Small-signal Regime Research Articles

Data-driven forced oscillation localization using inferred impulse responses

Poorly damped oscillations pose threats to the stability and reliability of interconnected power systems. In this work, we propose a comprehensive data-driven framework for inferring the sources of forced oscillation (FO) using solely synchrophasor measurements. During normal grid operations, fast-rate ambient data are collected to recover the impulse responses in the small-signal regime, without requiring the system model. When FO events occur, the source is estimated based on the frequency domain analysis by fitting the least-squares (LS) error for the FO data using the impulse responses recovered previously. Although the proposed framework is purely data-driven, the result has been established theoretically via model-based analysis of linearized dynamics under a few realistic assumptions. Numerical validations demonstrate its applicability to realistic power systems including nonlinear, higher-order dynamics with control effects using the IEEE 68-bus system, and the 240-bus system from the IEEE-NASPI FO source location contest. The generalizability of the proposed methodology has been validated using different types of measurements and partial sensor coverage conditions.

3D small-gain formula allowing strong focusing and harmonic lasing for a ring-based x-ray free electron laser oscillator

We present a detailed derivation of a formula for the small-gain calculation for an x-ray free electron laser oscillator (XFELO) based on a medium-energy (3–4 GeV) storage ring. We found harmonic lasing and strong focusing are essential for this beam energy range. Taking the small-signal low-gain formula developed by Kim and his colleagues, we modified it in such a way that the gain can be calculated without the “no focusing approximation,” and a strong focusing can be applied, as well as harmonic lasing. In this formula, the gain is represented as a product of two factors with one of them depending only on the harmonic number, undulator period, and gap. Using this factor, we show that it is favorable to use harmonic lasing to achieve hard x-ray FEL working in the small-signal low-gain regime with the medium-energy electron beam. Our formula also allows FEL optimization by varying the vertical gradient of the undulator, the vertical dispersion, and the horizontal and vertical focusing, independently. As an example, we applied this formula to study the feasibility of an XFELO option for the National Synchrotron Light Source II (NSLS-II) upgrade. Since a quite high peak current is required for the FEL, collective effects of beam dynamics in medium-energy synchrotrons significantly affect the electron beam parameters. We carried out a multiparameter optimization taking collective effects into account. Note, even though our example is for a ring-based XFELO at 3 to 4 GeV, the formula and, in particular, the approach developed here may be applied to other types of FELs. Published by the American Physical Society 2024

Analytical solution to second-harmonic generation of ultrashort laser pulse

We present an analytical method to evaluate the second-harmonic generation (SHG) process of ultrashort laser pulses in a nonlinear medium within the small-signal regime. Building upon the broadband nonlinear coupled wave theory, we derive an analytical solution that allows one to investigate the fundamental physics and detailed dynamics of the nonlinear interaction between ultrashort laser pulses. We find that SHG for ultrashort laser pulses in a nonlinear crystal arises from a series of self-SHG and self sum-frequency generation processes involving different frequency components. We have applied the analytical method to investigate specific pulse profiles with Gaussian and sech functions and found good agreement between analytical theory and numerical simulations, validating the accuracy of the analytical approach. The analytical method enables one to explore the evolution of the second-harmonic wave under various pulse profiles, pulse widths, and crystal thicknesses, and offers a more efficient and insightful approach to study the nonlinear optical dynamics of ultrashort laser pulses.

MMW Signal Gain in DML-Based Microwave Photonic Links Under Large Signal Regime

This paper presents a theoretical and experimental analysis of the millimeter wave (mmW) signal gain observed in photonically generated signals by using carrier suppressed (CS) external modulation in a centralized network architecture while the data is transmitted over a directly modulated laser (DML) operating under different signal regimes. Measurements of the frequency response under small and large signal regimes are presented for the sake of comparison. Moreover, the mmW signal gain has been measured for different standard single mode fiber (SSMF) lengths in order to identify the conditions and impact of large signal regime operation. The results are also validated by the experimental transmission of a 25 MHz QPSK signal transmitted over 40 GHz since the error-vector-magnitude (EVM) is measured for different input electrical power values as well as several received optical power (RoP) levels. Moreover, the spurious-free dynamic range (SFDR) ratio is measured to compare the third-order intermodulation distortion (IMD3) between small and large signal regime. The quantitative results demonstrate that proper system conditions allow the exploitation of the mmW signal gain towards the future deployment of high energy efficient networks.

