Pumping conditions for parametric gain with a nonlinear immittance element

Josephson traveling wave parametric amplifiers can have high gain and wide frequency range, high sensitivity, and low noise, which makes them promising for quantum computing, array receiver readout systems, spectroscopy, single-photon detectors, etc. In this paper, the authors investigate samples of traveling wave parametric amplifiers based on a three-layer Nb/AlOx/Nb superconductor–insulator–superconductor (SIS) structure with a SNAIL (Superconducting Nonlinear Asymmetric Inductive Elements) series array. Each SNAIL cell consists of the kinetic inductance of four SIS junctions and the nonlinear inductance of a smaller SIS junction. The cells are alternately connected in antiphase with respect to the magnetic flux, which ensures a change in the sign of the Kerr nonlinearity and a reduction in the phase mismatch for the pump frequency, signal frequency, and idler frequency. The transmission spectra of the samples were measured at temperatures of 4.2 and 2.8 K in the frequency range of 0.1–6 GHz.

A lifting-linearization method based on the Koopman operator and Dual Faceted Linearization is applied to the control of a robotic excavator. In excavation, a bucket interacts with the surrounding soil in a highly nonlinear and complex manner. Here, we propose to represent the nonlinear bucket-soil dynamics with a set of linear state equations in a higher-dimensional space. The space of independent state variables is augmented by adding variables associated with nonlinear elements involved in the bucket-soil dynamics. These include nonlinear resistive forces and moment acting on the bucket from the soil, and the effective inertia of the bucket that varies as the soil is captured into the bucket. Variables associated with these nonlinear resistive and inertia elements are treated as additional state variables, and their time evolution is represented as another set of linear differential equations. The lifted linear dynamic model is then applied to Model Predictive Contouring Control, where a cost functional is minimized as a convex optimization problem thanks to the linear dynamics in the lifted space. The lifted linear model is tuned based on a data-driven method by using a soil dynamics simulator. Simulation experiments on homogeneous soil verify the effectiveness of the proposed lifting linearization compared to its counterpart.

This work presents the theory and experimental demonstrations of frequency-controlled energy absorption in parametric mixing circuits which may find applications in the design of tunable notch filters and frequency-selective surfaces. A time-varying capacitance model is used to describe the energy exchange among the pump, signal, and idler frequencies in parametric mixing circuits. Analytical derivations reveal that under specific frequency ordering, the system exhibits a positive conductance at the signal frequency that is correlated with the pump frequency, leading to measurable energy absorption. A fabricated on-chip circuit operating between 1.3 and 2.3 GHz serves as a physical representation of the theoretical model, experimentally validating the predicted energy transfer behavior. The results establish a unified framework linking circuit-level phenomena to the fundamental physics of energy redistribution in parametric systems.

A model of the carotid vascular system with stenosis at the carotid bifurcation

An algorithm closely following Bergeron's method has been developed to calculate transients in a transmission system with step input. The transmission system includes a transmission line, a transformer, a load, and a thyrite arrester. It is shown how an exact solution can be obtained with the help of this algorithm when a resistive non-linearity is presented in the system.

A Superconducting QUantum Interference Device (SQUID) modulated by a fast oscillating magnetic flux can be used as a parametric amplifier, providing gain with very little added noise. Here, we develop linearized models to describe the parametrically flux-pumped SQUID in terms of an impedance. An unpumped SQUID acts as an inductance, the Josephson inductance, whereas a flux-pumped SQUID develops an additional, parallel element which we have coined the ``pumpistor.'' Parametric gain can be understood as a result of a negative resistance of the pumpistor. In the degenerate case, the gain is sensitive to the relative phase between the pump and signal. In the nondegenerate case, gain is independent of this phase. We develop our models first for degenerate parametric pumping in the three-wave and four-wave cases, where the pump frequency is either twice or equal to the signal frequency, respectively. We then derive expressions for the nondegenerate case where the pump frequency is not a multiple of the signal frequency, where it becomes necessary to consider idler tones which develop. For the nondegenerate three-wave case, we present an intuitive picture for a parametric amplifier containing a flux-pumped SQUID where current at the signal frequency depends upon the load impedance at an idler frequency. This understanding provides insight and readily testable predictions of circuits containing flux-pumped SQUIDs.

