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IEEE Transactions on Applied Superconductivity

Periodic Superconducting Microstrip Line With Nonlinear Kinetic Inductance

Hamid Reza Mohebbi, A. Hamed Majedi

Published Jun 1, 2009• 4 citations
Publisher

Abstract

This paper investigates linear and nonlinear microwave propagation in a periodic superconductor-normal conductor microstrip transmission line (S-N muTL). We derive closed-form equations for complex propagation constant, input impedance and complex resonant frequencies for linear infinite and finite periodic S-N muTL. Jumps on the curves of attenuation constants, input impedances and eigenfrequencies occur exactly at the Bragg frequencies. We demonstrate that the finite S-N muTL shows the same behavior as infinite periodic SmuTL, when there is enough number of unit cells. Furthermore, nonlinear microwave signal propagation analyses are carried out based on the self-consistent method, when the kinetic inductance of the superconducting segments is in the nonlinear regime.

DOI
10.1109/tasc.2009.2018085

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This paper investigates linear and nonlinear microwave propagation in a periodic superconductor-normal conductor microstrip transmission line (S-N muTL). We derive closed-form equations for complex propagation constant, input impedance and complex resonant frequencies for linear infinite and finite periodic S-N muTL. Jumps on the curves of attenuation constants, input impedances and eigenfrequencies occur exactly at the Bragg frequencies. We demonstrate that the finite S-N muTL shows the same behavior as infinite periodic SmuTL, when there is enough number of unit cells. Furthermore, nonlinear microwave signal propagation analyses are carried out based on the self-consistent method, when the kinetic inductance of the superconducting segments is in the nonlinear regime.
The nonlinear response associated with the current dependence of the superconducting kinetic inductance was studied in capacitively shunted NbTiN microstrip transmission lines.It was found that the inductance per unit length of one microstrip line could be changed by up to 20% by applying a dc current, corresponding to a single-pass time delay of 0.7 ns.To investigate nonlinear dissipation, Bragg reflectors were placed on either end of a section of this type of transmission line, creating resonances over a range of frequencies.From the change in the resonance linewidth and amplitude with dc current, the ratio of the reactive to the dissipative response of the line was found to be 788.The low dissipation makes these transmission lines suitable for a number of applications that are microwave-and millimeter-wave band analogs of nonlinear optical processes.As an example, by applying a millimeter-wave pump tone, very-wide-band parametric amplification was observed between about 3 and 34 GHz.Use as a current variable delay line for an on-chip millimeter-wave Fourier transform spectrometer is also considered.
The nonlinear response associated with the current dependence of the superconducting kinetic inductance was studied in capacitively shunted NbTiN microstrip transmission lines. It was found that the inductance per unit length of one microstrip line could be changed by up to 20% by applying a dc current, corresponding to a single-pass time delay of 0.7 ns. To investigate nonlinear dissipation, Bragg reflectors were placed on either end of a section of this type of transmission line, creating resonances over a range of frequencies. From the change in the resonance linewidth and amplitude with dc current, the ratio of the reactive to the dissipative response of the line was found to be 788. The low dissipation makes these transmission lines suitable for a number of applications that are microwave- and millimeter-wave band analogs of nonlinear optical processes. As an example, by applying a millimeter-wave pump tone, very-wide-band parametric amplification was observed between about 3 and 34 GHz. Use as a current variable delay line for an on-chip millimeter-wave Fourier transform spectrometer is also considered.
Strategies are explored to reduce the electromagnetic simulation time of electrically large superconducting transmission line structures while retaining model accuracy. The complex surface reactance of an infinite thin-film superconducting sheet is evaluated with the BCS (Bardeen-Cooper-Schrieffer) theory and used as an input to model the phase velocity and characteristic impedance of finite width transmission line structures. Commercially available electromagnetic simulation software are employed for the calculations and the results are compared with limiting analytic forms from the literature. The influences of line width, metallization thickness, and substrate height on microstrip transmission line propagation are considered in detail and a scaling approach is presented to compensate for the leading order effect in numerical simulations. These findings are particularly important near the energy gap of the superconductor due to the influence of the kinetic inductance on the transmission line dispersion.
High-kinetic-inductance (HKI) transmission lines provide a promising platform for compact nonlinear superconducting microwave devices. Existing theoretical descriptions are typically based on the slowly varying envelope approximation, which becomes inadequate for strongly nonlinear resonant structures with pronounced spatial field variations. Here, we develop a theoretical framework for single-frequency nonlinear wave propagation in HKI transmission lines by formulating the problem as a boundary value problem that retains the full spatial dependence of the electromagnetic fields. Applying the method to resonant transmission-line geometries, we demonstrate power-dependent resonance shifts, bistable transmission solutions, and strongly direction-dependent transport arising from asymmetric impedance barriers, yielding transmission contrasts of up to 93%93\%93% without magnetic bias fields. The framework is further extended to a three-port stub geometry, where nonlinear interference produces shifted anti-resonances and Duffing-like spectral distortions. Our approach provides a versatile tool for the analysis and design of strongly nonlinear superconducting microwave devices.
We report our experimental investigations on the radio frequency (RF) and microwave nonlinear behavior of the NbN nanowire meanderline. We construct a lumped element model of the NbN nanowire meanderline, which consists of a kinetic inductance, a normal resistance, and a parasitic capacitance that is a load of a transmission line. Two complementary measurements, which are based on the one-port scattering (S)-parameter technique, are used to explore the nonlinearity in the kinetic inductance and the normal resistance of the NbN nanowire meanderline under dc current and voltage bias conditions. In the first series of experiments, the kinetic inductance has directly been measured from zero up to 99% of the critical current and to the voltage bias, where the hotspot plateau occurs. The Ginsburg-Landau (G-L) theory has been employed to justify the results. The technical procedures required to achieve our desired level of accuracy have been described in detail. In the second series of experiments, the quality factor of the NbN nanowire meanderline has been measured, providing an alternative justification to the first experimental results.
Broadband parametric amplifiers (PAs), which utilize the nonlinear kinetic inductance of superconducting transmission lines, provide new access to ultimate sensing capability for radio astronomical observation and microwave quantum electronics. In this paper, the parametric amplification is investigated with a time-domain numerical method. The results present direct images of the traveling waves, which clarify the distinctively different features of the parametric gain in uniform and impedance-perturbed nonlinear transmission lines. The results indicate that the traveling-wave PAs (TWPAs) are susceptible to impedance mismatching because of the lack of isolation between the input and the output ports. In the experimental part of this paper, we tested, for the first time, microstrip TWPAs based on NbTiN. A parametric gain was observed at liquid helium temperature.