Comparison of rigorous and perturbation approaches for the complex conductivity and the wave impedance determination of thin superconducting films employing TE011 mode cavities and quasi TE011 mode single post dielectric resonators Jerzy Krupka and Jarek Wosik 1. Introduction Nowdays analysis of electromagnetic characteristics of various microwave devices consisting passive elements of different kind is usually performed employing commercially available electromagnetic simulators based on rigorous solutions of Maxwell’s equations with finite difference or finite element methods. Formulation of an electromagnetic problem for such simulators require knowledge of all dimensions of the elements from which the device is assembled as well as the knowledge of the intrinsic electromagnetic properties of the elements. Typically such material properties are described by the complex permittivity and the complex permeability tensors for time harmonic electromagnetic fields. Conductivity tensor, if present, is included into the imaginary part of the complex permittivity tensor. Formally at microwave frequencies the intrinsic electromagnetic properties of superconductors can be characterized by the complex conductivity or by the complex permittivity tensors. Usually there are two parameters reported for high temperature superconductors at microwave frequencies, namely, the surface resistance and the penetration depth. Determination of the electrical parameters of superconductors at temperatures close to and above the critical temperature is not as simple as it is for temperatures well below T c . At higher temperatures the superconducting film thickness (typically a few hundred nanometres) becomes comparable to or smaller than the penetration or normal state skin depth. In such a case, electromagnetic fields penetrate partly through the film and the sample cannot be treated as a bulk case. As a consequence, the surface impedance of the sample is no longer defined just in terms of the intrinsic properties of the superconductor, but also depends on other parameters, including thickness and substrate permittivity. Alternative approach is to describe the intrinsic electromagnetic properties of a superconductor by the complex conductivity (two fluid model) and define all other quantities such as the wave impedance, penetration depth or the effective surface impedance of dielectric-superconductor layers as the secondary quantities. It should be mentioned that choice of primary quantities for superconductor is arbitrary (the complex wave impedance or the complex conductivity can be alternatively used). For microwave engineers that use electromagnetic simulator as a tool the complex permittivity is a natural choice but for physicists the complex wave impedance is more sound for historical reasons (most existing literature records describe superconductors in terms of the wave or surface impedance). Majority of methods intended for characterization of material properties of superconductors at microwave frequencies employ resonance cavities and other resonators, since resonators exhibit high measurement sensitivity due to their large Q-factor values. There are few types of resonators that are used for measurements of the wave impedance of superconductors but most frequently used operate on axially symmetric TE011 or quasi TE011 modes. Sapphire dielectric rod resonators, cylindrical TE011 mode cavities and single post dielectric resonators belong to this class. As it has been already mentioned majority of the authors that performed for measurements of high temperature superconductors reported the complex wave impedance or the complex effective surface impedance