Scattering coefficients of superconducting microwave resonators. I. Transfer matrix approach
Qiming Chen, Meike Pfeiffer, Matti Partanen, Florian Fesquet, Kedar Honasoge, Fabian Kronowetter, Yuki Nojiri, Michael Renger, Kirill G. Fedorov, Achim Marx, Frank Deppe, Rudolf Groß
Abstract
We describe a unified classical approach for analyzing the scattering coefficients of superconducting microwave resonators with a variety of geometries. To fill the gap between experiment and theory, we also consider the influences of small circuit asymmetry and the finite length of the feedlines, and describe a procedure to correct their influences in typical experiments. We show that, similar to the transmission coefficient of a hanger-type resonator, the reflection coefficient of a necklace- or cross-type resonator also contains a so-called reference point that can be used to characterize the internal quality factor of the resonator. Our results provide a comprehensive understanding of superconducting microwave resonators from the design concepts to the characterization details.