Induction Heating of Two Magnetically Independent Loads With a Single Transmitter

This article introduces the design of a system capable of heating two magnetically independent ferromagnetic loads placed on different horizontal planes, which uses a combination of induction heating and inductive coupling, called inductively coupled heating. The system uses a single primary inductor acting as a transmitter to transfer power to a secondary inductor attached to the bottom load, which is connected electrically with a third inductor that heats the top load. Since power of the whole system is supplied by a simple half-bridge inverter, the ratio of the delivered power to each of the loads, which is critical for cooking results, is entirely dependent on the system's geometry, coil's number of turns, and compensation capacitors. A finite-element model is used to simulate the magnetic fields generated by inductor currents and calculate the impedance matrix. With the impedance, capacitor values and inductors’ number of turns are selected with the objective of achieving a high power ratio between the top and bottom zones, as well as minimizing stress in the electronics. First, a prototype was built to validate the impedance results in the small-signal regime, and then, the full power regime was used to verify power and current simulations

Spatio-spectral beam control in multimode diode-pumped Raman fibre lasers via intracavity filtering and Kerr cleaning

Multimode fibres provide a promising platform for boosting the capacity of fibre links and the output power of fibre lasers. The complex spatiotemporal dynamics of multimode beams may be controlled in spatial and temporal domains via the interplay of nonlinear, dispersive and dissipative effects. Raman nonlinearity induces beam cleanup in long graded-index fibres within a laser cavity, even for CW Stokes beams pumped by highly-multimode laser diodes (LDs). This leads to a breakthrough approach for wavelength-agile high-power lasers. However, current understanding of Raman beam cleanup is restricted to a small-signal gain regime, being not applicable to describing realistic laser operation. We solved this challenge by experimentally and theoretically studying pump-to-Stokes beam conversion in a graded-index fibre cavity. We show that random mode coupling, intracavity filtering and Kerr self-cleaning all play a decisive role for the spatio-spectral control of CW Stokes beams. Whereas the depleted LD pump radiation remains insensitive to them.

A 178.9-dB FoM 128-dB SFDR VCO-Based AFE for ExG Readouts With a Calibration-Free Differential Pulse Code Modulation Technique

This article presents a voltage-controlled oscillator (VCO)-based analog front end (AFE) for ExG readout applications with both a wide dynamic range (DR) and high linearity. By using a differential pulse code modulation (DPCM) technique, VCO non-linearity is mitigated by operating the VCO in the small-signal linear regime. To minimize power consumption from the power-hungry gain error calibration, the effect of VCO gain variation within the DPCM loop is investigated, leading to a calibration-free DPCM via a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta \Sigma $ </tex-math></inline-formula> truncator. At the circuit level, a coarse–fine phase decoding scheme is proposed to increase signal-to-quantization-noise ratio (SQNR) while avoiding metastability issues. Fabricated in 65 nm, the AFE occupies an area of 0.056 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . It achieves 94.2-dB SNDR and 95.1-dB DR in 500 Hz of bandwidth while dissipating 1.68- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{W}$ </tex-math></inline-formula> power from a single 0.8-V supply, yielding a Schreier FoM of 178.9 dB. Importantly, the techniques enable a virtually distortion-less spectrum with a noise-floor limited spurious-free dynamic range (SFDR) of 128 dB. In addition, the AFE is validated with ECG and EOG recording, demonstrating complete signal capturing in the presence of motion/stimulation artifacts.

