The effect of complex dispersion and characteristic impedance on the gain of superconducting traveling-wave kinetic inductance parametric amplifiers

TL;DR

This paper investigates how complex dispersion and characteristic impedance influence the gain of superconducting traveling-wave kinetic inductance parametric amplifiers, revealing their critical impact on amplifier performance and design.

Contribution

It introduces a multiple-scales method to incorporate complex dispersion and impedance effects into amplitude equations, improving the accuracy of amplifier gain predictions.

Findings

Complex dispersion and impedance can significantly alter gain, even suppressing it.

Including these effects leads to better amplifier design insights.

The new equations improve the reliability of performance predictions.

Abstract

Superconducting traveling-wave parametric amplifiers are a promising amplification technology suitable for applications in submillimeter astronomy. Their implementation relies on the use of Floquet transmission lines in order to create strong stopbands to suppress undesired harmonics. In the design process, amplitude equations are used to predict their gain, operation frequency, and bandwidth. However, usual amplitude equations do not take into account the real and imaginary parts of the dispersion and characteristic impedance that results from the use of Floquet lines, hindering reliable design. In order to overcome this limitation, we have used the multiple-scales method to include those effects. We demonstrate that complex dispersion and characteristic impedance have a stark effect on the transmission line's gain, even suppressing it completely in certain cases. The equations presented here can, thus, guide to a better design and understanding of the properties of this kind of amplifiers.