Scattering of electromagnetic waves by a thin impedance film in a rectangular waveguide

The scattering of electromagnetic waves by bodies with surface impedance (w) in a waveguide is considered. An integral equation for the total magnetic field tangential to the surface of the body is presented; and this equation is formulated for the jump of tangential components of the total magnetic field when the body is a thin (compared with the depth of the skin layer) film. This equation is used to obtain the stationary functional of the impedance (Z) for the shunt of an equivalent circuit describing the thin film in a rectangular waveguide. Asymptotic expressions are obtained for Z in cases of large and small values of w, and in the case of a narrow film.