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The Microwave SQUID Multiplexer (μ MUX) is the device of choice for the readout of a large number of low-temperature detectors in a wide variety of experiments within the fields of astronomy and particle physics. While it offers large multiplexing factors, the system noise performance is highly dependent on the cold- and warm-readout electronic systems used to read it out, as well as the demodulation domain and parameters chosen. In order to understand the impact of the readout systems in the overall detection system noise performance, first, we extended the available μ MUX simulation frameworks, including additive and multiplicative noise sources in the probing tones (i.e., phase and amplitude noise), along with the capability of demodulating the scientific data, either in the resonator's phase or the scattering amplitude. Then, considering the additive noise as a dominant noise source, the optimum readout parameters to achieve minimum system noise were found for both open-loop and flux-ramp demodulation schemes in the aforementioned domains. Later, we evaluated the system noise sensitivity to multiplicative noise sources under the optimum readout parameters. Finally, as a case study, we evaluated the optimal demodulation domain and the expected system noise level for a typical software-defined radio readout system. This work leads to an improved system performance prediction and noise engineering based on the available readout electronics and the selected demodulation domain. [ABSTRACT FROM AUTHOR]

In this paper, we present the design and performance evaluation of a prototype device based on gain-driven polariton, which can function as an amplifier. This device can outperform a single microwave cavity in terms of phase noise and stability. Employed as a standalone amplifier, it demonstrates consistency between input and output phase noise, achieving a gain of up to 35 dB with a typical output of 5 dBm at 4.26 GHz. Despite its limited bandwidth, the device provides an effective solution for small signal amplification, ensuring minimal noise introduction. [ABSTRACT FROM AUTHOR]

A numerical model describing a magnonic active ring oscillator (MARO) based on a microscopic spin-wave delay line is proposed. The model considers excitation, propagation, and reception of the magnetostatic surface waves in a yttrium iron garnet (YIG) magnetic film with a thickness in the nanometer range. The waves are excited and received with a microscopic coplanar antenna. We employed the model to analyze the influence of the YIG-film thickness and the distance between the antennas on the MARO performance characteristics. We showed that an increase in the delay time inserted by the delay line reduces the phase noise of the MARO and increases the auto-oscillation threshold. In addition, we found a relation between the auto-oscillation threshold, the thickness of the YIG film, and the distance between the antennas. The relation helps design miniature MAROs and suggests a way to reduce the phase noise of the device. The model predicts a phase noise level of −115 dBc/Hz at a 10 kHz offset from an oscillation frequency in the vicinity of 5 GHz for the MARO based on a 100 nm-thick YIG film and 56 μm of distance between the coplanar nano-antennas of the YIG-film based delay line. We believe that this is a clear way forward to microminiaturize the time-delay feedback microwave auto-oscillators. A further reduction in the phase noise down to −125 dBc/Hz at a 10 kHz offset is found in a model of cascaded connection of several microscopic spin-wave delay lines. [ABSTRACT FROM AUTHOR]

Phase-sensitive amplification of squeezed states is a technique to mitigate high detection loss, which is especially attractive at 2 µ m wavelengths. We derived an analytical model proving that amplified squeezed states can mitigate phase noise significantly. Our model discloses two practical parameters: the effective measurable squeezing and the effective detection efficiency of amplified squeezed states. A realistic case study includes the dynamics of the gain-dependent impedance matching conditions of the amplifier. Our results recommend operating the optical parametric amplifier at high gains because of the signal-to-noise ratio's robustness to phase noise. Amplified squeezed states are relevant in proposed gravitational wave detectors and interesting for applications in quantum systems degraded by the output coupling loss in optical waveguides. [ABSTRACT FROM AUTHOR]

This study focuses on optimizing the resonator geometry via the aspect ratio design of a width-extensional mode resonator to improve its quality factor (Q), which is one of the critical performance parameters for resonators in either sensing (Allan deviation) or frequency reference (phase noise) applications. The proposed approach uses finite element analysis to reduce the strain energy at anchor supports by altering the resonator geometric structure, thereby reducing energy loss through anchors. Moreover, process limitations on feature sizes are used as constraints to find aspect ratios that can not only increase the Q but also reduce spurious modes near the targeted frequency. The devices were fabricated using AlN thin film piezoelectric on a substrate (TPoS) process. The simulated energy dissipation trends for specific length-to-width (L / W) ratios closely match the measured changes in the resonator Q values in vacuum. In vacuum, the highest Q -factor achieved by the device is close to 8816, with a motional resistance of a few tens of ohms. Additionally, a board-level oscillator realized using a commercial low-noise amplifier exhibits phase noise performance of −141.21 dBc Hz−1 and −164.25 dBc Hz−1 at 1 kHz and 1 MHz frequency offsets, respectively. The calculated figures of merit for these offsets are 204 and 168, respectively. [ABSTRACT FROM AUTHOR]

Single-mode semiconductor laser operating near the 2 μm wavelength is of great interest for trace-gas detection, remote sensing, and infrared spectroscopy. Here, we present the 2 μm-wavelength-range laser sources with high output power, precise wavelength control, and narrow spectral linewidth enabled by hybrid integration of a GaSb-based gain chip with silicon nitride Bragg gratings. Low-kappa gratings are used as the laser feedback component to accurately select the lasing wavelength and increase the photon lifetime to achieve narrow-linewidth laser emission. The hybrid laser outputs 33.7 mW optical power with a side mode suppression ratio better than 40 dB near the 2 μm wavelength at room temperature. More than 20 lasers with an excellent wavelength spacing of 2.68 nm is demonstrated. The wavelength deviation is less than ±0.1 nm for all lasers. The intrinsic linewidth of the hybrid integrated external cavity laser with a 4.35 mm long feedback grating is measured to be ∼8.8 kHz using the phase noise demodulation method. [ABSTRACT FROM AUTHOR]

Summary: In the first part of this paper, we closely examine well‐known methods for balancing the output power level of the pseudo‐differential current‐reuse voltage‐controlled oscillator. We scrutinize their effectiveness in terms of canceling output mismatches, insensitivity to process, voltage, and temperature variations, and their capability of not degrading phase noise performance. Through analyses and simulations, it is shown that contrary to common belief, some techniques are not as effective as previously thought and should be employed only under specific circumstances. The best conventional approach is proven to be the use of a common‐mode shunting capacitor at the inductor's center tap node to create a virtual ground. In the second part, it is demonstrated that the current‐reuse voltage‐controlled oscillator can intrinsically produce balanced outputs without using any additional techniques or extra passive or active components. Using single‐ended tank capacitors instead of differential ones, the common‐mode voltage of the outputs is shunted to the real ground. This technique reintroduces a reference voltage to the tank circuit, forcing the oscillator to achieve equilibrium between positive and negative swings. The proposed current‐reuse oscillator is designed and post‐layout simulated in a 65‐nm CMOS process, covering a frequency range of 4.84–6.38 GHz with an average power consumption of 0.65 mW. It produces balanced outputs with an amplitude error of less than ±0.2% and achieves a phase noise of −126.7 dBc/Hz and FoMT of 201.8 dB at a 3‐MHz offset frequency. [ABSTRACT FROM AUTHOR]

