The mode-locking mechanism of Kerr-lens mode-locked lasers is analyzed using the nonlinear ABCD matrix formalism. Our findings demonstrate that positioning the Kerr medium at the beam waist and operating the resonator near the stability boundary significantly enhances the nonlinear effect, thereby facilitating self-starting mode-locking without requiring any external initiation mechanisms.

Fiber-optic interferometers are widely used in phase modulation (PM) time transfer systems. To achieve stable phase demodulation, resisting the phase drift within the interferometer is essential. Moreover, using lithium niobate phase modulator in the interferometer inevitably introduces residual intensity modulation (RIM) due to its inherent imperfections. A stable phase control method based on optical power detection is proposed to resist phase drift and concomitantly suppress RIM. Furthermore, the characteristics of phase control at the extremum point (EP) and near-extremum point (NEP) of the interferometric response curve are analyzed and compared. Analysis shows that EP control offers lower demodulation stability but higher sensitivity to intensity fluctuations than NEP control. A fiber-optic time transfer experiment validates the applicability and effectiveness of the proposed method and confirms the analysis. The proposed method enhances the interferometer’s demodulation stability and shows good application prospects in phase signal detection.

Frequency-noise power spectral density (FN-PSD) is a key metric for evaluating laser performance, but conventional measurement schemes often require complex frequency- and phase-discriminator-based setups followed by extensive signal post-processing. Here, we demonstrate a compact laser frequency-noise measurement module based on an acousto-optic-modulator-based Michelson interferometer. An approximate relationship between the measured beat spectrum and the FN-PSD is established for this architecture, enabling direct beat-spectrum-based reconstruction. A two-parameter stability-based bandwidth-integration calibration method is further developed for carrier-power determination, improving its robustness against carrier-profile variations induced by electrical spectrum analyzer settings and laser-source characteristics. The system is implemented as a compact packaged module with a footprint comparable to a B5-size notebook, improving system integration and eliminating the need for pre-measurement polarization adjustment. Experiments with both a fiber laser and a semiconductor laser show good agreement between the reconstructed spectra and OE4000 measurements, verifying the proposed reconstruction scheme and carrier-power calibration strategy.

In this paper, we propose a method of stable frequency transfer over a 400 km link without an external power supply by combining distributed Raman amplifiers (DRAs) and remote optical pump amplifiers (ROPAs). We elaborate on the advantages of these technologies and their physical limitations in unrepeatered frequency transfer. In this study, by integrating a Bi-ROPA and a first-order DRA in a single-fiber bidirectional configuration over a 400 km ultralong-haul unrepeatered frequency link (with an average loss of 0.2 dB/km), a frequency instability of 8 x 10-14 at 1 s integration time and 2 x 10-16 at 10,000 s integration time has been achieved.

High-precision time and frequency transfer plays a pivotal role in metrology, geodesy, deep-space exploration and other scientific applications. Based on current time synchronization research, extending point-to-point schemes into a wide-area network can significantly increase the range of applications. Therefore, we design and implement a cascaded fiber optic time synchronization system, which is the most basic form of networking. This paper considers two different modulation formats for time synchronization systems from the perspective of fiber nonlinear effects, namely the intensity modulation with direct detection (IMDD) scheme and the phase modulation with self-coherent detection (PMSCD) scheme. The analysis indicates that the constant-envelope characteristic of the PMSCD scheme provides superior transmission performance. Accordingly, we deployed the PMSCD system over a 500 km intercity fiber link and the IMDD system over a 68 km metropolitan fiber link, forming a 568 km cascaded system that achieves time synchronization precision better than 50 ps. This work offers a practical reference for the future development of high-precision fiber-optic time and frequency synchronization networks.