Signal Conditioning Stage in S-Band Communication Subsystem for CubeSat Applications

This work presents the design, performance evaluation, manufacture, and characterization of an RF front-end signal conditioning chain on a substrate that achieves the best performance at S-band frequencies and complies with the dimensions of the international standard for CubeSat-type nanosatellites. In this development, the signal conditioning chains were carried out on the high-frequency substrates RO4350B, CuClad 250, and RT/duroid 5880, considering scattering parameters in a small-signal regime. Concerning the power output, after the filtering and amplifying stages, the conditioning chain delivered 2 watts at 2.25 GHz. Moreover, up to 40 dB gain was achieved, and a good impedance matching at −20 dB for both input and output ports was observed. The numerical simulations and experimental results showed that an RO4350B substrate allows the smallest design dimensions, and these comply with the dimensions of the CubeSat standard. The manufactured RF front-end signal conditioning chain on RO4350B requires an area of 95 mm2, and it is ready to be used in a proof-of-concept space mission in a CubeSat.

Radiation-induced conductivity in polystyrene, a common insulating polymer with a hopping conduction

Radiation-induced conductivity (RIC) of polystyrene has been studied experimentally and numerically mostly in a small-signal regime in a broad time range from some nanoseconds to seconds. It has been established that hole transport is dispersive with a low value of the dispersion parameter α = 0.35. We have suggested a direct method of determination of the frequency factor of the Rose–Fowler–Vaisberg model, which has been parameterized using computer simulations by the trial and error method. The main outstanding concern is the application of the Onsager theory of geminate recombination concerning the field dependence of the free carrier yield and the possible frequency factor increase at high electric fields. The effect of hopping transport on the RIC in this common insulating polymer is still to be understood.

Experimental demonstration of 1011 temporal contrast in pure nanosecond optical parametric chirped pulse amplifiers.

The temporal contrast of ultrashort and ultraintense laser pulses can significantly influence the laser-plasma interactions. As the optical parametric chirped pulse amplification (OPCPA) has been widely adopted in these laser facilities, the inherent optical parametric fluorescence, exhibiting a pedestal in the time window of the pump pulse, has become a significant problem. In this paper, we investigated experimentally its influence on the contrast of the compressed pulses at 808 nm using a multistage OPCPA amplifier. Compared to the highest value of 108 ever reported in the literature for such a type of regime, by adjusting the pump energy allocation between OPCPA stages and controlling the gain of small signal regime, we for the first time, to the best of our knowledge, realized a 1011 temporal contrast in a pure nanosecond OPCPA design at a gain exceeding 7×108, without adopting any other noise cleaning methods, such as picosecond OPCPA, cross-polarized wave generation, etc. This indicates that the OPCPA has a very significant potential for contrast improvement and to become a candidate for the future high-energy amplifiers in ultrashort high-power laser facilities.

Injection locking and noise reduction of resonant tunneling diode terahertz oscillator

We studied the injection-locking properties of a resonant-tunneling-diode terahertz oscillator in the small-signal injection regime with a frequency-stabilized continuous THz wave. The linewidth of the emission spectrum dramatically decreased to less than 120 mHz (half width at half maximum) from 4.4 MHz in the free running state as a result of the injection locking. We experimentally determined the amplitude of injection voltage at the antenna caused by the injected THz wave. The locking range was proportional to the injection amplitude and consistent with Adler’s model. While increasing the injection amplitude, we observed a decrease in the noise component of the power spectrum, which manifests the free-running state, and an alternative increase in the injection-locked component. The noise component and the injection-locked component had the same power at the threshold injection amplitude as small as 5 × 10−4 of the oscillation amplitude. This threshold behavior can be qualitatively explained by Maffezzoni’s model of noise reduction in general limit-cycle oscillators.

