THEORY OF MICROWAVE TRANSMISSION AND REFLECTION IN TYPE-II SUPERCONDUCTORS IN THE MIXED-STATE

We develop a phenomenological theory for microwave transmission and reflection in type-II superconducting films that self-consistently includes the effects of vortices. The theory includes the effects of vortex inertia, pinning, flux flow, and flux creep in a unified manner by using a complex dynamic vortex mobility. The treatment of vortex dynamics in the linear-response regime includes nonlocal vortex interactions in addition to two-fluid effects. Our results, including the complex effective wave number, rf conductivity, and transmission and reflection coefficients, are expected to be valid over a wide range of magnetic induction, frequency, and temperature. Numerical results illustrate the temperature and field dependences of these quantities for typical experimental conditions.