Scattering coefficients of superconducting microwave resonators. I. Transfer matrix approach

Qi-Ming Chen; Meike Pfeiffer; Matti Partanen; Florian Fesquet; Kedar E. Honasoge; Fabian Kronowetter; Yuki Nojiri; Michael Renger; Kirill G. Fedorov; Achim Marx; Frank Deppe; Rudolf Gross

doi:10.1103/PhysRevB.106.214505

Scattering coefficients of superconducting microwave resonators. I. Transfer matrix approach

Qi-Ming Chen, Meike Pfeiffer, Matti Partanen, Florian Fesquet, Kedar E. Honasoge, Fabian Kronowetter, Yuki Nojiri, Michael Renger, Kirill G. Fedorov, Achim Marx, Frank Deppe, Rudolf Gross

DOI 10.1103/PhysRevB.106.214505 · Physical Review B

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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.