The scattering coefficients of superconducting microwave resonators: I. Transfer-matrix approach

TL;DR

This paper presents a unified classical transfer-matrix approach to analyze and accurately characterize the scattering coefficients of various superconducting microwave resonators, accounting for practical measurement influences.

Contribution

It introduces a comprehensive method for analyzing resonator scattering coefficients, including corrections for asymmetries and finite feedline lengths, bridging experiment and theory.

Findings

The transfer-matrix approach effectively models different resonator geometries.

Correction procedures improve measurement accuracy.

Reflection coefficients can be used to characterize resonator properties in a single step.

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 them in typical measurement results. We show that, similar to the transmission coefficient of a hanger-type resonator, the reflection coefficient of a necklace- or bridge-type resonator does also contain a reference point which can be used to characterize the electrical properties of a microwave resonator in a single step. Our results provide a comprehensive understanding of superconducting microwave resonators from the design concepts to the characterization details.