Frequency combs are powerful tools for many applications and high performances are achieved by stabilizing these lasers. For operation in the mid‐infrared, quantum cascade lasers (QCL) are ideal candidates as they present numerous advantages. However, stabilized QCL‐combs lack a detailed characterization of their noise properties due to the sensitivity limits of current analyzing techniques. To overcome these challenges, what is believed to be the first tightly locked dual QCL‐comb system is developed. Its use is twofold. First, phase noise analysis of the dual‐comb signal shows residual phase noise below 600 mrad for all comb lines, and the comb coherence as well as the performances of the repetition frequency locking mechanism is characterized. Second, coherent averaging with a 7 × 105 Hz1/2 figure‐of‐merit system is demonstrated, which is compatible with high‐precision spectroscopy. [ABSTRACT FROM AUTHOR]

In this paper, a voltage differencing buffered amplifier (VDBA)-based second-order sinusoidal oscillator (SO) configuration, which provides voltage output at low impedance, is proposed. The circuit employs single VDBA, three resistors and two grounded capacitors, which presume its easy monolithic integration with preferred circuit simplicity. The nonidealities of VDBA due to parasitic and tracking errors are taken into consideration to study the nonideal behavior of proposed SO. Mathematical modeling of phase noise is computed in the paper. Active and passive sensitivities are calculated for the proposed configuration and are found to be less than unity rendering circuit insensitive to component variations followed by phase noise study. The functionality of the proposed topology is validated through cadence virtuoso ADE spectre tool at 180-nm technology node. Experimental verification is executed through commercially available ICs AD844 by good results. The total harmonic distortion (THD) is found to be below 3.5%. The observed frequency of oscillation is found to be in close agreement with the theoretical values. The PVT and Monte Carlo statistical analyses are also carried out to confirm the sensitivity of the proposed SO. [ABSTRACT FROM AUTHOR]

This paper presents advancements in the performance of digital phase-locked loop (DPLL)s, with a special focus on addressing the issue of required gain calibration in the time-to-digital converter (TDC) within phase-domain DPLL structures. Phase-domain DPLLs are preferred for their simplicity in implementation and for eliminating the delta–sigma modulator (DSM) noise inherent in conventional fractional-N designs. However, this advantage is countered by the critical need to calibrate the gain of the TDC. The previously proposed dual-interpolated TDC(DI-TDC) was proposed as a solution to this problem, but strong spurs were still generated due to the TDC resolution, which easily became non-uniform due to PVT variation, degrading performance. To overcome these problems, this work proposes a DPLL with a new calibration system that ensures consistent TDC resolution matching the period of the digitally controlled oscillator (DCO) and operating in both the foreground and background, thereby maintaining consistent performance despite PVT variations. This study proposes a DPLL using a calibrated dual-interpolated TDC that effectively compensates for PVT variations and improves the stability and performance of the DPLL. The PLL was fabricated in a 28-nm CMOS process with an active area of only 0.019 mm2, achieving an integrated phase noise (IPN) performance of −17.5 dBc, integrated from 10 kHz to 10 MHz at a PLL output of 570 MHz and −20.5 dBc at 1.1 GHz. This PLL operates within an output frequency range of 475 MHz to 1.1 GHz. Under typical operating conditions, it consumes only 930 µW with a 1.0 V supply. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive acceleration lock compensation technology for phase-locked loops (PLLs) based on a novel dual-mode programmable ring voltage-controlled oscillator (ring-VCO). In addition, a time-to-digital converter (TDC) is designed to accurately quantify the phase difference from the phase frequency detector (PFD) in order to optimize the dead-zone effect while dynamically switching an auxiliary charge pump (CP) module to realize fast phase locking. Furthermore, a TDC-controlled three/five-stage dual-mode adaptively continuously switched VCO is proposed to optimize the phase noise (PN) and power efficiency, leading to an optimal performance tradeoff of the PLL. Based on the 180 nm/1.8 V standard CMOS technology, the complete PLL design and a corresponding simulation analysis are implemented. The results show that, with a 1 GHz reference signal as the input, the output frequency is 50–324 MHz, with a wide tuning range of 260 MHz and a low phase noise of −98.07 dBc/Hz@1 MHz. The key phase-locking time is reduced to 1.11 μs, and the power dissipation is lowered to 1.86 mW with a layout area of 66 μm × 128 μm. A significantly remarkable multiobjective performance tradeoff with topology optimization is realized, which is in contrast to several similar design cases of PLLs. [ABSTRACT FROM AUTHOR]

This paper proposed to design a CMOS based LC-voltage control oscillator using substrate bias effect and low-voltage folded-cascode current mirror circuit using an LC tank circuit at 2.5 GHz oscillation Frequency. The paper delves into the substrate-biasing technique, which adjusts the threshold voltage of a CMOS transistor, and the low-voltage folded-cascode current mirror circuit that utilizes CMOS technology to improve the performance of the current mirror circuit. The folded-cascode current mirror circuit comprises of a cascode structure in the input stage and a folded structure in the output stage, which is used to increase the output impedance and provide a more stable output current. The paper concludes that the folded-cascode current mirror circuit is a powerful tool in CMOS circuit design, offering improved performance and accuracy over the traditional current mirror circuit. In this simulation is carried out through cadence virtuoso generic process design kit (GPDK) with 90 nm technology. The simulation results exhibits phase noise of − 154.92 dBc/Hz @ 1 MHz, low power consumption of 4.8mW and the Figure of Merit − 216.09 dBc/Hz at 2.5 GHz oscillation frequency. [ABSTRACT FROM AUTHOR]

The concept of dynamical freezing is a phenomenon where a suitable set of local observables freezes under a strong periodic drive in a quantum many-body system. This happens because of the emergence of approximate but perpetual conservation laws when the drive is strong enough. In this work, we probe the resilience of dynamical freezing to random perturbations added to the relative phases between the interfering states (elements of a natural basis) in the time-evolving wave function after each drive cycle. We study this in an integrable Ising chain in a time-periodic transverse field. Our key finding is, that the imprinted phase noise melts the dynamically frozen state, but the decay is "slow": a stretched-exponential decay rather than an exponential one. Stretched-exponential decays (also known as Kohlrausch relaxation) are usually expected in complex systems with time-scale hierarchies due to strong disorders or other inhomogeneities resulting in jamming, glassiness, or localization. Here we observe this in a simple translationally invariant system dynamically frozen under a periodic drive. Moreover, the melting here does not obliterate the entire memory of the initial state but leaves behind a steady remnant that depends on the initial conditions. This underscores the stability of dynamically frozen states. [ABSTRACT FROM AUTHOR]

