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.

Astro-combs are critical for achieving cm⋅s-1 radial velocity (RV) precision in exoplanet detection, as they offer dense reference lines well matched to stellar absorption features. We demonstrate a blue-band astro-comb by filtering a 1 GHz ytterbium fiber frequency comb with a passively stabilized zero-dispersion Fabry-Pérot cavity (FPC) and fully characterize the filtered spectrum using a homemade Fourier transform spectrometer (FTS). Our key finding is that the FPC transmission lines exhibit non-uniform spacing, with deviations mostly within 4 MHz (up to 10 MHz) relative to the average free spectral range of ~44.789 GHz-challenging the conventional assumption of uniformly spaced calibration markers. Despite this non-uniformity, averaging over 1340 resolvable comb teeth suppresses single-line RV errors (2 m·s-1) to an overall RV precision of 5.5 cm·s-1. Long-term stability tests over 45 days yield RV precision between 7 and 8 cm⋅s-1, confirming suitability for exoplanet detection campaigns. This work underscores the need for detailed spectral characterization of astro-combs, as FPC-induced spacing non-uniformity fundamentally influences calibration accuracy and provides critical insights for advancing cm·s-1-level RV precision.

We demonstrate a compact astro-comb with ~30 GHz line spacing covering the 560–900 nm range, seeded by a 1 GHz Yb:fiber laser frequency comb phase-locked to a rubidium clock for long-term frequency stability. The comb spacing is multiplied by a passively stabilized Fabry–Pérot cavity, which is vacuum-sealed (3.3 × 10−5 Pa) and temperature-controlled at 25 ± 0.05 °C, exhibiting a resonance linewidth of 80.56 MHz. Characterization using a high-resolution Fourier-transform spectrometer reveals sharp, evenly spaced comb lines with a maximum side-mode suppression ratio of 23.86 dB. The estimated radial velocity (RV) precision reaches ~63 cm/s, and further reduction in measurement noise is expected to achieve <10 cm/s precision, meeting the stringent requirements of next-generation astronomical spectrographs.

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).

Objective This study addresses the challenge of generating high-quality, visible-to-blue supercontinuum (SC) spectra using GHz-repetition-rate femtosecond laser frequency combs. While GHz combs offer advantages in mode spacing and system integration, especially for astronomical spectrograph calibration and precision metrology, their low single-pulse energy limits efficient spectral broadening. To overcome this, we develop and experimentally demonstrate a pre-chirped, dual-stage nonlinear fiber amplification scheme, achieving SC generation from 440 nm to 1500 nm at nJ-level pulse energies. The results provide a stable, broadband light source for advanced GHz frequency comb applications and pave the way for future extension into violet and ultraviolet (UV) regimes. Methods The experiment employs a 1 GHz mode-locked fiber laser as the seed source, producing 54 fs pulses with a 33 nm bandwidth. A portion of the output is amplified using a two-stage nonlinear fiber amplifier. The first stage, based on a single-mode polarization-maintaining (PM) fiber, boosts the power from 22 mW to 146 mW. The second stage, using a double-cladding PM fiber, further increases the output to 1.93 W. Pre-chirp control and precise dispersion management enable pulse compression to 110 fs and enhance nonlinear interactions (Fig. 4 and Table 1). The compressed pulses are injected into a tapered photonic crystal fiber (PCF), engineered to shift the zero-dispersion wavelength and support efficient supercontinuum (SC) generation extending into the blue. The resulting SC spans 440-1500 nm. Spectral characteristics are measured using optical spectrum analyzers (Fig. 5), and the SC stability is assessed through long-term spectral recording and power monitoring over 6 h (Fig. 6). Results and Discussions The experiment successfully generates a broadband SC spectrum covering 440 nm to 1500 nm with an average power of 1.5 W and a pulse energy of 1.5 nJ. The compressed pulses exhibit a 3 dB bandwidth of 28.8 nm and a pulse duration of 110 fs (Fig. 4). The SC spectrum shows a uniform power distribution across the visible range, with the blue region (440-550 nm) achieving over 20 mW power (Fig. 5). Stability measurements over 6 h demonstrate minimal power fluctuation (<1 mW) and consistent spectral profiles (Fig. 6). Notably, increasing the pump power to 11 W extends the spectrum to 420 nm but introduces a dip in the 570-700 nm range due to soliton self-frequency shift (SSFS) effects. These results highlight the effectiveness of the proposed amplification and spectral broadening strategies in achieving high-quality SC generation under low-energy conditions. SC spanning 440 nm to 1500 nm is achieved using a GHz repetition-rate system at pulse energies of only 1.5 nJ and pulse durations of 110 fs after compression. The visible portion (>50 mW), including 20 mW in the 440-550 nm blue region, exhibits spectral flatness with intensity variation within 20 dB [Fig. 5(a)]. The system second-order dispersion (SOD) is compensated to near zero, while the third-order dispersion (TOD) is self-compensated through nonlinear phase accumulation during amplification. As a result, the compressed pulses exhibit high peak powers, minimal sidelobes, and clean temporal profiles [Table 1 and Fig. 4(b)]. As pump power increases, the appearance of spectral dips (e.g., 570-700 nm) is attributed to SSFS, which red-shifts the pulse center wavelength and disrupts the phase-matching conditions for dispersive wave generation in this band. This mechanism highlights the importance of managing soliton dynamics and dispersion design for SC uniformity [Fig. 5(b)]. The visible (440-900 nm) SC output power remains stable within <1 mW fluctuation over 6 h continuous operation at 9 W pump power. Spectral shape and peak positions show no significant drift, demonstrating the system thermal and mechanical stability for metrology applications (Fig. 6). Conclusions This work presents an effective strategy for generating broadband supercontinuum light from a GHz-repetition-rate femtosecond fiber laser using pre-chirped, dual-stage nonlinear amplification. Despite the low pulse energy (similar to 1.5 nJ), the system delivers 110 fs pulses and achieves spectral broadening from 440 nm to 1500 nm, with similar to 20 mW power in the blue region. The resulted spectrum is flat, stable, and well-suited for high-precision applications such as astronomical spectrograph calibration. These results confirm the viability of nonlinear amplification and dispersion control at high repetition rates and establish a scalable approach for extending GHz frequency combs into the violet and ultraviolet. This work provides a solid technical foundation for advancing GHz comb systems in precision metrology and broadband spectroscopy.