Distributed nonlinear resistive elements are incorporated into an antenna theory (AT) model with fixed inductive loading (ATIL-F) to realistically model the current wave propagation along the lightning return-stroke channel (RSC). Resistive elements are considered as a nonlinear distributed load whose resistance is a function of both current and time. This is adopted from the numerical models of a spark channel and consequent shockwave from a lightning discharge, yielding a changing value of the channel radius from the base to the cloud along the RSC. It is demonstrated that the proposed model is more consistent with the nonlinear behavior of a lightning channel inferred from experimental physical observations. The model also satisfies most of the well-known characteristics of RSC, including the temporal and spatial current and charge distributions, some important features observed in radiated electromagnetic fields, and wave propagation speed profiles along the channel when compared with those predicted by the ATIL-F model.

This paper discusses the properties of mixers in terms of linear-network theory. In Part I the network equations are derived from the fundamental properties of nonlinear resistive elements. Part II contains a résumé of the appropriate formulas of linear-network theory. In Part III the network theory is applied, first to the case of simple nonlinear resistances, and next to the more general case where the nonlinear resistance is embedded in a network of parasitic resistive and reactive passive-impedance elements. In Part IV application of the previous results is made to the measurement of performance properties. The "impedance" and the "incremental" methods of measuring loss are contrasted, and it is shown that the actual loss is given by the incremental method when certain special precautions are taken, while the impedance method is in itself incomplete.

Ferroresonance is a phenomenon that occurs in the transformer core, and is characterized by the presence of abnormal voltages. An electrical circuit that can cause ferroresonance has elements of resistance (R), capacitance (C), and non-linear inductance (L). In this research, the phenomenon of a surge in the value of the transformer current and voltage, which has changed drastically (jump phenomenon) after being triggered by an increase in the source voltage of about 1%, has been found out. The emergence of this jump phenomenon can trigger the emergence of ferroresonance. This will cause the transformer not to work normally in its linear region but in non-linear (saturation) regions. The test has been carried out on a 220 V 3-phase low-voltage transformer with H-core type and M-core type. Then the initiation factors such as source voltage variation and capacitance variation have been given to the system. Trends in the waveforms of voltage, current, voltage at source, transformer capacitor have been analyzed. The test results have showed that the given initiation factor can explain the correlation between the jump phenomenon characteristics and the presence of ferroresonance in the H-core and M-core transformers. When ferroresonance has appeared, the voltage value has been relatively high in the H-core type transformer. The largest value of voltage and current of the transformer occurs at 30 uF in S-phase with a transformer voltage value of 265.8 V and a current value of 5.7 A. Whereas, the ferroresonance mode in H-core and M-core is the fundamental ferroresonance mode.

We report the theoretical analysis of an optical parametric oscillator that contains an intracavity crystal that generates the difference frequency between the signal and the idler produced by the optical parametric oscillator crystal. Phase mismatch in the difference-frequency mixer is considered. The cavity is singly resonant at the signal frequency. We find that high conversion efficiency of the difference and idler frequencies can be achieved over a large dynamic range of the incident pump intensity. A physical example that produces 3.192 μm from a 1.064-μm pump laser is predicted to produce 97.5% quantum efficiency in one polarization component and 197% quantum efficiency in the orthogonal-polarization component for a total power conversion efficiency of 98.2%.

Unusually low noise, combined with high stable gain over fairly wide bands, has been obtained with electron beam amplifiers of a new kind. This paper explains how this performance is achieved by the action of a transverse quadrupole field upon a fast cyclotron wave. The first two sections give a qualitative description of the device and of the amplifying mechanism. A physical picture of the fast cyclotron wave is used to explain the interchange of signal and noise in the input coupler and the mechanism of parametric amplification in the quadrupole region. The third section presents a detailed analysis of the amplification process. It shows that the fast cyclotron wave is amplified in accordance with a cosh function of distance traveled through the quadrupole, and that a new cyclotron wave at idler frequency (difference between pump and signal frequencies) is generated which grows as a sinh function of distance. The fourth section describes experimental tubes built to date. These operate on frequency bands between 400 and 800 mc. Typical bandwidth is 40 to 50 mc independent of gain, which may be adjusted to 20 or 30 db. Residual noise temperature of the electron beam in good specimens within this experimental lot is 70°K; input coupler loss raises this figure to about 100°K. This is equivalent to a noise figure of 1.4 db if the device is used, for instance, in radio astronomy.

