Phase Noise Research Articles

Dual-driving parametric locking of GHz phonon sources to sub-hertz linewidth in optomechanical systems

In the exploration of collective dynamics and advanced information processing, synchronization and frequency locking of mechanical oscillations are cornerstone phenomena. Traditional synchronization techniques, which typically involve a single mechanical mode, are limited by their inability to distinguish between intrinsic mechanical oscillations and external signals after locking. Addressing this challenge, we introduce a parametric approach that enables simultaneous frequency locking of two gigahertz mechanical modes within an optomechanical crystal cavity. By modulating the pump light to match the sum and difference frequencies of the mechanical modes, we significantly narrow their linewidths from tens of kilohertz to below 1 Hz at room temperature and ambient pressure. This dual-locking scheme also drastically reduces the phase noise of the mechanical modes by 76.6 dBc/Hz at a 100 Hz offset, while allowing flexible tuning of the locked modes’ frequencies via input signal adjustments. Our method not only facilitates direct observation of mechanical oscillations under the locking regime but also enriches the understanding of coherent phonons in multimode regimes, opening new avenues for optomechanical applications in signal processing.

Ultralow-phase-noise and broadband frequency-hopping coupled optoelectronic oscillator under quiet point operation

Advancements in microwave photonics have yielded novel approaches for generating high-purity microwave sources. Among these, optoelectronic oscillators (OEOs) and coupled optoelectronic oscillators (COEOs) have demonstrated the capability to generate frequency-independent microwaves with exceptionally low phase noise. Nonetheless, the tunability of the oscillators is rather limited due to the necessity for narrowband electronic bandpass filters, presenting challenges in achieving both wide and rapid tuning capabilities. Here, we present a COEO featuring ultralow phase noise, flexible tuning capability, and high robustness. This is achieved through a quiet point (QP)-operated harmonic mode-locked fiber laser, which effectively mitigates optical amplifier noise and supermode competition, thus significantly diminishing the necessity for ultra-narrow electronic filters. Due to the liberated tuning ability, we present an oscillator that can be tuned from 2 GHz to 18 GHz, with phase noise as low as −140 dBc/Hz at 10 kHz under the QP operation. We then illustrate the practical application of the proposed oscillator in generating frequency-hopping signals with consistent spurious modes less than −85 dBc, absolute phase noise below −135 dBc/Hz at 10 kHz, hopping resolution of 1.25 MHz, and fractional frequency stability below 6.1×10−12 at 1 s averaging time when locked to a reference. The presented COEO structure emerges as a compelling solution for agile and low-noise microwave sources in advanced wireless communication and radar systems.

Investigating the impact of supply voltage fluctuations on phase noise in quartz crystal oscillators.

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 10MHz 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.

Analysis and Design of a Sub-Sampling PLL of Low Phase Noise and Low Reference Spur

Analysis and Design of a Sub-Sampling PLL of Low Phase Noise and Low Reference Spur

Exploiting Carrier Frequency Offset and Phase Noise for Physical Layer Authentication in UAV-Aided Communication Systems

Exploiting Carrier Frequency Offset and Phase Noise for Physical Layer Authentication in UAV-Aided Communication Systems

Research on the Application of Dynamic Process Correlation Based on Radar Data in Mine Slope Sliding Early Warning.

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.

CW‐Seeded Parametric Combs with Quantum‐Limited Phase Noise

CW‐Seeded Parametric Combs with Quantum‐Limited Phase Noise

Overcoming laser phase noise for low-cost coherent optical communication

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.

Adaptive feedback control for intelligent phase noise suppression in a figure-9 fiber laser

Phase noise characteristics of ultrafast fiber lasers are critical to practical applications, such as high-resolution photonics sampling. Herein, we investigated the impact of pump power and linear phase shift difference of counter-propagating light in the nonlinear amplifying loop mirror on phase noise suppression in a figure-9 fiber laser. Based on these results, we proposed a method for intelligent suppression of phase noise through real-time feedback control. By adaptively controlling the linear phase shift difference and pump power, the phase noise can be effectively suppressed in the high offset frequency region even in variable environments. In particular, a reduction of ∼21.40% of integrated timing jitter in the offset frequency region from 10 kHz to 1 MHz was achieved. Our approach was proved to be effective and automatic to obtain ultrafast lasers with low phase noise and may also facilitate the related applications.