Single-shot spectroscopy enables the capture of an entire transient event within a single measurement, providing critical insights into rapid and non-repetitive processes across diverse fields such as biomedical diagnostics, environmental monitoring, material stress analysis, advanced manufacturing, and telecommunication network fluctuation detection. Despite its promise, current single-shot spectroscopic systems are fundamentally constrained by an inherent incompatibility between spectral bandwidth, spectral resolution, and acquisition speed, limiting their versatility and broader adoption. Here, we introduce a reconfigurable single-shot spectroscopy method that offers full programmability over spectral bandwidth, resolution, and acquisition speed, enabling programmable navigation of the trade-off. By selecting optimal configurations, our approach compensates for the traditional limitations in spectral resolution, achieving a record-breaking resolution of 86 femtometers in the 1.5 μm band-comparable to state-of-the-art Michelson-based Fourier transform spectrometers. Leveraging this technique, we successfully capture rapid dynamic spectral fluctuations of phase-shift fiber Bragg gratings induced by both continuous (9 kHz) and sudden (0.1 ms) vibrations. This innovation broadens the application landscape and paves the way for the commercialization of single-shot spectroscopy.

In precision frequency transfer systems, stringent requirements are imposed on the phase stability of transmitted signals. Throughout the transmission process, the inherent challenges of long-haul signal propagation inevitably introduce multiple noise components, including, but not limited to, thermal noise, phase fluctuations, and environmental interference. The system is inclined to use the conventional evaluation index - Allan deviation (ADEV) to reflect the system stability in order to evaluate the noise level. Whereas, ADEV can only provide numerical expression and lacks the time-frequency details, a complete evaluation system is therefore required by the system. In this paper, we present a groundbreaking integration of ADEV and wavelet-transformed empirical mode decomposition (EMD-WT), establishing a novel analytical framework that enables simultaneous characterization of noise types and time-frequency domain properties. This synergistic approach achieves unprecedented dual-domain resolution in noise discrimination in frequency transfer systems.

Atmospheric turbulence in free space affects communication links, leading to a deterioration of the frequency stability of frequency-transmission systems. We establish a relation between the effect of phase fluctuations induced by atmospheric turbulence and the instability of frequency transmission in free space. Considering the optical coupling efficiency as an intermediary between the frequency-transmission system and atmospheric turbulence, we analyze the transfer behavior of frequency stability under varying turbulence conditions, combined with the Gamma-Gamma channel statistical model. In this study, we experimentally validate the model over a 1 km free-space link. Frequency stabilities of 4.1 & times; 10-12 at 1 s and 4.7 & times; 10-15 at 1000 s are demonstrated. The observed optical power fluctuations and the system Allan deviation (ADEV) are in excellent agreement with the simulation results, fully confirming the model's accuracy and applicability in assessing the degradation effects of atmospheric turbulence. This work provides a theoretical tool for quantitatively analyzing the limits of frequency transmission in complex atmospheric environments and offers important guidance for optimizing the design of urban free-space optical frequency transfer systems.

Photonic time-stretch microwave channelization enables simultaneous multi-channel monitoring using a single optical channel and shows strong potential for military electronic spectrum detection. However, its resolution and accuracy have been limited compared to mature parallel approaches. We present an improved system that overcomes these shortcomings by employing pulse picking to adjust the repetition rate of a mode-locked laser, introducing a pre-modulation dispersion of -829 ps/nm, and using a second dispersion compensation fiber stage with optical amplification to further stretch RF-modulated optical pulses in the time domain. After photodetection and sampling, digital signal processing performs spectral transformation, slicing, and analysis. The enlarged optical time window allows fine channel discrimination and precise frequency estimation. Experiments demonstrate a record-breaking resolution of 73 MHz and accuracy of f 2 MHz in serial photonics channelization.

In this Letter, we propose a fiber-optic round trip time transfer system tolerant to the received optical signal noise ratio (OSNR) degradation through forward frequency transfer. Typically, OSNR degrades with increased transmission distance and noise accumulation in fiber-optic time transfer systems, affecting the received signal-to-noise ratio (SNR) and system stability. The broad bandwidth of time signals limits the effectiveness of filtering to improve the received SNR. The proposed system overcomes these limitations by incorporating a forward-transmitted frequency (FTF) signal and a phase-locked pulse generator (PLPG), enhancing the received SNR and generating high-precision time pulses with minimal jitter. Theoretical simulations confirm the insensitivity to OSNR degradation of the system in short-term stability. Experiments over laboratory fiber links of 320 km, 640 km, and 960 km demonstrate short-term stabilities below 10 ps, with no significant deterioration despite increased transmission distance and OSNR degradation. Given its superior performance and noise resistance, this system holds significant promise for future ground-based fiber-optic time-frequency systems.