Objective: The objective of this study was to determine the gender‐specific normative values of masking level difference (MLD) in healthy young adults for two different measurement conditions. Methods: One hundred young adults between the ages of 19 and 25 were included. Tympanometry, pure tone audiometry, and MLD were performed. In the first MLD measurement condition, the threshold level where the signal was out of phase and the noise was in phase (SπNo) was subtracted from the threshold level where the signal and noise were in phase (SoNo). In the second MLD measurement condition, the threshold level where the signal was in phase and the noise was out of phase (SoNπ) was subtracted from the threshold level where the signal and noise were in phase (SoNo). The mean test scores were obtained in decibels. Comparisons were made in terms of gender and conditions. Results: The mean MLD for SoNo‐SπNo condition was 10.3 ± 1.99 dB. For SoNo‐SoNπ condition, the mean MLD was 6.72 ± 2.38 dB. A significant difference was determined between the MLD under two different measurement conditions (p <.05). There was no significant difference in terms of gender (p >.05). Conclusion: Mean normative values of MLD test scores in gender‐specific healthy young adults for two different measurement conditions are presented. [ABSTRACT FROM AUTHOR]

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We report a novel widely tunable Ka-band optoelectronic oscillator (OEO) realized by integrating a Mach–Zehnder modulator (MZM), a thermally-tunable add-drop micro-ring resonator (MRR), and a Mach–Zehnder interferometer (MZI) on the thin film lithium niobate platform, with the MZM and the MRR sequentially situated in one of the MZI arms. The MZM is for modulating the optical carrier, while the add-drop MRR is for selecting a single modulation sideband to beat with the unmodulated optical carrier from the other arm of the MZI, such that the OEO oscillation frequency is determined by the frequency spacing between the optical carrier and the selected modulation sideband, while the frequency tuning range is determined by the free spectral range of the MRR. By tuning the resonances of the add-drop MRR, the oscillation frequency can be tuned from 20 to 35 GHz, with the phase noises of −85 dBc/Hz @10 kHz and −116 dBc/Hz @100 kHz in the whole tuning range, which represent much higher oscillation frequency, much wider frequency tuning range, and lower phase noise than those of the photonic integrated OEOs realized with other material platforms reported previously. [ABSTRACT FROM AUTHOR]

Here, we report on a simplified laser frequency noise measurement technique employing an acousto-optic modulator, a delay line, and a real-time oscilloscope. The technique is a slight modification of the typical delayed heterodyne method. Instead of using a swept frequency spectrum to analyze the laser emission spectrum, the waveform captured on a real-time oscilloscope is used to directly calculate the laser frequency noise. The oscilloscope bandwidth and sampling requirements can be kept modest by choosing a modulator driven at a few hundred megahertz, making this technique attractive for a large number of laboratories. We show the frequency noise measurements of two different lasers with linewidths at 2.7 kHz and 2 MHz. We took the opportunity to investigate the noise floor of the frequency noise measurement system, and we found that the noise floor of the frequency noise measurement depends on the power level of the laser that is being characterized, with the kilohertz linewidths laser requiring more power to reduce the noise floor to acceptable levels. [ABSTRACT FROM AUTHOR]

In recent years, neural networks have been used to solve phase retrieval problems in imaging with superior accuracy and speed than traditional techniques, especially in the presence of noise. However, in the context of interferometric imaging, phase noise has been largely unaddressed by existing neural network architectures. Such noise arises naturally in an interferometer due to mechanical instabilities or atmospheric turbulence, limiting measurement acquisition times and posing a challenge in scenarios with limited light intensity, such as remote sensing. Here, we introduce a 3D–2D Phase Retrieval U-Net (PRUNe) that takes noisy and randomly phase-shifted interferograms as inputs and outputs a single 2D phase image. A 3D downsampling convolutional encoder captures correlations within and between frames to produce a 2D latent space, which is upsampled by a 2D decoder into a phase image. We test our model against a state-of-the-art singular value decomposition algorithm and find PRUNe reconstructions consistently show more accurate and smooth reconstructions, with a ×2.5–4 lower mean squared error at multiple signal-to-noise ratios for interferograms with low (<1 photon/pixel) and high (∼100 photons/pixel) signal intensity. Our model presents a faster and more accurate approach to perform phase retrieval in extremely low light intensity interferometry in the presence of phase noise and will find application in other multi-frame noisy imaging techniques. [ABSTRACT FROM AUTHOR]

Phase noise is a crucial impairment in coherent optical communication. In this paper, a dual-polarization 16 quadrature amplitude modulation coherent optical orthogonal frequency division multiplexing (DP 16-QAM CO-OFDM) modulation system with a hybrid optical filter has been proposed for phase noise reduction. This hybrid filter is a combination of an optical designed filter and an optical Gaussian filter. Linewidth of the input laser has been varied to generate phase noise. The simulation results have been obtained in terms of bit error rate (BER). It has been seen that the use of a hybrid optical filter mitigates the adverse effect of phase noise. [ABSTRACT FROM AUTHOR]

Holographic displays have been a long-standing ambition for decades to realize true-to-life reconstruction. However, their practical adoption is hindered by their subpar image quality compared to two-dimensional displays, which is fundamentally limited by restricted spatial frequency bandwidth and artifacts. We address the limitation by using a symmetry-broken amplitude-only spatial light modulator, demonstrating image quality comparable to that of two-dimensional displays. The broken conjugate symmetry induced by phase noise of modulators eliminates conjugate image that causes issues in amplitude-only holograms and allows direct reconstruction without additional optical elements. The proposed method provides enhanced robustness against artifacts caused by sub-pixel structures of modulators, enabling experimental reconstruction of high-quality holograms. The full bandwidth and the robustness result in a 5-decibel improvement in peak signal-to-noise ratio compared to state-of-the-art holograms. Furthermore, the hologram has 24 times higher optical efficiency and a smaller volume than the traditional amplitude-only holograms while real-time synthesis is enabled by using a neural network. [ABSTRACT FROM AUTHOR]

