Angular dependence of microwave transmission and reflection of type-II superconducting film in the mixed state

By using the phenomenological theory of vortex dynamics, we have extended the microwave transmission and reflection of a type-II superconducting film to a complicating case with an oblique applied static magnetic field. We have calculated the microwave transmittance and reflectance as functions of the static field's magnitude and angle Ψ relative to the normal of superconductor surface, and the angle α defined by the plane containing the surface normal and static magnetic field relative to the incident microwave field. Numerical results illustrate that the microwave properties are essentially independent of Ψ when α = 0°, and also independent of α when Ψ = 0°, respectively. Moreover, they are affected substantially as Ψ and α increase, especially at 90°.