We demonstrated a divided pulse amplification of burst pulse trains.The intraburst rate is 1 GHz,and the burst rate ranges from 1.5 kHz to 15 MHz.Under the pump power of 100 W,the burst pulse energy is adjustable from 2.2 μJ to 22 mJ.The pulse width of combined and compressed pulses is 275 fs with beam quality M2 of 1.2.

This research topic is based on the time-domain self-imaging effect (Talbot effect) and uses all-fiber technology to achieve an increasement in the time-domain repetition frequency of optical frequency comb signals outside the laser cavity. A 10 GHz signal source is generated from a 250 MHz laser signal without affecting the shape and duration of original individual pulses. It can avoid the limitations of some traditional methods and prepare for the subsequent increasement of the frequency difference between the comb teeth of an optical frequency comb from megahertz to the gigahertz level, while maintaining a high signal-to-noise ratio.

We demonstrate an optical fiber -based, multiple -access frequency transmission using two optical frequency combs. The experimental results using the Allan deviation analysis show that with the phase compensation technique, the frequency instabilities at the remote site are 8.7 x 10 -15 / 1 s and 1.0 x 10 -17 / 1 0 3 s, and at the accessing node along the fiber link, the frequency instabilities are 6.9 x 10 -15 / 1 s and 1.1 x 10 -17 / 1 0 3 s. Similarly, the power spectral density of phase noise was analyzed in the frequency domain. These experimental results demonstrate that the compensation scheme improved the performance by two to three orders of magnitude. Thus, the proposed frequency transmission technique has potential application for disseminating ultrastable frequency references in the optical fiber network. (c) 2024 Optica Publishing Group

The time-to-digital converter (TDC) is a key technology for achieving accurate time delay measurements in fiber-optic time transmission and synchronization system. Current architectures for TDC implementation mainly consist of coarse counters paired with different fine counter architectures. Here, we propose and implement a new fine counter architecture that synthesizes the time interval between pulses and the reference clock into a single pulse. The width of synthesized pulse is measured to enhance precision through the reuse of measurement units. The TDC stability is evaluated through the back-to-back (BTB) experiment. The short-term time deviation (TDEV) is 8.07 ps@1s, and the long-term TDEV is 0.18ps@10(4)s. Additionally, the proposed TDC is applied in a laboratory-built round-trip time synchronization system over 680km fiber link. The timing jitter of the system is measured to be 38.02ps.