In long-haul fiber-optic time and frequency (T/F) transfer systems, the accumulation of amplified spontaneous emission (ASE) from amplifiers degrades the optical signal-to-noise ratio (OSNR) of the transmitted signal, thereby affecting the performance of the system. Therefore, we propose a scheme for OSNR monitoring and optimization in fiber-optic time transfer systems. The OSNR monitor exploits the difference in coherence between the signal and the ASE. It employs a Michelson delay line interferometer at the receiver, commonly used to demodulate the phase-modulated time signal (one pulse per second). By adjusting amplifier gains, we achieve optimal OSNR, and the Michelson interferometer continuously monitors OSNR changes to ensure reliable system operation. This scheme was verified over a 480 km laboratory fiber link containing five high-isolation bi-directional erbium-doped fiber amplifiers (HI-BiEDFAs). Experimental results show an SNR improvement of over 7 dB compared to the initial gain settings. The time deviation of the round-trip time transfer system is 18.84 ps at 1 s and 0.90 ps at 10,000 s, showing more than a twofold improvement in short-term stability over the traditional method of maintaining constant output power of HI-BiEDFAs. This scheme offers both pulses demodulation and OSNR monitoring without any additional modules, and the flexible utilization of monitoring data, enabling state awareness across the network-a key technological vision for future applications.

Laser synchronization is a technique of stabilizing the frequency difference between two lasers so that their frequencies change in synchronization. This technique is vital for both scientific and industrial applications. Conventional synchronization systems, whether digital or analog, exhibit inherent limitations in terms of accuracy and bandwidth. Current hybrid synchronization systems are usually based on hybrid digital and analog phase-locked loops (PLLs), which can partially address this limitation. However, since they are structured serially, their bandwidth remains constrained by the design of the analog component. This paper presents a hybrid “digital + analog” laser synchronization system with a parallel structure. The system's digital and analog locking loops operate independently, providing long-term stability and locking accuracy, respectively. This approach addresses the accuracy and bandwidth limitations present in serial hybrid digital and analog PLLs. We synchronized a single-frequency laser (SFL) to a mode-locked laser (MLL), achieving a frequency offset fluctuation of less than 2.5 Hz over 24 hours. Additionally, by synchronizing two SFLs to a repetition-frequency locked MLL, we achieved indirect synchronization between SFLs with a frequency offset of 10.6 GHz and a fluctuation of less than 5 Hz in 24 hours. These results demonstrate the robust long-term and short-term stability of the system. Based on this synchronization system, we proposed a photonic-assisted microwave frequency identification scheme with a detection error of less than 0.6 MHz. The high performance of the synchronization system enables the proposed frequency identification scheme to achieve high measurement accuracy and a theoretically extensive frequency range.

Secure precision time synchronization is important for applications of cyber-physical systems (CPSs). However, several attacks, especially the time delay attack (TDA), deteriorate the performance of the time synchronization system seriously. The multiple paths scheme is thought as an effective security countermeasure to decrease the influence of TDA. However, the effective secure combination algorithm is still missed for precision time synchronization. In this article, a secure combination algorithm based on the Dempster-Shafer (D-S) theory is proposed for the multiple paths method. Special optimizations are done for the combination algorithm to solve the potential problems due to untrusted evidence. Theoretical simulation shows that the proposed algorithm works much better than the fault-tolerant algorithm (FTA) and the attack detection method based on a single path. An experimental demonstration proves the feasibility and superiority of the proposed algorithm, where the time stability with 27.97, 1.57, and 1.12 ps at average time 1, 10, and 100 s is achieved under TDAs and local clock jumps. The proposed algorithm can be used to improve the security and resilience of many important synchronization protocols, such as network time protocol (NTP), precision time protocol (PTP), and two-way fiber-optic time transfer (TWFTT).

