Electromagnetic models for multilayer superconducting transmission lines

TL;DR

This paper introduces a rigorous conformal mapping method for analyzing electromagnetic behavior of multilayer superconducting transmission lines, applicable to various multilayer configurations and compatible with existing design software.

Contribution

The paper presents a new conformal mapping approach and an effective conductivity approximation for multilayer superconducting transmission lines, enhancing analysis accuracy and software compatibility.

Findings

Numerical results for Al-Ti bilayers demonstrate the method's effectiveness.

The homogeneous approximation's validity is discussed.

The approach is suitable for both microstrip and coplanar waveguides.

Abstract

Thin-film superconducting transmission lines play important roles in many signal transmission and detection systems, including qubit coupling and read-out schemes, electron spin resonance systems, parametric amplifiers, and various ultra high sensitivity detectors. Here we present a rigorous method for computing the electromagnetic behaviour of superconducting microstrip transmission lines and coplanar waveguides. Our method is based on conformal mapping, and is suitable for both homogeneous superconductors and proximity-coupled multilayers. We also present an effective conductivity approximation of multilayers, thereby allowing the multilayers to be analysed using existing electromagnetic design software. We compute the numerical results for Al-Ti bilayers and discuss the validity of our full computation and homogeneous approximation.