To establish ubiquitous and energy-efficient wireless sensor networks (WSNs), short-range Internet of Things (IoT) devices require Bluetooth low energy (BLE) technology, which functions at 2.4 GHz. This study presents a novel approach as follows: a fully integrated all-digital phase-locked loop (ADPLL)-based Gaussian frequency shift keying (GFSK) modulator incorporating two-point modulation (TPM). The modulator aims to enhance the efficiency of BLE communication in these networks. The design includes a time-to-digital converter (TDC) with the following three key features to improve linearity and time resolution: fast settling time, low dropout regulators (LDOs) that adapt to process, voltage, and temperature (PVT) variations, and interpolation assisted by an analog-to-digital converter (ADC). It features a digital controlled oscillator (DCO) with two key enhancements as follows: ΔΣ modulator dithering and hierarchical capacitive banks, which expand the frequency tuning range and improve linearity, and an integrated, fast-converging least-mean-square (LMS) algorithm for DCO gain calibration, which ensures compliance with BLE 5.0 stable modulation index (SMI) requirements. Implemented in a 28 nm CMOS process, occupying an active area of 0.33 mm2, the modulator demonstrates a wide frequency tuning range of from 2.21 to 2.58 GHz, in-band phase noise of −102.1 dBc/Hz, and FSK error of 1.42% while consuming 1.6 mW. [ABSTRACT FROM AUTHOR]

An optoelectronic oscillator (OEO) system is built up with a high-speed silicon microring modulator. The modulator is based on a p-n doped ring resonator with a radius of 10 μm. Its electro-optic (EO) 3 dB bandwidth is ∼31.7 GHz, which makes it suitable for generating multi-GHz radio frequency signals. By using this modulator, one of the essential components of an OEO, the EO converter, has been dramatically miniaturized. At the same time, assisted by the ring resonator, the phase noise of the generated 10 GHz signal (nearly −90 dBc/Hz at 10 kHz offset) is not compromised compared to other integrated OEOs with mm footprint modulators. This is an important step toward a compact, scalable, and fully integrated silicon photonics-based OEO system together with our existing integrated light sources and photodetectors. [ABSTRACT FROM AUTHOR]

This article comprehensively reviews and studies CMOS transformer tank voltage‐controlled oscillators (VCOs) designed to improve the frequency tuning range (FTR) and minimize phase noise (PN) across a broad frequency range, particularly for mm‐wave and fifth‐generation applications. The study focuses on enhancing the performance of the oscillators to meet the demanding requirements of these advanced applications. This study thoroughly investigates and compares various strategies to increase the FTR, minimize PN, and reduce power dissipation in transformer tank VCOs. The aim is to establish fundamental guidelines for implementing transformer‐based tank VCOs. The study comprehensively reviews and analyzes the overall architecture of transformer‐based tank VCOs, presenting a detailed examination of the methods employed to enhance VCO performance. Additionally, the study illustrates the impact of the coupling factor on the VCO's performance parameters, detailing and demonstrating the overall tank circuit quality factor (Q) and resonator coupling factor (κ). A thorough understanding of PN methodology and the limitations of FTR has led to the development of innovative architectures. These include transformer‐based capacitive feedback (FB) oscillators with resistively adjusted variable inductors, as well as class‐F and inverse class‐F VCOs. These novel architectures contribute significantly to the improvement of oscillator performance. [ABSTRACT FROM AUTHOR]

Aiming at the characteristics that the signal noise ratio (SNR) gradually decreases from the near to far range of the swath, an adaptive phase filtering algorithm based on Goldstein filtering and combined with multiple quality-guided graphs was proposed. Firstly, the components used to determine the filtering parameters were obtained through residue density, pseudo-coherence coefficient and pseudo-SNR, the three quality-guided graphs. Then, the filter parameters were calculated by weighting the three components. Finally, the size of filtering window was determined according to the account of residues, and the interferometric phase noise was removed in frequency domain. Simulated data, TSX/TDX data and airborne interferometric imaging radar altimeter data were used to verify the performance of the new algorithm. Compared with the results of Goldstein filtering and its improved algorithms, the results showed that the proposed algorithm can effectively filter out phase noise while maintaining the edge characteristics of interferometric fringe. The section of filtering result can well match with the section of simulated pure interfeometric phase. Moreover, the algorithm proposed in this paper can effectively remove the noise in the interferogram of TSX/TDX sea ice data, and the residues' filtering rate was above 86%, which can effectively remove the phase residues of the sea ice surface while maintaining the characteristics of the sea ice edge. Experimental results showed that the new algorithm provides an effective phase noise filtering method for imaging radar altimeter data processing. [ABSTRACT FROM AUTHOR]

During the modulation process of the VSI motor drive system, the nonlinear errors caused by the dead-time and conduction voltage drop will increase the phase current harmonic distortion and the torque ripple. To solve this problem, a novel dead-time free modulation scheme is proposed in this paper. In the non-zero crossing region of the phase current, the switching tube, whose body diode can provide a continuation path, is set as off-state, the driving signal is only implemented on another switching tube with the same bridge arm, and the errors caused by the conduction voltage drop and switching delay are compensated to the pulse duration. At the same time, to suppress the zero current clamp effect that exists near the zero crossing point of the phase current, another modulation scheme for the phase current crossing zero in advance is proposed, which avoids the complicated determination and calculation of the current polarity near the zero crossing point of the current. Both of the above modulation schemes eliminate the dead-time, and the switching principle is presented. In addition, to suppress the impact of the current ripple and high-frequency noise on the accuracy of the phase current detection, a second-order resonance digital filter without phase shift is introduced. Finally, compared to two deadtime compensation methods, the effectiveness and superiority of the proposed dead-time free modulation scheme are verified by the experimental results. [ABSTRACT FROM AUTHOR]

With the gradual expansion of mining scale in open-pit coal mines, slope safety problems are increasingly diversified and complicated. In order to reduce the potential loss caused by slope sliding and reduce the major threat to the safety of life and property of residents in the mining area, this study selected two mining areas in Xinjiang as cases and focused on the relationship between phase noise and deformation. The study predicts the specific time point of slope sliding by analyzing the dynamic history correlation tangent angle between the two. Firstly, the time series data of the micro-variation monitoring radar are used to obtain the small deformation of the study area by differential InSAR (D-InSAR), and the phase noise is extracted from the radar echo in the sequence data. Then, the volume of the deformation body is calculated by analyzing the small deformation at each time point, and the standard deviation of the phase noise is calculated accordingly. Finally, the sliding time of the deformation body is predicted by combining the tangent angle of the ratio of the volume of the deformation body to the standard deviation of the phase noise. The results show that the maximum deformation rates of the deformation bodies in the studied mining areas reach 10.1 mm/h and 6.65 mm/h, respectively, and the maximum deformation volumes are 2,619,521.74 mm3 and 2,503,794.206 mm3, respectively. The predicted landslide time is earlier than the actual landslide time, which verifies the effectiveness of the proposed method. This prediction method can effectively identify the upcoming sliding events and the characteristics of the slope, provide more accurate and reliable prediction results for the slope monitoring staff, and significantly improve the efficiency of slope monitoring and early warning. [ABSTRACT FROM AUTHOR]