Time and frequency standards constitute fundamental requirements for diverse applications spanning daily life technologies to advanced scientific research. Among precision time dissemination methods, microwave-clock-based dual comb time transfer has emerged as a promising approach that achieves ultra-precise time interval measurements through linear optical sampling. However, conventional peak detection methodologies employed in such systems exhibit critical limitations: vulnerability to amplitude noise interference and inherent accuracy constraints imposed by analog sampling rates. To address these challenges, we present a novel digital time differential measurement paradigm integrating three key algorithmic innovations: (1) adaptive signal detection and extraction protocols, (2) multi-stage noise suppression processing, and (3) optimized centroid determination techniques. This comprehensive digital processing framework significantly enhances both measurement stability and operational efficiency, demonstrating single-shot temporal resolution at 17.6 fs stability levels. Our method establishes new capabilities for high-precision time-frequency transfer applications requiring robust noise immunity and enhanced sampling dynamics.

Significance Metrology is the scientific and technological discipline concerned with the quantification, measurement, and standardization of physical quantities, with the overarching goal of ensuring the accuracy, reliability, and traceability of measurement results. Among various physical quantities, time and frequency-enabled by the advancement of high-precision atomic and optical clocks-have become the most precisely measurable quantities within the seven base units of the international system of units (SI), forming a cornerstone of modern metrology. Time-frequency transfer refers to the low-loss dissemination of high-precision time and frequency signals from a source to a remote location, where they are faithfully recovered. High-precision time-frequency transfer underpins key advances in global positioning, navigation, and timing (PNT), supports fundamental tests of physics, and enables highly sensitive detection of environmental perturbations. Because metrology aims to achieve uniformity of units and guarantee the accuracy and reliability of measurement values, the evaluation metrics of the metrological system play a fundamental and indispensable role. However, in the field of time-frequency transfer, different research groups tend to adopt different evaluation metrics when reporting their results, which creates considerable difficulty for cross-comparison of studies. Moreover, an often overlooked issue is the specific conditions and scope of applicability required for the use of the Allan variance (AVAR) as an evaluation metric. In particular, from the perspective of structure functions, AVAR is essentially the first-order structure function of the frequency process. Using AVAR as an evaluation metric is therefore appropriate only when the physical system is first-order stationary, a prerequisite that is not universally satisfied. When this condition is not met, it is necessary to analyze the system's stability and employ higher-order structure functions as more appropriate evaluation metrics. Accordingly, it is important to summarize and clarify the primary roles, application scenarios, and distinctive advantages of the various metrics, thereby providing both a theoretical basis and practical guidance for selecting suitable evaluation criteria in time-frequency metrology research. Progress The analysis and evaluation of high-precision time-frequency signals can be divided into two domains: frequency and time. From the frequency-domain perspective, the focus is primarily on analyzing the power spectral density (PSD) of phase time and instantaneous frequency. Time-domain analysis, however, is more widely employed at present, where an important evaluation metric is AVAR, which characterizes the stability of a physical system across different time scales and resolves the divergence issues inherent to the conventional variance. The development of AVAR can be summarized as follows. The 1964 IEEE-NASA conference highlighted the lack of standardized criteria for assessing high-precision frequency signals and the resulting difficulty in comparing the short-and long-term accuracy of different physical systems. Consequently, Allan and other researchers conducted a series of studies, culminating in a 1971 report by the IEEE Time and Frequency Committee that formally defined and named the Allan variance. With continuing advances in time-frequency technology, the concept of AVAR was further extended. Subsequently, to address practical application scenarios and specific measurement challenges, a variety of related stability metrics were derived from AVAR, including the overlapping Allan variance (OAVAR), the time variance (TVAR), and the modified Allan variance (MVAR), etc. Their computational methods (Fig. 1) and mutual relationships (Fig. 2) are illustrated in this review.To address the limitations of AVAR and meet the requirements of specialized application scenarios, researchers have successively proposed several additional time-domain stability metrics, including the Hadamard variance (HVAR), total variance (TOTVAR), theoretical variance #1 (Theo1), and TheoH, which combines Theo1 with AVAR. Each of these metrics represents a specific improvement upon the conventional Allan variance. These refinements can be categorized into three branches (Fig. 3), each reflecting a distinct conceptual approach. The first branch, represented by MVAR, is based on the idea of overcoming the inability of conventional AVAR to distinguish certain types of noise. The second branch, exemplified by HVAR, consists of a family of metrics defined through higher-order differencing, aimed at dealing with higher-order perturbation terms. The third branch, represented by TOTVAR, Theo1, and TheoH, was introduced to enhance data utilization and increase confidence in long-term stability estimates, thereby providing improved evaluation of long-term stability. This review summarizes the principal evaluation metrics used in time-frequency transfer along with their primary functions or advantages (Table 1). Conclusions and Prospects This study systematically reviews and analyzes the stability evaluation metric framework of time-frequency signals, with a focus on frequency-and time-domain methods for assessing the stability of transferred signals, including key metrics such as PSD and AVAR. By establishing a unified metric framework, this review provides guidance on selecting appropriate stability metrics under varying noise types, time scales, and the amount of collected data. It is pointed out that most of these metrics lack direct conversion relationships, making it difficult to compare across different studies. Therefore, it is recommended that research groups report at least the PSD to improve the comparability of results. In addition, this work systematically reviews the multiple derived metrics of AVAR developed for different application scenarios. Overall, this review provides a reference and foundation for standardizing the evaluation metric framework in the field of time-frequency transfer research. In addition, the discussion presented here is not limited to time-frequency transfer; it offers guidance and reference for research groups in time-frequency and oscillator-related fields when selecting appropriate evaluation metrics.

