Abstract
Perturbation of a microwave cavity by a small sample with variable dielectric, magnetic, or conducting properties is considered. The complex frequency shift is derived in terms of a volume integral, or equivalently, in terms of a surface integral. These are used to obtain a general formula for thin films in the microwave electric field maximum. The complex frequency shift depends on the depolarization factor of the film and on its thickness in a nontrivial way. The previously known expressions for the complex frequency shift are shown to be good approximations of the present solution in the low and high conductivity limits. Our formula is applied to calculate the signal shapes in superconducting films of various geometric parameters and conductivities. It is shown that a diversity of signal shapes can result, and experimental support of those shapes is provided. The role of the dielectric substrate on which the thin film is grown is simply reduced to an asymmetry effect.
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