Electromagnetic models for superconducting millimetre-wave and sub-millimetre-wave microstrip transmission lines

Yassin, G.; Withington, S.

doi:10.1088/0022-3727/28/9/028

Cited by 46 publications

(43 citation statements)

References 16 publications

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“…To explore the basic properties of the model, it is beneficial to use a microstrip geometry so that we can take advantage of the equations developed by Yassin and Withington. 27 These equations, based on conformal mapping, allow the loss to be calculated accurately and analytically. Using them results in the propagation constant, ␥ = ␣ + i␤, which includes the losses, and the characteristic impedance of the line, Z 0 .…”

Section: ͑6͒mentioning

confidence: 99%

Readout-power heating and hysteretic switching between thermal quasiparticle states in kinetic inductance detectors

Visser

Withington

Goldie

2010

Journal of Applied Physics

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A model is presented for readout-power heating in kinetic inductance detectors. It is shown that the power dissipated by the readout signal can cause the temperature of the quasiparticle system in the superconducting resonator to switch between well-defined states. At low readout powers, only a single solution to the heat balance equation exists, and the resonance curve merely distorts as the readout power is increased. At high readout powers, three states exist, two of which are stable, and the resonance curve shows hysteretic switching. The power threshold for switching depends on the geometry and material used but is typically around Ϫ70 dBm for Aluminum resonators. A comprehensive set of simulations is reported, and a detailed account of the switching process is given. Experimental results are also shown, which are in strong qualitative agreement with the simulations. The general features of the model are independent of the precise cooling function, and are even applicable for resonators on suspended, thermally isolated, dielectric membranes, where an increase in quasiparticle lifetime is expected. We discuss various extensions to the technique, including the possibility of recovering the cooling function from large-signal measurements of the resonance curve.

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Section: ͑6͒mentioning

confidence: 99%

Readout-power heating and hysteretic switching between thermal quasiparticle states in kinetic inductance detectors

Visser

Withington

Goldie

2010

Journal of Applied Physics

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“…To connect the calculated σ 1 and σ 2 with the experiment, we calculate Q i and f res through equations for a microstrip geometry [28] with the same central strip dimensions as the measured resonator [18]. The results are plotted in Figs.…”

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confidence: 99%

Evidence of a Nonequilibrium Distribution of Quasiparticles in the Microwave Response of a Superconducting Aluminum Resonator

et al. 2014

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In a superconductor, absorption of photons with an energy below the superconducting gap leads to redistribution of quasiparticles over energy and thus induces a strong nonequilibrium quasiparticle energy distribution. We have measured the electrodynamic response, quality factor, and resonant frequency of a superconducting aluminium microwave resonator as a function of microwave power and temperature. Below 200 mK, both the quality factor and resonant frequency decrease with increasing microwave power, consistent with the creation of excess quasiparticles due to microwave absorption. Counterintuitively, above 200 mK, the quality factor and resonant frequency increase with increasing power. We demonstrate that the effect can only be understood by a nonthermal quasiparticle distribution. DOI: 10.1103/PhysRevLett.112.047004 PACS numbers: 74.25.nn, 07.57.Kp, 74.40.Gh, 74.78.-w A superconductor can be characterized by the density of states, which exhibits an energy gap due to Cooper pair formation, and the distribution function of the electrons, which in thermal equilibrium is the Fermi-Dirac distribution. When a superconductor is driven by an electromagnetic field, nonlinear effects in the electrodynamic response can occur, which are usually assumed to be due to a change in the density of states, the so-called pair-breaking mechanism [1]. These nonlinear effects can be described along the lines of a current dependent superfluid density n s ðT; jÞ ∝ n s ðTÞ½1 − ðj=j c Þ 2 , where j is the actual current density, j c the critical current density, and T the temperature. Observations such as the nonlinear Meissner effect [2] and nonlinear microwave conductivity [3,4] can be explained by a broadening of the density of states and a decreased n s . The quasiparticles are assumed to be in thermal equilibrium and a Fermi-Dirac distribution fðEÞ ¼ 1=½expðE=k B TÞ þ 1 is assumed, with E the quasiparticle energy and k B Boltzmann's constant.Here we demonstrate that a microwave field also has a strong effect on fðEÞ in the superconductor, and induces a nonlinear response. We present measurements of the electrodynamic response, quality factor, and resonant frequency of an Al superconducting resonator (at 5.3 GHz) as a function of temperature and microwave power at low temperatures T c =18 < T < T c =3. The response measurements, complemented with quasiparticle recombination time measurements, are explained consistently by a model based on a microwave-induced nonequilibrium fðEÞ. Redistribution of quasiparticles [5,6] due to microwave absorption [7] has been shown earlier to cause enhancement of the critical current [8], the critical temperature (T c ), and the energy gap [9]. These enhancement effects are most pronounced close to T c and were observed for temperatures T > 0.8T c . A representation of gap suppression and gap enhancement is shown in the inset to Fig. 1(b) [8]. The consequences of the redistribution of quasiparticles for the electrodynamic response were only studied theoretically for T > 0.5T c [10]. Redistributi...

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“…13. Typically, the tuning inductance is a short section of thin-film superconducting microstrip line [216]- [218]. For Fig.…”

Section: Tuning Circuits Materials Properties and Terahertz Opermentioning

confidence: 99%

Superconducting detectors and mixers for millimeter and submillimeter astrophysics

2004

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Electromagnetic models for superconducting millimetre-wave and sub-millimetre-wave microstrip transmission lines

Cited by 46 publications

References 16 publications

Readout-power heating and hysteretic switching between thermal quasiparticle states in kinetic inductance detectors

Readout-power heating and hysteretic switching between thermal quasiparticle states in kinetic inductance detectors

Evidence of a Nonequilibrium Distribution of Quasiparticles in the Microwave Response of a Superconducting Aluminum Resonator

Superconducting detectors and mixers for millimeter and submillimeter astrophysics

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