To obtain precise and accurate timing signals across a wide area, the technique of fiber-optic time transfer is widely applied. As one of the main concerns in time transfer systems, transmission stability can be improved by applying filtering algorithms, and the Kalman filter (KF) usually plays a key role. The KF can be applied to enhance the precision of the transmission delay measurements within the system, and further improving the accuracy of delay compensation. Although the KF is optimal for linear Gaussian systems, it is not always effective for fiber-optic time transfer due to the nonlinear, nonstationary nature of fiber link time delay drift. The difficulty lies in the fact that the fixed state transition matrix in KF cannot track the unexpected fiber delay drift to achieve unbiased predictions. This limitation poses a potential risk of long-term stability degradation when applied to delay compensation. To address this issue, a time-varying state transition matrix is necessary. This article proposes a solution by introducing a data-driven neural network, specifically the long short-term memory (LSTM) model. The proposed method is experimentally validated over optical fiber transmission links spanning distances from 160 to 1280 km, demonstrating its ability to enhance short-term stability while preserving long-term stability, distinguishing it from the traditional KF. The short-term stability optimization is close to 1/root 2 across three different fiber lengths, which is equivalent to a 3-dB signal-to-noise ratio (SNR) improvement of the received one pulse-per-second (1PPS) signal. This result offers a promising solution for enhancing the precision and reliability of fiber-optic time transfer systems in a variety of applications.

In this letter, a novel phase compensation scheme is proposed and demonstrated for single-fiber bi-directional radio frequency (RF) transfer system. By introducing a temperature sensor-assisted tunable electrical delay line (EDL) into the dual-phase-locked loop (dual-PLL) module, the residual cumulative phase fluctuations introduced by strong temperature variations, as calculated by our theoretical model, can be further compensated. The performance is validated by transmitting a 2.4-GHz RF signal over 296 km of outdoor optical fiber. Results show that with an ambient temperature variation of 16.5 degrees C, the proposed scheme reduces the root mean square (RMS) phase jitter of the system by 72.7% and improves the frequency stability of the system at 40,000 s by more than half an order of magnitude compared to the scheme that only uses dual-PLL for phase compensation. Our proposed scheme enables RF transfer tolerant to strong temperature variations, providing a promising option for stable RF transfer in complex environments.