VA 22901 ABSTRACT' ~. This paper presents the results of a theore- tical study of low noise ampl.ification techniques for wide bandwidth optical arid inf.rared heterodyne receivers; noise figures of 1..5 dB or less over a bandpass of 10 MIIz to 1.5 GHz: are the goal. Data for the state of the art trarisisto.r amplifiers is presented showing that the btst obtainable noise figure is 1.5 dB. Other methods of obtaining the low noise figure are presented with emphasis on wide bandwidth parametric and photoparametric amp- lifiers. devices but wide bandwidths are hard to obtain, thus the design criteria for wide bandwidth opera- tion are discussed. Theoreti-cal d,sta is presented showing gain as a function of: did(? capacitance, resistance,signal frequency and idler frequency. Finally, the feasibility of these (devices for use in a heterdyne receiver is discussed. Low noise is easily obtainable with these

This paper focuses on a numerical simulation of the arc plasma behavior in the arc splitting process, considering the eddy currents in the electrodes and the splitter plate. Based on three-dimensional (3D) magneto-hydrodynamic (MHD) theory, a thin layer of nonlinear electrical resistance elements is used in the model to represent the voltage drop of plasma sheath and the formation of new arc root in order to include the arc splitting process in the simulation. In the arcing process, eddy currents in metal parts are generated by a time-varying magnetic field. The arc model is calculated with the time-varying magnetic field term, so that the eddy current effects can be considered. The effect of nonlinear permeability of a ferromagnetic material is also involved in the calculation. Using the simulation results for the temperature, velocity and current density distribution, the arc splitting process is analyzed in detail. The calculated results are compared with the simulation neglecting eddy currents.

An analysis is presented of variable-capacitance parametric amplifiers for the case where there is a loss resistance in series with the capacitance. Such a resistance provides the major form of loss in a reverse-biased semiconductor diode. It is shown that the coupling of two circuits by a pumped variable capacitance can be described by a simple equivalent circuit which has a direct physical interpretation. The characteristics of regenerative amplifiers and convertors, and of non-inverting convertors, are deduced from the equivalent circuits. The gain, bandwidth and noise properties of these amplifiers or convertors are shown to depend on two parameters of the pumped variable capacitance C, the mean Q at the signal frequency and the normalized amplitude of the variation of 1/C at the pump frequency. The noise temperature in each case is a function only of the product of these two parameters and the ratio of signal to idler (or output) frequencies. Particular attention is given to finding the optimum operating conditions and a brief discussion is given of the effects of variations of the capacitance at harmonics of the pump frequency, and of higher sidebands.

There have been impressive advances in the area of microresonator-based frequency combs (microcombs) during the last decade, making their way into applications in a wide variety of fields [1]. Although microcombs are commonly generated making use of third-order ( χ (3) ) nonlinear processes, several groups have recently started to investigate frequency comb generation based on the second-order ( χ (2) ) nonlinearity as it bears potential benefits like the linear electro-optic effect for either tuning or stabilization, or the possibility to convert light into more challenging spectral regions like the UV or mid-infrared [2] , [3]. For the latter, one approach is to start with optical parametric oscillation (OPO) and to operate it close to degeneracy. Then, a series of second-order nonlinear processes takes place, generating equidistant comb lines around both the pump frequency and the sub-harmonic frequency [2] , [4] . A promising χ (2) material to move into the mid-infrared region is cadmium silicon phosphide (CdSiP 2 ) which is transparent from 1 to 6.5 µm and has a high nonlinearity of 84.5 pm/V. Furthermore, OPO has already been shown for a CdSiP 2 mm-sized whispering gallery resonator pumped at telecom wavelength [5]. Based on these observations, we investigate OPO operation close to the point of degeneracy and this way, the possibility to generate frequency combs both around 1.5 µm and 3 µm. In this work, we have observed OPO with thresholds below 100 µW and conversion efficiencies of around 17 %. We could tune the OPO output wavelengths from 2.3 to 5 µm by coupling the pump light into different modes of the resonator and by controlling its temperature. One of the pump modes investigated enabled operation near degeneracy. Measured signal and idler wavelengths for this pump mode are plotted in figure 1a ) for different temperatures. However, OPO near degeneracy is prone to instabilities, as several parametric oscillations can be excited under similar conditions. Here, by tuning the temperature in the mK range and the pump detuning with respect to the resonance in the MHz range, the minimum obtained difference between signal and idler frequencies was 120 GHz (4 FSRs). Nonetheless, in this state we have already observed sidebands generated around the pump corresponding to SHG as shown in figure 1b ). Why operation closer to the point of degeneracy is hampered, is currently under investigation. A possibility to gain further insight and control on OPO operation might be to make use the linear electro-optic effect for fine tuning of the relative position of the resonances between the pump and the sub-harmonic frequencies.