Microwave surface impedances of BCS superconducting thin films

The microwave propagation-dominated problem in the multilayer structure made of a BCS superconducting film and a dielectric substrate is investigated theoretically by using the modified two-fluid model and transmission line theory. The effective microwave surface impedances are studied as functions of temperature, frequency, and film thickness, as well as substrate thickness. Special attention is paid to the substrate resonance phenomenon in the resonant structure. The influence of BCS coherence effects on surface impedance and resonant behavior is clearly demonstrated. The resonant effect in the stack structure is well interpreted with the help of the transverse resonance technique in the microwave theory.