Bardeen, J., & Mattis, D. C. (1958). Theory of the anomalous skin effect in normal and superconducting metals. Phys. Rev., 111(2), 412–417.
Abstract: Chambers' expression for the current density in a normal metal in which the electric field varies over a mean free path is derived from a quantum approach in which use is made of the density matrix in the presence of scattering centers but in the absence of the field. An approximate expression used for the latter is shown to reduce to one derived by Kohn and Luttinger for the case of weak scattering. A general space-and time-varying electromagnetic interaction is treated by first-order perturbation theory. The method is applied to superconductors, and a general expression derived for the kernel of the Pippard integral for fields of arbitrary frequency. The expressions derived can also be used to discuss absorption of electromagnetic radiation in thin superconducting films.
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Kawamura, J., Blundell, R., Tong, C. - Y. E., Golts'man, G., Gershenzon, E., & Voronov B. (1996). Superconductive NbN hot-electron bolometric mixer performance at 250 GHz. In Proc. 7th Int. Symp. Space Terahertz Technol. (pp. 331–336).
Abstract: Thin film NbN (<40 A) strips are used as waveguide mixer elements. The electron cooling mechanism for the geometry is the electron-phonon interaction. We report a receiver noise temperature of 750 K at 244 GHz, with / IF = 1.5 GHz, Af= 500 MHz, and Tphysical = 4 K. The instantaneous bandwidth for this mixer is 1.6 GHz. The local oscillator (LO) power is 0.5 1.tW with 3 dB-uncertainty. The mixer is linear to 1 dB up to an input power level 6 dB below the LO power. We report the first detection of a molecular line emission using this class of mixer, and that the receiver noise temperature determined from Y-factor measurements reflects the true heterodyne sensitivity.
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Trifonov, A., Tong, C. - Y. E., Blundell, R., Ryabchun, S., & Gol'tsman, G. (2015). Probing the stability of HEB mixers with microwave injection. IEEE Trans. Appl. Supercond., 25(3), 2300404 (1 to 4).
Abstract: Using a microwave probe as a tool, we have performed experiments aimed at understanding the origin of the output-power fluctuations in hot-electron-bolometer (HEB) mixers. We use a probe frequency of 1.5 GHz. The microwave probe picks up impedance changes of the HEB, which are examined upon demodulation of the reflected wave outside the cryostat. This study shows that the HEB mixer operates in two different regimes under a terahertz pump. At a low pumping level, strong pulse modulation is observed, as the device switches between the superconducting state and the normal state at a rate of a few megahertz. When pumped much harder, to approximate the low-noise mixer operating point, residual modulation can still be observed, showing that the HEB mixer is intrinsically unstable even in the resistive state. Based on these observations, we introduced a low-frequency termination to the HEB mixer. By terminating the device in a 50-Ω resistor in the megahertz frequency range, we have been able to improve the output-power Allan time of our HEB receiver by a factor of four to about 10 s for a detection bandwidth of 15 MHz, with a corresponding gain fluctuation of about 0.035%.
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Lobanov, Y., Shcherbatenko, M., Finkel, M., Maslennikov, S., Semenov, A., Voronov, B. M., et al. (2015). NbN hot-electron-bolometer mixer for operation in the near-IR frequency range. IEEE Trans. Appl. Supercond., 25(3), 2300704 (1 to 4).
Abstract: Traditionally, hot-electron-bolometer (HEB) mixers are employed for THz and “super-THz” heterodyne detection. To explore the near-IR spectral range, we propose a fiber-coupled NbN film based HEB mixer. To enhance the incident-light absorption, a quasi-antenna consisting of a set of parallel stripes of gold is used. To study the antenna effect on the mixer performance, we have experimentally studied a set of devices with different size of the Au stripe and spacing between the neighboring stripes. With use of the well-known isotherm technique we have estimated the absorption efficiency of the mixer, and the maximum efficiency has been observed for devices with the smallest pitch of the alternating NbN and NbN-Au stripes. Also, a proper alignment of the incident Eâƒ<2014>-field with respect to the stripes allows us to improve the coupling further. Studying IV-characteristics of the mixer under differently-aligned Eâƒ<2014>-field of the incident radiation, we have noticed a difference in their shape. This observation suggests that a difference exists in the way the two waves with orthogonal polarizations parallel and perpendicular Eâƒ<2014>-field to the stripes heat the electrons in the HEB mixer. The latter results in a variation in the electron temperature distribution over the HEB device irradiated by the two waves.
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Seliverstov, S., Maslennikov, S., Ryabchun, S., Finkel, M., Klapwijk, T. M., Kaurova, N., et al. (2015). Fast and sensitive terahertz direct detector based on superconducting antenna-coupled hot electron bolometer. IEEE Trans. Appl. Supercond., 25(3), 2300304.