Fiber-delay measurement is one of the key fundamental technologies in numerous fields. Here, we propose and experimentally demonstrate a high-precision and concise optical time delay measurement system based on the technique of linear optical sampling, reaching the precision better than 100 fs under averaging. The use of only two optical frequency combs without locking the carrier-envelope-offset frequency greatly simplifies the structure of the time-delay measurement system. We also experimentally investigate the current limitations on the precision of the system. The timing jitter noises of two sources are mainly non-common mode and are both restricted to the frequency sources. Our results indicate that the proposed device can measure fiber length fluctuations below 10 µm, paving the way for further analyses of the external disturbances on the fiber link.

We demonstrate fiber-based multiple-access frequency transmission using two optical frequency combs. The optical frequency comb connects the optical and microwave domains. The highly stable microwave frequency was transmitted in a 3km optical-fiber link. The experimental results show that with the phase compensation technique, the frequency instabilities at the remote site are 8.7 × 10 −15 and 1.0×10 −17 for averaging times of 1 s and 10 3 s. At the accessing node along the fiber link, frequency instabilities are 6.9×10 −15 and 1.1 × 10 −17 for averaging times of 1 s and 10 3 s. Compared to the uncompensated transmission, frequency instabilities are reduced by two orders of magnitude for both the remote site and the accessing node. Thus, the proposed frequency transmission technique has potential application for disseminating ultra-stable frequency references to multiple precision devices.

Two-way fiber-optic time transfer (TWFTT) is a promising precise time synchronization technique with subnanosecond stability. However, the asymmetric delay attack is a severe threat, which can deteriorate the performance of the TWFTT system. In this article, a clock model-based scheme is used to defend the subnanosecond asymmetric delay attack. For the scheme, a security threshold is set according to a two-state clock model, and the estimated frequency difference is excluded from the measured time difference to detect the subnanosecond asymmetric delay attack. Systematic detection and mitigation scheme for asymmetric delay attack is developed in this article. Theoretical simulation and experimental demonstration are implemented to explore the feasibility of the method. A TWFTT system of time stability with 24.5, 3.98, and 2.95 ps at average times of 1, 10, and 100 s is shown under subnanosecond asymmetric time delay attack experimentally for the first time. The proposed method provides a promising secure subnanosecond precise time synchronization technique against asymmetric delay attacks.

SummaryMixer is usually used as the phase discriminator in a frequency transfer system, of which characteristics are directly related to the stability of the transfered signal. This experiment verifies the system characteristics of amplitude and phase noise conversion in mixers. The output noise of the mixer are minimum when two inputed signals are nearly orthogonal, which is called the Sweet Point. Compared with other cases, amplitude fluctuations at Sweet Point can be reduced by an order of magnitude and the measured instability can be improved.

We demonstrate a reliable network to disseminate high-precision RF frequency by optical frequency comb via fiber link. Dense wavelength division multiplexing and MEMS optical switches are used in this network, which realize protection switching. In this network, high-precision frequency is transferred to multi-nodes. The fiber link is monitored in real time and the synchronized signal can be automatically recovered immediately. We propose a phase noise compensation technique that the fractional frequency instability was measured to be at 9.2 X 10-17/102s on 20 km optical fiber link. This work paves the way for ultra-stable frequency transmission and distribution networks.

Long-term ultra-precision synchronization between optical frequency combs (OFCs) and microwave oscillators is important for various fields, including scientific observation, smart grid, positioning and navigation, etc. Here, a phase-locked loop system based on fiber loop optical-microwave phase detector (FLOM-PD) is proposed to realize the synchronization of the repetition rate of OFCs and rubidium atomic clocks. Firstly, the scheme and locking process of the system are elaborated, then the mathematical model of the system is established, and the feasibility of the scheme is proved by theoretical analysis and experimental verification. After synchronization, the instability of the system reaches 8.69×10 −12 at 1 s and 2.94×10 −13 at 1 000 s, indicating that the phase synchronization system can achieve ultra-precision and stability of OFCs repetition rate.