Very low-frequency (VLF) electromagnetic waves can penetrate dense, conductive media such as earth and saltwater, with minimal attenuation, enabling long-distance signal transmission via ionospheric reflection. These characteristics make VLF ideal for applications in submarine navigation, subterranean mapping, underground communication, and ionospheric remote sensing. Conventional VLF signal reception has relied on magnetic loop antennas due to their low noise performance; however, their large size and reduced sensitivity due to low quality factors (Q) limit their use in portable and compact applications, particularly in underwater and underground environments. To address these challenges, we propose an ultra-compact room-temperature extremely sensitive femto-tesla magnetic sensor based on a strain-mediated high-Q Metglas/Quartz magnetoelectric (ME) resonator operating at its electromechanical resonance (EMR) at 24.55 kHz for VLF signal reception. The Metglas/Quartz ME sensor demonstrates sensitivity and magnetic noise performance enhancement by an order of magnitude compared to conventional Metglas/PZT ME sensors, achieving an ultra-low equivalent magnetic noise level of 5 fT/Hz(1/2), owing to high magnetic permeability and magnetostriction of Metglas and the high quality factor of Quartz at EMR. Moreover, the Metglas/Quartz ME VLF receiver exhibits overwhelming near-field and far-field VLF signal reception capability, realizing a successful reception of a VLF signal similar to 400 km away from the NAA VLF Transmitter Cutler, with a 55 dB signal-to-noise (SNR) ratio. The demonstrated ultra-compact high-Q Metglas/Quartz ME sensor capable of femto-tesla VLF signal reception shows significant improvements in magnetic sensing capability, size, power consumption, and cost compared to traditional magnetic loop antennas, making it a promising solution for portable VLF signal reception in challenging environments.

Single longitudinal mode (SLM) fiber lasers are of significant research and practical value due to their unique performance and broad application potential in modern science, technology and industry. A SLM erbium-doped fiber laser (EDFL) with a power asymmetric ring configuration is proposed and experimentally validated. Compared with other saturable absorber structures, the proposed scheme with few fiber mode significantly reduces the optical path inside the cavity, requiring only one transmission through the main laser cavity. It is demonstrated to exhibit a remarkably narrow linewidth and an exceptional optical signal-to-noise ratio (OSNR). Experimental investigations reveal that a coefficient of 0.4 yields enhanced stability, with the maximum variations in the central wavelength confined to 0.008 nm. The wavelength of the proposed SLM EDFL exhibits a tuning range of 1552.460 nm to 1552.620 nm. The EDFL with a high OSNR of 68.78 dB and an narrow linewidth of 840 Hz is achieved at a pump power of 100 mW. This study presents a groundbreaking new approach to the design and performance of such lasers.

In this Letter, we propose a fiber-optic round trip time transfer system tolerant to the received optical signal noise ratio (OSNR) degradation through forward frequency transfer. Typically, OSNR degrades with increased transmission distance and noise accumulation in fiber-optic time transfer systems, affecting the received signal-to-noise ratio (SNR) and system stability. The broad bandwidth of time signals limits the effectiveness of filtering to improve the received SNR. The proposed system overcomes these limitations by incorporating a forward-transmitted frequency (FTF) signal and a phase-locked pulse generator (PLPG), enhancing the received SNR and generating high-precision time pulses with minimal jitter. Theoretical simulations confirm the insensitivity to OSNR degradation of the system in short-term stability. Experiments over laboratory fiber links of 320 km, 640 km, and 960 km demonstrate short-term stabilities below 10 ps, with no significant deterioration despite increased transmission distance and OSNR degradation. Given its superior performance and noise resistance, this system holds significant promise for future ground-based fiber-optic time-frequency systems.