The impact of power supply voltage fluctuations on the phase noise of quartz crystal oscillators (XOs) remains an open issue. Currently, there is a lack of comprehensive analysis on this matter. This work presents a novel phase-noise drive sensitivity (PNDS) model for the XO to reveal its mechanism. This model based on five noise modulation processes demonstrates the distribution of the PNDS in the frequency domain clearly, and there exists a PNDS bandwidth fS that limits the supply voltage fluctuation, which is similar to the effect of the noise bandwidth of the classical Leeson model. Using the PNDS, we successfully predict the phase noise of a 10 MHz oscillator under different supply voltage noises. In addition, experimental results show that the PNDS floor is determined by the phase modulation of the sustaining amplifier, while the amplitude-frequency effect of the resonator and the tuning of the diode often play crucial roles in the near-carrier PNDS. [ABSTRACT FROM AUTHOR]

Summary: This paper presents more compatible three‐stage inverter‐based ring voltage controlled oscillators (VCOs) by modifying the current‐starved delay cell to oscillate with high tuning range. Unlike some ring structures in which extra transistors are used as current boosting to enhance the frequency tuning range, no extra elements are used in the proposed three‐stage VCOs for increasing the tuning range. Besides, a new method is introduced to couple two proposed ring VCOs for designing a six‐phase ring VCO. The coupling method can be generalized to some other ring VCOs to generate multiphase signals. The proposed circuits have wide frequency tuning ranges and show good noise performances. The proposed six‐phase VCO can oscillate from 1.62 GHz to 3.45 GHz, which illustrates 72.2% tuning range. The phase noise of the proposed VCO is −97.5 dBc/Hz at 1 MHz offset frequency. The circuit figure of merit is −181.5 dBc/Hz. The post‐layout simulation results of the proposed six‐phase VCO are provided based on the TSMC 0.18 μm CMOS process. [ABSTRACT FROM AUTHOR]

Performing noise characterizations of lasers and optical frequency combs on sampled data offers numerous advantages compared to analog measurement techniques. One of the main advantages is that the measurement setup is greatly simplified. Only a balanced detector followed by an analog-to-digital converter is needed, allowing all the complexity to be moved to the digital domain. Secondly, near-optimal phase estimators are efficiently implementable, providing accurate phase noise estimation in the presence of measurement noise. Finally, joint processing of multiple comb lines is feasible, enabling the computation of the phase noise correlation matrix, which includes all information about the phase noise of the optical frequency comb. This tutorial introduces a framework based on digital signal processing for phase noise characterization of lasers and optical frequency combs. The framework is based on the extended Kalman filter (EKF) and automatic differentiation. The EKF is a near-optimal estimator of the optical phase in the presence of measurement noise, making it very suitable for phase noise measurements. Automatic differentiation is key to efficiently optimizing many parameters entering the EKF framework. More specifically, the combination of EKF and automatic differentiation enables the efficient optimization of phase noise measurement for optical frequency combs with arbitrarily complex noise dynamics that may include many free parameters. We show the framework's efficacy through simulations and experimental data, showcasing its application across various comb types and in dual-comb measurements, highlighting its accuracy and versatility. Finally, we discuss its capability for digital phase noise compensation, which is highly relevant to free-running dual-comb spectroscopy applications. [ABSTRACT FROM AUTHOR]

This study presents a new wide-tunable, area-efficient and low-phase noise quadrature voltage-controlled oscillator(QVCO). Initially, a modified Colpitts voltage-controlled oscillator (VCO) is proposed in which all transistors are cross-connected in a self-biased scheme to increase negative resistance and facilitate the startup condition. Besides, instead of a passive inductor, a modified tunable active inducer (AI) is used in the proposed Colpitts VCO. Then a new AI-based QVCO is presented by the in-phase anti-phase coupling of two identical Colpitts VCOs. The core VCOs are coupled by the current source transistors of the AI and in this way, no extra coupling devices are used. The proposed AI-based QVCO is designed and simulated in TSMC 0. 1 8 μ m CMOS technology by Cadence. Post-layout simulation results show that the proposed QVCO occupies only 0. 0 2 4 mm 2 of chip area, and has a phase noise of −106.6 dBc/Hz at 1 MHz offset from the 0.7 GHz oscillation frequency. A wide frequency tuning range (FTR) of 68% (i.e., 0.68–1.4 GHz) is achieved by adjusting the tuning voltage of the active inductor (AI), and the total power consumption is 7.2 mW. Coarse and fine frequency tuning of the QVCO is available by changing the emulated inductors and varactors, respectively, that gives K vco of 1100 and 34 MHz/V, respectively. [ABSTRACT FROM AUTHOR]

Optical frequency combs have revolutionized frequency metrology and spectroscopic measurements, enabling the most precise measurements of all physical quantities. However, precision frequency metrology heavily relies on mode‐locked laser combs, which are only directly available for a few selected near‐infrared wavelength ranges. Recently, a strong tendency emerged for combs in the mid‐infrared molecular fingerprint region. To this end, several methods for wavelength conversion have been proposed and demonstrated, which nevertheless cost a degradation of coherence properties. Here a first approach is presented toward measuring resulting phase noise fluctuations, exploiting the temporal resolution of the dispersive temporal interferometry (DTI) technique for experimentally unveiling the carrier‐envelope phase dynamics of a cw‐seeded femtosecond optical parametric amplifier (OPA). Particularly, it is experimentally demonstrated for the first time that unexpectedly low seed power levels suffice to exceed vacuum fluctuations by more than an order of magnitude, resulting in pulse‐to‐pulse phase fluctuations of 82 mrad at rather moderate cw seed levels of 8 mW. Additionally, a formula is provided that allows exact prediction of the experimentally observed noise levels. This study therefore provides new insight into the role of vacuum fluctuations in OPAs, which open up an avenue for coherent dual‐comb systems in the mid‐infrared and beyond. [ABSTRACT FROM AUTHOR]