Uncertainty of the initial phase estimation of a sinewave in the presence of phase noise, additive noise or jitter

This paper presents the derivation of a simple analytical expression for the precision of the initial phase estimates obtained through a least-squares procedure. That expression depends on number of samples, phase noise standard deviation and additive noise standard deviation. This study is applicable to the estimates obtained through the sine fitting algorithm with known frequency and to the Discrete Fourier Transform algorithm. The analytical expression supplied was verified using a Monte Carlo simulation with numerically created data. The non-ideal phenomena treated in this work is the presence of jitter in the sampling instant, phase noise in the oscillator and additive noise in the system both of which must be normally distributed with a known value of standard deviation. It is useful information for an engineer in order to choose the proper number of samples to acquire to achieve a desired level of precision on the estimates made and thus carry out an efficient data acquisition with no unnecessary samples thus optimizing the test duration.

An octave tuning range quad-core VCO using a multi-mode resonator

This paper presents a novel multi-core multi-mode electric-magnetic (E-M) mixed-coupling voltage-controlled oscillator (VCO), achieving wide tuning range and phase noise optimization simultaneously through a multi-core structure. A symmetric multi-mode resonator is proposed to address the issue of differential signal mismatch caused by transformer asymmetry. An inductor ring is used to balance the inductance of each mode and its effect in each mode is analyzed in detail. A symmetrical switch network is employed for mode switching, offering advantages such as reduced parasitics and mismatch. The utilization of a varactor combined with a fixed capacitor enables electrical coupling, ensuring overlapping frequency bands even with variations in process, voltage, and temperature (PVT), and extending the tuning range. Furthermore, a switched resistor array is employed to bias the negative resistance pair and minimize the contribution of 1/f noise upconversion to the phase noise. Designed in a 40-nm complementary metal–oxide–semiconductor (CMOS) technology with a core area of 0.16 mm2, the VCO achieves a simulated continuous tuning range of 81.5%, spanning from 11.1 to 26.4 GHz. Operating at a 1.1 V supply with a power consumption of 16 mW, the phase noise at 12.15 GHz is −118.6 dBc/Hz at a 1 MHz offset, corresponding to a figure-of-merit (FoM) of 188.3 dBc/Hz and a FoMT of −206.3 dBc/Hz.

Robust laser phase noise measurement by integration heterodyne for coherent beam combining applications

Phase noise characteristics are critical for coherent beam combination engineering. Heterodyne with integration method for phase noise measurement has been studied numerically and experimentally, which reveals that the method is not only simple to implement with the least equipment but also capable of phase retrieval using under-sampling data. The integration method is compared with the traditional low-pass filter (LPF) method from both numerical and experimental perspectives. By introducing an evaluation criterion of measurement accuracy, the errors of the integration method are 0.44% and 0.08% for white noise and pink noise cases, respectively, which are smaller than that achieved by LPF one (1.52% and 0.25%). The errors of the integration method are below 1.4% when under-sampling data has been employed, which means that large consumption of data processing can be avoided, and the method is robust. Phase noise measurements in quiet laboratory and disturbed conditions are implemented, and the error between the results of the sampling rate of 250 MHz and 31.25 MHz is less than 0.08%, which is consistent with the simulation and demonstrates the excellent performance of the integration method.

Parallel indirect time-of-flight ranging using on-chip dual-frequency combs

The significant advancements in autonomous vehicle applications demand detection solutions capable of swiftly recognizing and classifying objects amidst rapidly changing and low-visibility conditions. Light detection and ranging (LiDAR) has emerged as a robust solution, overcoming challenges associated with camera imaging, particularly in adverse weather conditions or low illumination. Rapid object recognition is crucial in dynamic environments, but the speed of conventional LiDARs is often constrained by the 2D scanning of the laser beam across the entire scene. In this study, we introduce a parallelization approach for the indirect time-of-flight (iToF) ranging technique. This method enables efficient and high-speed formation of 1D clouds, offering the potential to have extended range capabilities without being constrained by the laser coherence length. The application potential spans mid-range autonomous vehicles ranging to high-resolution imaging. It utilizes dual-frequency combs with slightly different repetition rates. The method leverages the topology of the target object to influence the phase of the beating signal between the comb lines in the RF domain. This approach enables parallel ranging in one direction, confining the scanning process to a single dimension, and offers the potential for high-speed LiDAR systems. A tri-comb approach will be discussed that can provide an extended unambiguous range without compromising the resolution due to the range–resolution trade-off in iToF techniques. The study starts by explaining the technique for parallel detection of distance and velocity. It then presents a theoretical estimation of phase noise for dual combs, followed by an analysis of distance and velocity detection limits, illustrating their maximum and minimum extents. Finally, a study on the mutual interference conditions between two similar LiDAR systems is presented, demonstrating the feasibility of designing simultaneously operating LiDARs to avoid mutual interference.