We demonstrate a high-precision, high robustness frequency offset locking method,which made the frequency offset between mode-locked laser and continuous-wave laser below less than 3 Hz. The coarse frequency lock control is realized by the feedback control of PZT with electrical delay line as the reference. The fine frequency compensation is realized by feed-forward control of an acousto-optic modulator. The fractional frequency instability was 7.4×10 -10 for an averaging time of 1 s, 3.3×10 -8 for an averaging time of 10 000 s when the narrow linewidth laser is free-running. In this experiment, the fractional frequency instability can be achieved at 1.1×10 -15 for an averaging time of 1 s, at 3.6×10 -18 for an averaging time of 10 000 s when the system is fine frequency locked. Compared with the unlocked laser, the fractional frequency instability can be improved about 5-6 orders of magnitude. This work lays the foundation for simple structure, high robustness and high precision laser frequency control situation, such as quantum precision measurement and optical lattice clocks.

We propose a physical model of estimating noise and asymmetry brought by high isolation Bi-directional erbium-doped fiber amplifiers (Bi-EDFAs), no spontaneous lasing even with high gain, in longdistance fiber-optic time and frequency (T/F) synchronization system. It is found that the Rayleigh scattering noise can be suppressed due to the high isolation design, but the amplified spontaneous emission (ASE) noise generated by the high isolation Bi-EDFA and the bidirectional asymmetry of the transmission link caused by the high isolation Bi-EDFA will deteriorate the stability of the system. The calculated results show that under the influence of ASE noise, the frequency instability of a 1200 km system composed of 15 high isolation Bi-EDFAs is 1.773 × 10−13/1 s. And the instability caused by asymmetry is 2.6064 × 10−16/30000–35000 s if the total asymmetric length of the bidirectional link length is 30 m. The intensity noises originating from the laser and detector, the transfer delay fluctuations caused by the variation in ambient temperature and the jitter in laser output wavelength are also studied. The experiment composed of three high isolation Bi-EDFAs is done to confirm the theoretical analysis. In summary, the paper shows that the short-term instability of the T/F synchronization system composed of high isolation Bi-EDFAs is limited by the accumulation of ASE noise of amplifiers and the laser frequency drift, while the long-term instability is limited by the periodic variation in ambient temperature and the asymmetry of the amplifiers. The research results are useful for pointing out the direction to improve the stability of the fiber-optic T/F synchronization system.

Precise and secure time synchronization between two remote sites is necessary in many practical scenarios. Recently, the two-way fiber time transfer (TWFTT) system has become an attractive option for high-precision time synchronization. However, TWFTT is implemented based on symmetric link assumption, and such assumption may be maliciously utilized to cause significant time asynchronization to TWFTT. In this paper, we propose two novel controllable asymmetry attack schemes for TWFTT, namely, the link asymmetry attack and the attenuation asymmetry attack. We theoretically analyze the controllability and the effectiveness of these two attacks. Experimental results show that our link asymmetry attack can introduce 2.49 ns time offset per asymmetric link length (in meters), and our attenuation asymmetry attack can introduce at most 36.6 times time offset (compared to normal situation) when the attenuation is 45.3%. Our work can provide instructive insights for future studies of protecting TWFTT from delay asymmetry attacks.

为了能更加灵活方便地实现高精度的时频信号传递,以空间链路代替光纤进行时频传递,阐述了自由空间光频梳频率传递基本原理,实验通过102 m的自由空间链路,将锁定至铷原子钟上的飞秒光频梳发送到远端,采用高速探测器直接探测,通过高精度频率计数器采集光频梳重复频率数据.实验结果表明:该系统最终实现接收端100 MHz重复频率信号在30 min内抖动范围为3.5 mHz,重复频率稳定度为4.26×10-12/s、4.81×10-13/100 s.

为了将光频梳锁定至原子钟以实现光频梳的高精度稳定,提出了一种集成化重复频率锁定系统方案.利用光纤环路光学-微波鉴相器(FLOM-PD)进行光波和微波之间的直接鉴频鉴相.同时,开发了精密反馈控制模块,阐述了其基本原理,搭建了锁定系统,通过高精度频率计采集锁定后激光器脉冲重复频率数据.实验结果表明:该方案锁定后频率短期稳定度和长期稳定度分别达到8.71×10-12/s、4.95×10-14/1024 s,实现了整个系统的集成化.