Electron Transport in Polyethyleneterephthalate

The electron transport is studied experimentally by measuring pulsed radiation-induced conductivity in polyetheleneterephthalate under bulk irradiation of polymer films by fast electron pulses in a small-signal regime. Numerical simulation is performed using a multiple trapping model with an exponential energy trap distribution. It is shown that, contrary to the reported interpretation of this phenomenon, there is no electron extraction to electrodes under these experimental conditions. In reality, the electron dispersive transport in PET occurs in the presence of the monomolecular capture of electrons by deep traps of biographic origin.

Theoretical Analysis of the Radiation-Induced Conductivity in Polymers Exposed to Pulsed and Continuous Electron Beams.

We have performed comparative numerical calculations using a multiple trapping (MT) formalism with an exponential and an aggregate two-exponential trap distributions for describing two mostly used experimental setups for studying the radiation-induced conductivity (RIC) and the time-of-flight (TOF) effects. Computations have been done for pulsed and long-time electron-beam irradiations in a small-signal regime. Predictions of these two approaches differ appreciably in both setups. The classical MT approach proved very popular in photoconductive polymers generally and in molecularly doped polymers in particular, while a newly proposed complex MT worked well in common polymers. It has been shown that the complex MT successfully accounts for the presence of inherent deep traps, which may or may not have an energy distribution.

Comparative study on coherent noise in optical parametric and quasi-parametric chirped-pulse amplification

The coherent noise inherent to optical parametric chirped-pulse amplification (OPCPA) poses a fundamental limitation on the temporal quality of current ultrashort ultraintense lasers as well as their applications in strong-field physics research. Here we present a peer comparison of coherent noise between OPCPA and one of its alternatives — quasi-parametric chirped-pulse amplification (QPCPA). In the initial amplification stage termed as small-signal regime, the spectrum of chirped signal pulse in either OPCPA or QPCPA is exposed to the imperfections in pump pulse and optics, resulting in coherent noise pedestals in the time domain. While in the final amplification stage featured by amplifier saturation, the nonlinear growths of coherent noise become sharply different. We demonstrate that the non-parametric saturation behavior of QPCPA can greatly smooth the spectral distortions of signal, and thus bring down the coherent noise. Consequently, QPCPA scheme allows an improvement of pulse contrast by 2–3 orders of magnitude. The results presented in this paper provide a new perspective on high-contrast amplification of ultrashort pulses.

Subharmonic Temporal Response and Spontaneous Breaking of Discrete Time Symmetry in Plasmonic Distributed Feedback Laser

Distributed feedback (DFB) lasers exploiting plasmonic structures as cavities are basic elements for various applications from sensorics to optoelectronics. Herein, the time response of a plasmonic DFB laser in the small‐signal modulation regime is studied. It is shown that the temporal period of the plasmonic DFB laser response can be equal to an integral multiple of the period of the pumping modulation, i.e., the temporal response can be subharmonic. This behavior of systems with time‐dependent parameters is a manifestation of spontaneous breaking of the discrete time symmetry. The appearance of subharmonic frequencies in the plasmonic DFB laser response is a consequence of synchronization of the beat frequency of the modes of plasmonic structures. Synchronization occurs when this beat frequency is nearly equal to the modulation frequency divided by an integer. It is shown that the ratio of the response period to the pump modulation period is determined by the size of the pumped region in the active medium, and the modulation frequency for the plasmonic DFB laser in the small‐signal modulation regime can reach several terahertz. These facts pave the way for the creation of tunable optoelectronic devices with a controlled temporal response.

The Cyclotron Auto-Resonance Maser: Analytical and numerical study

We study the small signal regime of Cyclotron Auto-Resonance Maser (CARM), using different computational tools. The analysis is motivated by the necessity of an accurate benchmarking of the design parameter for the CARM device under construction at ENEA Frascati center. The main goal is that of comparing the results from three different procedures, the analytical formulation and two different numerical items: the home-made code GRAAL (Gyrotron Radiation Auto-Resonance Amplification Laser) and the, commercially available, software package CST. We prove the substantial consistence between the different methods and comment on the reasons leading to the discrepancies. The extension to the non-linear regime is finally touched on.