Earthquake source inversion by integrated fiber-optic sensing

We present an earthquake source inversion using a single time series produced by integrated fiber-optic sensing in a phase noise cancellation (PNC) system used for frequency metrology. Operating on a 123 km long fiber between Bern and Basel (Switzerland), the PNC system recorded the Mw3.9 Mulhouse earthquake that occurred on 10 September 2022 around 10 km north-west of the northern fiber end. A generalised least-squares inversion in the 4 - 13 s period band constrains the components of a double-couple moment tensor with an uncertainty that corresponds to around 0.2 moment magnitude units, nearly independent of prior information. Uncertainties for hypocenter location and original time are more variable, ranging between 4 - 20 km and 0.1 - 1 s, respectively, depending on whether injected prior information is realistic or almost absent. This work is a proof of concept that quantifies the resolvability of earthquake source properties under specific conditions using a single-channel stand-alone integrated (non-distributed) fiber-optic measurement. It thereby constitutes a step towards the integration of long-range phase-transmission fiber-optic sensors into existing seismic networks in order to fill significant seismic data gaps, especially in the oceans.

High-Accuracy Phase Frequency Detection Technology Based on BDS Time and Frequency Signals.

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.

Single-frequency erbium-doped fiber laser based on self-injection feedback

In this paper, a single-frequency erbium-doped fiber laser based on self-injection feedback is reported, which uses a high-reflectivity broadband fiber Bragg grating, an ordinary commercial high-doped erbium fiber and a low-reflectivity broadband fiber Bragg grating to form the main resonant cavity, and a stable narrow linewidth single-frequency laser output is achieved by connecting a single-mode fiber and a low reflectivity narrowband fiber Bragg grating to form self-injection feedback. Then, a saturated double-pass erbium-doped fiber amplifier and a saturable absorber were added to the self-injection optical path, which well suppressed the relative intensity noise and phase noise and the relaxation oscillation intensity was well suppressed by about 18.08 dB, and the phase noise was 36.7dBc·Hz−1 suppression, the edge-mode rejection ratio is increased by 13 dB, and the final laser linewidth is about 270 Hz, and the output power is 8.5 dBm.

Optical attenuator-oriented quantum hacking on continuous-variable quantum key distribution with local local oscillator

Continuous-variable quantum key distribution with local local oscillator (LLO-CVQKD) eliminates the security loophole caused by transmitting high power local oscillator (LO). However, in order to establish a common phase frame between the sender and receiver, a low power phase reference needs to be transmitted with quantum signals, which may bring in new security problems for eavesdroppers to obtain information illegally. Especially in trusted phase noise model, phase noise associated with detectors is regarded as trusted noise in order to obtain a higher secret key rate and transmission distance, which further provides opportunities for eavesdroppers. To this end, we propose an optical attenuator-oriented attack strategy against the LLO-CVQKD system under the trusted phase noise model, where Eve can inject suitable light into the optical attenuator in reference light path to reduce the attenuation level of it, thereby controlling the intensity of the reference pulses and resulting in an underestimated excess noise. Simulation results show that the proposed attack strategy can render the estimated secret key rate much higher than the actual values. When the transmission distance exceeds 25 km, the eavesdropper can obtain approximately 90% of the key information by adjusting the intensity of the reference pulses to twice the original value.

A 40.3–50.5 GHz locking range transformer‐based injection‐locked frequency divider utilizing a high third harmonic rejection buffer

AbstractInjection‐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.

W-band photonics-aided OFDM system integrating sensing and communication with phase noise suppression scheme

Photonic-aided technology offers many advantages in millimeter-wave (MMW) communication and sensing, such as low equipment cost and wide bandwidth. The combination of photonics-aided systems with orthogonal frequency division multiplexing (OFDM) waveforms enables high-performance integration of sensing and communication. In this paper, we propose and experimentally demonstrate a W-band photonic-aided OFDM system integrating sensing and communication (ISAC). To address the destruction of signal coherence by phase noise of the system, this paper proposes an OFDM sensing scheme combined with frequency-domain filtering to reduce the sidelobe interference caused by phase noise. Combined with offline digital signal processing algorithms, the system achieves high-precision ranging-Doppler imaging with a ranging resolution of 0.96 cm at a detection distance of 2 m. In terms of communication, after 10 m of wireless transmission, the net rate reaches 47.06 Gbit/s. The proposed system makes full use of the system's resources by using OFDM signals as both the sensing and communication signals. This may be beneficial for some potential applications of 6G in the future.

Phase Noise Compensation Algorithm for Space-Borne Azimuth Multi-Channel SAR.

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.