Abstract: We characterize superconducting antenna-coupled hot-electron bolometers for direct detection of terahertz radiation operating at a temperature of 9.0 K. The estimated value of responsivity obtained from lumped-element theory is strongly different from the measured one. A numerical calculation of the detector responsivity is developed, using the Euler method, applied to the system of heat balance equations written in recurrent form. This distributed element model takes into account the effect of nonuniform heating of the detector along its length and provides results that are in better agreement with the experiment. At a signal frequency of 2.5 THz, the measured value of the optical detector noise equivalent power is 2.0 × 10-13 W · Hz-0.5. The value of the bolometer time constant is 35 ps. The corresponding energy resolution is about 3 aJ. This detector has a sensitivity similar to that of the state-of-the-art sub-millimeter detectors operating at accessible cryogenic temperatures, but with a response time several orders of magnitude shorter.
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Gershenzon, E. M., Gol’tsman, G. N., Gousev, Y. P., Elant’ev, A. I., & Semenov, A. D. (1991). Electromagnetic radiation mixer based on electron heating in resistive state of superconductive Nb and YBaCuO films. IEEE Trans. Magn., 27(2), 1317–1320.
Abstract: A theory of an electron-heating mixer which makes it possible to calculate all the characteristics of the device is developed. It is shown that positive conversion gain is possible for such a mixer in the millimeter to near-infrared wavelength range. The dynamic range and the optimum heterodyne power can be selected from a very wide interval by varying the mixing element volume. Measurements made for Nb within the frequency range of 120-750 GHz confirm the theory. The conversion loss obtained at T=1.6 K and normalized to the element reaches 0.3 dB in the intermediate frequency band of 40 MHz; the possible noise temperature is 50 K. The estimation of noise temperature and output band for YBaCuO at T=77 yields 200 K and more than 10 GHz, respectively.
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Hajenius, M., Barends, R., Gao, J. R., Klapwijk, T. M., Baselmans, J. J. A., Baryshev, A., et al. (2005). Local resistivity and the current-voltage characteristics of hot electron bolometer mixers. IEEE Trans. Appl. Supercond., 15(2), 495–498.
Abstract: Hot-electron bolometer devices, used successfully in low noise heterodyne mixing at frequencies up to 2.5 THz, have been analyzed. A distributed temperature numerical model of the NbN bridge, based on a local electron and a phonon temperature, is used to model pumped IV curves and understand the physical conditions during the mixing process. We argue that the mixing is predominantly due to the strongly temperature dependent local resistivity of the NbN. Experimentally we identify the origins of different transition temperatures in a real HEB device, suggesting the importance of the intrinsic resistive transition of the superconducting bridge in the modeling.
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Gershenzon, E. M., Gershenzon, M. E., Gol'tsman, G. N., Semyonov, A. D., & Sergeev, A. V. (1984). Heating of electrons in superconductor in the resistive state due to electromagnetic radiation. Solid State Communications, 50(3), 207–212.
Abstract: The effect of heating electrons with respect to phonons in a thin superconducting film driven into the resistive state by the current and the external magnetic field has been observed and investigated. This effect caused by the electromagnetic radiation is manifested in the increased resistance of the film and is not selective over the frequency range from 1010 to 1015 Hz. That the effect is frequency independent under the conditions of strong electron scattering caused by static defects is explained by the decisive role of electron -electron collisions in forming the distribution function. The characteristic time of resistance change, obtained experimentally, corresponds to the relaxation time of the order parameter near the superconducting transition and to the relaxation time of the nonelastic electron-phonon interaction at lower temperatures and in lower magnetic fields.
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Zhang, W., Miao, W., Zhong, J. Q., Shi, S. C., Hayton, D. J., Vercruyssen, N., et al. (2014). Temperature dependence of the receiver noise temperature and IF bandwidth of superconducting hot electron bolometer mixers. Supercond. Sci. Technol., 27(8), 085013 (1 to 5).
Abstract: In this paper we study the temperature dependence of the receiver noise temperature and IF noise bandwidth of superconducting hot electron bolometer (HEB) mixers. Three superconducting NbN HEB devices of different transition temperatures (Tc) are measured at 0.85 THz and 1.4 THz at different bath temperatures (Tbath) between 4 K and 9 K. Measurement results demonstrate that the receiver noise temperature of superconducting NbN HEB devices is nearly constant for Tbath/Tc, less than 0.8, which is consistent with the simulation based on a distributed hot-spot model. In addition, the IF noise bandwidth appears independent of Tbath/Tc, indicating the dominance of phonon cooling in the investigated HEB devices.
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Zhang, W., Miao, W., Yao, Q. J., Lin, Z. H., Shi, S. C., Gao, J. R., et al. (2012). Spectral response and noise temperature of a 2.5 THz spiral antenna coupled NbN HEB mixer. Phys. Procedia, 36, 334–337.
Abstract: We report on a 2.5 THz spiral antenna coupled NbN hot electron bolometer (HEB) mixers, fabricated with in-situ process. The receiver noise temperature with lowest value of 1180 K is in good agreement with calculated quantum efficiency factor as a function of bias voltage. In addition, the measured spectral response of the spiral antenna coupled NbN HEB mixer shows broad frequency coverage of 0.8-3 THz, and corrected response for optical losses, FTS, and coupling efficiency between antenna and bolometer falls with frequency due to diffraction-limited beam of lens/antenna combination.
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