In this paper, to analyze the tuning range (TR) of transistors, we introduced two streamlined modeling approaches that can precisely predict the extent and direction of the TR. The first approach, known as the average DC (Id) method, employed a simplified circuit model to dissect transistor characteristics, enabling us to understand the general trajectory of the TR. The second approach involved the transient current Id (tc) method, which offers a nuanced portrayal of the transistor's real‐world performance. By analyzing the current fluctuations within the transistor during transient states, its tuning capabilities could be more accurately ascertained. Further, this paper presents several designs for ultra‐wide‐tuning‐range complementary metal–oxide–semiconductor (CMOS) voltage‐controlled oscillators (VCOs) that employ a novel two‐mode current‐starved delay cell, featuring a tunable transistor‐based current source for coarse frequency adjustment operating in synergy with a varactor for precise tuning. Using the 65‐nm CMOS process, three prototype VCOs (Designs 2/3/4) based on the new cell and targeting different numbers of phases and performance were fabricated, thoroughly characterized, and compared with their traditional inverter‐based counterpart (Design 1). Design 1 featured an inverter‐based four‐phase structure, with an output frequency range of 3.14–9.82 GHz, i.e., a radio frequency (RF) TR of 103%, with phase noise (PN) ranging from 137.7 to 132.1 dBc/Hz at an offset of 100 MHz, figure of merit with tuning range and area (FoMTA) varying from 200.7 to 205.1 dBc/Hz, and area of 0.0036 mm2. In contrast, Designs 2/3/4, based on the new delay cell, featured 8/3/4 phases, with output frequencies in the ranges of 1.14–9.17, 1.26–16.53, and 1.15–18.32 GHz, respectively, resulting in increased RF TRs of 155.8%, 171.7% and 176.4%, as well as PN at an offset of 100 MHz in the ranges of 142.1–138, 130.5–131.3, and 131.9–129.6 dBc/Hz, respectively. This yielded better FoMTAs in the ranges of 201.2–209.9, 205.3–217.9, and 194.1–209.9 dBc/Hz, thus allowing the VCOs to maintain consistent performance across the frequency band and occupy comparable or smaller silicon areas of 0.00425, 0.000972, and 0.00348 mm2 in the same 65 nm technology. These designs showcase the versatility and efficiency of the two‐mode current‐starved delay architecture, which offers wide TRs, tiny areas, and competitive performance metrics for various applications in RF integrated circuits. [ABSTRACT FROM AUTHOR]

Artificial-intelligence-generated content has driven explosive data traffic growth in data-center interconnects. Traditional direct detection solutions struggle with limited spectral efficiency and distance, prompting the shift to coherent optics for cost-sensitive short-reach links. One specific challenge is integrating low-cost lasers while overcoming severe phase noise on high-order modulation formats. Here, we propose a residual carrier modulation scheme for precise and efficient carrier frequency and phase recovery. The residual optical carrier can continuously track phase fluctuations without redundancy compared with discrete time-domain pilots, and address the digital-to-analog convertor resolution reduction issue of frequency-domain digital pilots. In proof-of-concept experiments, we transmit a net 1-Tb/s probabilistic-shaped 256-ary quadrature amplitude modulated (PS-256-QAM) signal using a 3 MHz distributed feedback (DFB) laser. Our scheme improves bitrate by 41% compared to conventional time-domain pilots, achieving a record laser linewidth sum and symbol duration product of 6.89 × 10−5. This approach supports MHz linewidth DFB lasers in low-cost coherent optical communications. The authors propose a residual carrier modulation scheme to overcome laser phase noise in coherent optical systems. The method improves bitrate and spectral efficiency by 41% using low-cost lasers, and showcase potential in cost-sensitive scenarios. [ABSTRACT FROM AUTHOR]

Context. The measurement of pulsar pulse times-of-arrival (ToAs) is a crucial step in detecting low-frequency gravitational waves. To determine ToAs, we can use template-matching to compare each observed pulse profile with a standard template. However, using different combinations of templates and template-matching methods (TMMs) without careful consideration can lead to inconsistent results. Aims. In pulsar timing array (PTA) experiments, distinct ToAs from the same observations can be obtained due to the use of diverse templates and TMMs. In other words, employing diverse approaches can yield different timing results and would thus have a significant impact on subsequent gravitational wave searches. In this paper we examine several commonly used combinations to analyze their effect on pulse ToAs. Methods. We evaluated the potential impact of template and TMM selection on 13 typical millisecond pulsars within the European PTA. We employed pulsar timing methods, specifically the root mean square and reduced chi-square (χ2r) of the residuals of the best timing solution, to assess the outcomes. Additionally, we evaluated the system-limited noise floor (SLNF) for each pulsar at various telescopes operating around 1.4 GHz using frequency-resolved templates. Results. Our findings suggest that utilizing data-derived and smoothed templates in conjunction with the Fourier-domain with Markov chain Monte Carlo TMM is generally the most effective approach, though there may be exceptions that require further attention. Furthermore, we determine that pulse phase jitter noise does not significantly limit the current precision of the European PTA's timing, as jitter levels derived from other studies are much lower than the SLNF. [ABSTRACT FROM AUTHOR]

For the time and frequency signals of Beidou satellites, a high-accuracy phase frequency detection technology based on phase group synchronization is proposed. Using the Beidou receiver and satellite signals as the frequency standard and the measured signals, respectively. The Beidou receiver and the satellite signals are sent to the phase coincidence detector of the different frequencies to generate a phase coincidence point pulse, which is sent to the different frequency phase detector as a control signal to generate the phase differences between the Beidou receiver and satellite signals, and then complete the high-accuracy phase synchronization between the Beidou receiver and satellite signals. Experimental results show that when the delay resolution reaches ps level, the phase synchronization accuracy of the system can reach 10 ps, which has the characteristics of small phase noise, low development cost, simple circuit structure, and high synchronization accuracy compared with the traditional phase synchronization technologies. Therefore, it would be widely used in satellite positioning, astrometry, precision navigation, aerospace, satellite launch, power transmission, communications, radar, and other high-tech fields. [ABSTRACT FROM AUTHOR]

Azimuth multi-channel synthetic aperture radar (SAR) has always been an important technical means to achieve high-resolution wide-swath (HRWS) SAR imaging. However, in the space-borne azimuth multi-channel SAR system, random phase noise will be produced during the operation of each channel receiver. The phase noise of each channel is superimposed on the SAR echo signal of the corresponding channel, which will cause the phase imbalance between the channels and lead to the generation of false targets. In view of the above problems, this paper proposes a random phase noise compensation method for space-borne azimuth multi-channel SAR. This method performs feature decomposition by calculating the covariance matrix of the echo signal and converts the random phase noise estimation into the optimal solution of the cost function. Considering that the phase noise in the receiver has frequency-dependent and time-varying characteristics, this method calculates the phase noise estimation value corresponding to each range-frequency point in the range direction and obtains the phase noise estimation value by expectation in the azimuth direction. The proposed random phase noise compensation method can suppress false targets well and make the radar present a well-focused SAR image. Finally, the usefulness of the suggested method is verified by simulation experiments. [ABSTRACT FROM AUTHOR]

Injection‐locked dividers feature ultrahigh operating frequency, low power consumption, and low phase noise, making them suitable for Q‐band phase‐locked loop. This paper presents a transformer‐based divide‐by‐4 injection locking frequency divider with a high third harmonic rejection buffer based on 40‐nm CMOS technology. Employing a fourth‐order transformer resonator enhances the third‐order harmonic amplitude, increasing the injection efficiency and expanding the locking range. The proposed high third harmonic rejection buffer using a source degeneration inductor can effectively suppress the output of the third harmonic caused by the resonator, ultimately yielding a clean fundamental frequency signal. Simulation results demonstrate that the proposed divide‐by‐4 injection‐locked frequency divider (ILFD) achieves a locking range of 10.2 GHz (from 40.3 to 50.5 GHz) with 0 dBm input signal. The core divide‐by‐4 ILFD circuit consumes 4.6 mW power with a 0.9 V supply and occupies an area of 0.026 mm2. [ABSTRACT FROM AUTHOR]