Time-Resolved Radiation-Induced Conductivity of Polyimide and Its Description Using the Multiple Trapping Formalism.

Polymer dielectrics subjected to intense radiation fluxes exhibit a radiation-induced conductivity (RIC). Polyimide is a good dielectric with excellent mechanical and thermal properties featuring high radiation resistance currently widely used in the spacecraft industry. Its RIC has been extensively studied in several laboratories. The purpose of the present study is to make a direct measurement of the RIC for both pulsed and continuous irradiation using a current sensing technique, which is contrary to the indirect method employing a surface-potential decay technique that is now preferred by spacecraft charging engineers. Our experiments are done in a small-signal regime excluding any recombination and dose effects. In combination with existing computer codes, we managed to develop further the conventional multiple trapping formalism and the RIC theory based on it. The main idea is to supplement an exponential trap distribution responsible for a dominant dispersive carrier transport in polymers with a small concentration of inherent deep traps which may or may not have an energy distribution. In line with this reasoning, we propose a tentative set of RIC model parameters for polyimide that accounts for the observed experimental data. The findings and their implications are discussed in a broad context of previous studies.

Analysis of Oscillations in Confocal Gyrotron Travelling-Wave Amplifiers

In this article, key parameters that characterize field distribution and beam-wave coupling in confocal circuits are studied. The kinetic theory of confocal gyro-TWT considering launching loss is deduced based on it, which is capable of predicting the linear gain rate of confocal circuits with arbitrary mirror widths. Numerical results manifest that the output power/gain versus interaction position agrees well with the nonlinear results in the small-signal regime. In addition, main oscillations in confocal circuits including the near-cutoff oscillation and backward-wave oscillation (BWO) have been examined. Analytical expressions that can predict the near-cutoff oscillation threshold of uniform circuits without considering loss are derived and kz-f plots are introduced for lossy circuits. Furthermore, an algorithm that can automatically search the BWO start-oscillation thresholds of confocal circuits with arbitrary mirror widths has been developed.

Generation of the Pulse Signals, Which are Analogs of Temporal Solitons, in an Active Ring Resonator with a Klystron Amplifier and a Spin-Wave Transmission Line

We present the results of experimental studies of the oscillation regimes of the pulse signals, which are analogs of the temporal solitons, in a distributed active ring resonator with a multicavity klystron amplifier and a spin-wave transmission line. The soliton-like pulses are formed under conditions of three-wave parametric decay of a surface magnetostatic spin wave when the klystron amplifier operates in a small-signal regime. Parametric turbulence is shown to cause the chaotic nature of generated patterns, which is confirmed by the performed estimations of the senior Lyapunov exponent from experimental time series. In addition, the possibility of controlling the phase coherence, the autocorrelation time, and the noise-to-signal ratio of the generated chaotic soliton-like pulses by varying the beam current and the acceleration voltage of the klystron amplifier is demonstrated.

Microwave Rabi resonances beyond the small-signal regime

The coupling between microwave fields and atoms (or atom-like systems) is inherently weaker than for optical fields, making microwave signal manipulation for applications like quantum information processing technically challenging. In order to better understand this coupling and to develop tools for measuring it, we explore the microwave coupling to atoms using the "atomic candle" technique, and push it beyond the bounds of the small-signal regime in order to deliver a larger signal. In familiar two-level systems, responses beyond the usual Rabi oscillations can arise when a single-tone drive is phase-modulated, causing the steady-state populations to oscillate at integer harmonics of the modulation frequency. Resonant behavior of the first two harmonics for frequencies near the Rabi frequency, known as $\alpha$ and $\beta$ Rabi resonances, is widely used for microwave-field magnetometry and as a power standard known as the atomic candle. Here, we explore Rabi resonances beyond the small-signal approximation and report upon experimental observations of higher-harmonic population response for microwave hyperfine transitions in cold $^{87}\rm Rb$ atoms, which we compare to numerical simulations.