field strength in the layer. In the pertaining layer admittance coefficient, the integrated values of the conductance and the contrast permittivity profiles across the layer occur. The model is applied to the scattering of an incident plane wave with pulsed time signature by a layer of infinite extent. Expressions for pulse shapes of the scattered field are obtained. In them, the layer properties and the direction of incidence and polarization of the incident wave occur as parameters. Numerical results are presented for reflected and transmitted wave pulse shapes for some parameter values.