Non-Hermitian photonics, relaying on parity-time (PT) symmetry, have shown promise in achieving mode selection for optical or microwave single-mode oscillation. Typically, a PT-symmetric system is constructed using two coupled loops with identical geometry. This article utilizes the PT-symmetry property to select a single frequency mode in an optoelectronic oscillator (OEO). However, traditional OEO implementations often involve discrete components, limiting widespread adoption due to factors such as size, weight, power consumption, and cost. Our aim in this paper is to leverage integrated components within the OEO loop. The proposed structure incorporates an integrated micro-ring resonator (MRR) with a high-quality factor (Q-factor) that serves both as a modulator and a resonator. Additionally, we suggest employing an adjustable integrated power splitter utilizing a micro heater to balance the gain and loss of two mutually coupled OEO loops. In this configuration, two integrated photo detectors (PD) are also utilized. In this setup, the single-frequency mode can be easily identified by simultaneously utilizing the properties of PT-symmetry and an integrated high-Q-factor resonator, obviating the need for a narrowband microwave filter. By adjusting the center frequency of the microwave photonic filter (MPF), the frequency of the generated signal can be tuned over a wide range. For instance, setting the generated frequency of the microwave signal to 11.5 GHz results in a measured phase noise of − 76.5 dBc/Hz at a 10-kHz offset frequency, with a side mode suppression ratio (SMSR) of 40 dB. [ABSTRACT FROM AUTHOR]

A differential ring voltage‐controlled oscillator (DRVCO) is proposed in this paper as one of the critical blocks in communication systems. It consists of four stages of delay cells connected in a chain, creating a ring structure with auxiliary path interconnections. The oscillation frequency of the DRVCO can be controlled by adjusting the tuning voltage that controls the charging current. To achieve the desired performance for wireless applications, the Wu active inductor, which is a low‐noise and high‐quality factor active inductor, is employed in each delay cell for the first time. Using an active inductor provides a wide tuning range and also allows for proper phase noise and low power consumption. The proposed circuit is designed and simulated using standard 180‐nm CMOS technology with a 1.8‐V voltage source (VDD). The circuit is designed to achieve a tuning range of 2.15 GHz with a center frequency oscillation of 2.745 GHz, over the control voltage variation of 1.4 V (0 to 1.4 V). To achieve the desired performance, the circuit consumes an average power of 1.99 mW. It achieves a phase noise of − 91.2 dBc/Hz at 1 MHz offset frequency, indicating effective noise suppression. The figure of merit (FoM) for the circuit is − 156.9 dBc/Hz, representing its overall performance. The final layout of the circuit estimates an area of 0.00072 mm2. Various analyses, including Monte–Carlo simulations, PVT (process, voltage, temperature) variation analysis, and other relevant analyses, have been performed to ensure the reliable performance of the proposed circuit. [ABSTRACT FROM AUTHOR]

Cylindrical vector beams (CVBs) with unique spatial polarization states have attracted great interest in recent years. However, the generation of high-power CVBs faces a significant challenge due to the limited output power of a single laser. Here, we capitalize on the brightness enhancement offered by coherent beam combining (CBC) technique and propose an architecture for generating arbitrary CVBs based on a CBC system. The phase noise is effectively compensated using an all-fiber internal phase-locking technique. By designing the polarization direction of each beamlet in the laser array, the desired mode of CVB can be generated. This work could provide a reference for generating high-power CVBs. [ABSTRACT FROM AUTHOR]

Research on two-dimensional material-based phototransistors has recently become a topic of great interest. However, the high number of design features, which impact the performance of these devices, and the multi-physical nature of the device operation make the accurate analysis of these devices a challenge. Here, we present a simple yet effective numerical framework to overcome this challenge. The one-dimensional framework is constructed on the drift-diffusion equations, Poisson's equation, and wave propagation in multi-layered medium formalism. We apply this framework to study phototransistors made from monolayer molybdenum disulfide ( MoS 2 ) placed on top of a back-gated silicon-oxide-coated silicon substrate. Numerical results, which show good agreement with the experimental results found in the literature, emphasize the necessity of including the inhomogeneous background for accurately calculating device metrics such as quantum efficiency and bandwidth. For the first time in literature, we calculate the phase noise of these phototransistors, which is a crucial performance metric for many applications where precise timing and synchronization are critical. We determine that applying a low drain-to-source voltage is the key requirement for low phase noise. [ABSTRACT FROM AUTHOR]

In recent years, absolute gravity comparison experiments between cold atomic gravimeter and traditional gravimeter have been carried out by combining cold atomic gravimeter with stable platform. Due to the working characteristics of the stable platform, the tilt angle of the cold atomic gravimeter will change slightly in the process of dynamic measurement, and the measurement noise will be introduced. In order to improve the accuracy of dynamic measurement, this paper first analyzes the trajectory of the mirror and atom in the atomic gravimeter combined with carrier motion information, obtains the phase expression of the atomic interferometer using the translation and rotation matrix, evaluates the main terms of the gravity deviation using the 20-min navigation data on the ship in the South China Sea, and simplifies the higher-order small-terms in the main terms to deduce the simplified form of the gravity deviation. Then, the Fourier transform is used to transform the simplified expression into the power spectrum expression of phase noise, the corresponding noise sensitivity function is used in the form of trigonometric. The 20-min data is divided into 10 intervals, the root-mean-square (RMS) value of the overall gravity deviation is 1.5–3 mGal using the power spectrum of the platform angle, angular velocity and carrier acceleration in each interval. The variation fluctuation of the RMS value is consistent with the fluctuation of solving the gravity deviation through the trajectory. The conclusion provides the calculation method of gravity noise caused by dynamic tilt change and horizontal acceleration, and also provides the basis for platform design. [ABSTRACT FROM AUTHOR]

This article proposed a technique for a low‐power and fast start‐up voltage‐controlled oscillator (VCO) for a high data rate 5 G New Radio (5G‐NR) application. The 5G‐NR high data rate signals require a fast start‐up VCO to accommodate the short pulse width. In this proposed work, a cross‐coupled pair (XCP) is integrated with a center‐tapped orthogonal symmetry inductor placed at the gates of the XCP, forming an inductive booster VCO (IBVCO). The inductive impedance at the gate of the XCP preserve the symmetry signal profile of the output voltage swing while alleviating the intrinsic parasitic capacitance effect and flicker noise effect of the transistor under the absence of the tail current source. The concept proves with the improvement on the phase noise performance and generating a fast start‐up without affecting the VCO bandwidth. The VCO also provides the enhancement of the output voltage swing under low power consumption. The IBVCO has been fabricated in 180 nm complementary metal oxide semiconductor technology and consumes a minimum area of only 0.7 mm2. The IBVCO achieved a 13% tuning range from 3.3 to 3.75 GHz bandwidth with a supply voltage, VDD of 0.7 V. The total power consumption is 1 mW with a corresponding phase noise of −122.60 dBc/Hz and a Figure of Merit (FoM) of 193.48 dBc/Hz at 3.52 GHz carrier center frequency at 1 MHz offset. The start‐up time of the VCO achieved is 5 ns. [ABSTRACT FROM AUTHOR]

