Exact solutions of the Mattis Bardeen theory for thin superconducting films and bulk material

The Mattis-Bardeen theory describing the anomalous skin effect in superconductors is exactly solved for thin films and bulk material. When five material parameters (i.e., the energy gap, the critical temperature, the London penetration depth, the Fermi velocity, and the mean free path) are known, calculation of all frequencies, mean free paths, and temperatures can be carried out, leading to the determination of the surface impedance. The calculation agrees well with measurements of the quality factor on resonant cavities, absorption in bulk materials, and transmission through thin superconducting films in the microwave and in the far-infrared region. It is shown that the solution in the extreme anomalous limit cannot describe these measurements and that the Mattis-Bardeen theory describes measurements on strong-coupling superconductors well.