Robustness against Electronic Warfare/Electronic Defence attacks represents an important advantage of Noise Radar Technology (NRT). An evaluation of the related Low Probability of Detection (LPD) and of Intercept (LPI) is presented for Continuous Emission Noise Radar (CE‐NR) waveforms with different operational parameters, that is, "tailored", and with various "degrees of randomness". In this frame, three different noise radar waveforms, a phase Noise (APCN) and two "tailored" noise waveforms (FMeth and COSPAR), are compared by time–frequency analysis. Using a correlator (i.e. a two antennas) receiver, assuming a complete knowledge of the band (B) and duration (T) of the coherent emission of these waveforms, it will be shown that the LPD features of a CE‐NR do not significantly differ from those of any CE radar transmitting deterministic waveforms. However, in real operations, B and T are unknown; hence, assuming an instantaneous bandwidth estimation will show that the duration T can be estimated only for some specific "tailored" waveforms (of course, not to be operationally used). The effect of "tailoring" is analysed with prospects for future work. Finally, some limitations in the classification of these radar signals are analysed. [ABSTRACT FROM AUTHOR]

Cosmic microwave background (CMB) experiments have deployed focal planes with O (10 4) transition edge sensor (TES) bolometers cooled to sub-Kelvin temperatures by multiplexing the readout of many TES channels onto a single pair of wires. Digital Frequency-domain Multiplexing (DfMux) is a multiplexing technique used in many CMB polarization experiments, such as the Simons Array, SPT-3 G, and EBEX. The DfMux system studied here uses LC filters with resonant frequencies ranging from 1.5 to 4.5 MHz connected to an array of TESs. Each detector has an amplitude-modulated carrier tone at the resonant frequency of its accompanying LC resonator. The signal is recovered via quadrature demodulation where the in-phase (I) component of the demodulated current is in phase with the complex admittance of the circuit and the quadrature (Q) component is orthogonal to I. Observed excess current noise in the Q component is consistent with fluctuations in the resonant frequency. This noise has been shown to be non-orthogonal to the phase of the detector's responsivity. We present a detailed analysis of the phase of responsivity of the TES and noise sources in our DfMux readout system. Further, we investigate how modifications to the TES operating resistance and bias frequency can affect the phase of noise relative to the phase of the detector responsivity, using data from Simons Array to evaluate our predictions. We find that both the phase of responsivity and phase of noise are functions of the two tuning parameters, which can be purposefully selected to maximize signal-to-noise (SNR) ratio. [ABSTRACT FROM AUTHOR]

In a linear and quadratic optomechanical system with optical parametric amplifier's (OPA) phase noise, we conduct a study on normal-mode splitting, sideband cooling and force sensitivity. The system encompasses an optical cavity, a mechanical membrane and a degenerate OPA. When there is OPA's pump phase noise, normal-mode splitting still occurs and displays more complex splitting compared to scenarios without phase noise. Specifically, for increasing quadratic coupling, the left peak shrinks steadily until it vanishes, while the right peak increases to a larger value. Moreover, both the nonlinear gain of OPA and the quadratic coupling parameter play key roles in cooling the mechanical membrane in the presence of certain phase noise. Minimal phase noise and optimized values of the nonlinear gain of OPA and the quadratic coupling are essential for achieving enhanced cooling. Furthermore, in the presence of OPA's phase noise, when the value of quadratic coupling is negative, the standard quantum limit is beaten. Higher negative values of quadratic coupling prove beneficial in achieving more stable force sensitivity. We believe that in the realm of quantum optomechanics, this scheme may have viable applications in quantum manipulation and precision measurement. [ABSTRACT FROM AUTHOR]

In this paper, an optoelectronic oscillator (OEO) with ultra-low phase noise and high stability based on the injection-locked and phase-locked loop is proposed. In theory, the injection-locked frequency range of the injection signal is studied based on the phase dynamics equation, and the phase noise performance of the injection-locked OEO is analyzed. The role of the phase-locked loop on the frequency stability of the OEO is analyzed based on the phase-locked loop transfer function. In addition, this paper builds an injection-locked OEO based on a phase-locked loop. The injection-locked signal is the high-frequency output of the multiplication crystal oscillator (MCO). At the same time, this MCO synchronously outputs a low-frequency signal, which is used as the reference signal of the phase-locked loop. The experimental results show that the proposed OEO output frequency is 10 GHz, and the phase noise is −89.25 dBc/Hz@100 Hz, −121.71 dBc/Hz@1 kHz, and −145.39 dBc/Hz@10 kHz; the side-mode suppression ratio is 80 dB; the frequency stability is 2.06 × 10 − 11 @1 s, 9.03 × 10 − 11 @10 s, 1.03 × 10 − 10 @100 s, and 3.03 × 10 − 10 @1000 s. Consistent with the theoretical analysis results, the solution takes into account the frequency stability, side-mode suppression ratio, and phase noise performance. The simple structure is more advantageous in practical applications. [ABSTRACT FROM AUTHOR]

High-precision time–frequency is widely used in time measurement, satellite navigation, scientific research, and other fields. With the rapid development of optical clock technology, the fractional frequency instability and uncertainty of optical clock have reached 10−18 orders of magnitude, which is expected to contribute to generating the International Atomic Time and may even be used to redefine the "second" in the future. Therefore, the long-distance transfer of time–frequency signals between optical atomic clocks is of great significance. Free-space optical frequency transfer technology is one of the important technologies for solving the space-based optical clock comparison because of its high transfer precision and easy networking characteristics. In order to solve the long-distance space-based optical clock comparison, this paper investigates a free-space active phase noise compensation method using an Acousto-Optic Modulator (AOM), based on the traditional optical fiber phase noise compensation scheme. This new method is more flexible and scalable than the optical fiber time–frequency transfer technology. The optical frequency transfer over a 64 m free-space link is demonstrated. The fractional frequency transfer instability during free running is 9.50 × 10−16 at 1 s, and 4.44 × 10−16 at 2000 s, and the fractional frequency instability after compensation is 7.10 × 10−17 at 1 s, 3.07 × 10−19 at 2000 s, which is about 1–3 orders of magnitude better than that in free running, and provides a feasible scheme for space-based optical clock comparison. [ABSTRACT FROM AUTHOR]