Frequency comb-based microwave transfer over fiber with 7×10(-19) instability using fiber-loop optical-microwave phase detectors

Fiber re-circulating emulator for precise 504-km optical frequency combs transmission

The propagation distance confines the development of precise time-frequency transmission using optical frequency combs due to the dispersion of the link. Here we disseminate a fiber re-circulating loop to emulate 504-km comb-based transmission. An optical filter in combination with a spool of dispersion compensation fiber is utilized to restrict the dispersion effect. The residual instability reached 4.0 × 10^-14 at 1 s and 7.32 × 10^-18 at 10,000 s over the 504-km link. The result indicated that this approach could meet the demand for long-haul clock transmission and comparison in the giant fiber-optic gyroscope to detect the seismic and gravitational potential.

Open-loop polarization mode dispersion mitigation for fibre-optic time and frequency transfer

The non-reciprocal and dynamic nature of polarization mode dispersion (PMD) in optical fibers can be a problem for accurate time and frequency transfer. Here, a simple, passive solution is put forward that is based on transmitting optical pulses with alternating orthogonal polarization. The fast and deterministic polarization modulation means that the PMD noise is pushed far away from the frequencies of interest. Furthermore, upon reflection from a Faraday mirror at the receiver, the pulses have a well-defined polarization when they return to the transmitter, which facilitates stable optical phase detection and fibre phase compensation. In an open-loop test setup that uses a mode-locked laser and a simple pulse interleaver, the polarization mode dispersion is shown to be reduced by more than two orders of magnitude.

Absolute phase marking technology and fiber-optic remote coherent phase transmission

Fiber-optic time and frequency synchronization technology demonstrates ultra-high synchronization performance and has been gradually applied in various fields. Based on frequency synchronization, this study addressed the problems of period ambiguity and initial phase uncertainty of the phase signal to realize the coherent transmission of the phase. An absolute phase marking technology was developed based on high-speed digital logic with zero-crossing detection and an optimized control strategy. It can realize picosecond-level absolute phase marking and provide a picosecond-level ultra-low peak-to-peak jitter pulse marking signal to eliminate phase period ambiguity and determine initial phase and transmission delay. Thus, by combining the high-precision phase measurement capability of the synchronized frequency signal and long-distance ambiguity elimination capability of the pulse-per-second signal, a high-precision remote coherent phase transmission over an optical fiber is realized. After frequency synchronization, the peak-to-peak jitter between the local and remote phase-marking signals can be only 3.3 ps within 10,000 s measurement time. The uncertainty of the coherent phase transmission is 2.577 ps. This technology can significantly improve the phase coherence of fiber-optic time and frequency transmission and provide a new approach to achieve peak-to-peak picosecond-level reference phase marking and high-precision fiber-optic remote coherent phase transmission. This demonstrates broad application prospects in coherence fields such as radar networking.

Theoretical analysis for fiber-optic distribution of RF signals based on phase-locked loop

We establish an analytical model for the stable dissemination of radio-frequency (RF) signals via fiber-optic links. Based on the phase-locked loop theory, the contributions from the photonic RF source, transmission-path, and additional system noise have been taken into account, leading to the quantitative analysis of the phase noise evolution in the transmission link. Furthermore, the theoretical analysis reveals the relation between the system instability and the frequency of the transmitted signal, which is further verified. Assisted with the proposed model, the optimization for stabilized dissemination of RF signals with a certain length of transmission link or any specified noise floors can be achieved with minimized timing jitter performance, testifying the potential high stability obtained thanks to the higher transmitted signal frequencies. This quantitative model, enabling precise prediction of the frequency instability and timing jitter from the residual phase noise, can be a useful guide in designing a fiber-optic distribution system and evaluating its fundamental limits.

Distribution of optical-comb-based multi-frequency microwave signals over 100 km optical fiber with high phase stability

We demonstrate a long-distance multi-frequency microwave distribution system over an optical fiber link with high phase stability based on transferring an optical frequency comb (OFC). The phase fluctuation induced by the transmission link variations is detected by applying a reference OFC and is then compensated with the proposed optical voltage-controlled oscillator (OVCO) by adjusting the phase of the repetition rate of the transmitted OFC. By applying the OVCO, we perform the OFC-based multi-frequency microwave distribution over a 100 km standard single-mode fiber. The performance of the transmission system can be exhibited by evaluating the repetition rate (10.015 GHz) and second harmonic frequency (20.03 GHz) signals achieved at the remote end. The residual phase noise of the 10.015 GHz and 20.03 GHz signal is -64 dBc/Hz and -58 dBc/Hz at 1 Hz frequency offset from the carrier, respectively. The fractional frequency instability is 1.4×10^-16 and 2.4×10^-16 at 10000 s averaging time, respectively. And the timing jitter in the frequency range from 0.01 Hz to 1 MHz reaches 88 fs and 87 fs, respectively. Based on the phase-locked loop theory, we conduct a simulation model of the transmission system and the simulated results match well with experiments. It shows that by detecting the phase fluctuation with higher harmonic frequency signals in the simulation system, the performance of the transmission system can be further improved.

Stable frequency dissemination over multi-access fiber loop link with optical comb

An optical comb based stable frequency dissemination system is proposed and experimentally demonstrated over a multi-access optical fiber loop link. In the system, a new technique based on optical-microwave phase locking loop is designed for phase compensation. In the experiment, a mode-locked fiber laser at a repetition rate of 100 MHz is used to provide an optical source at local site, then it transmits along a 150 km fiber loop link. To testify the proposed system, two accessing nodes are measured in the loop link. The dissemination frequency instability is measured at 3.65 × 10^-15/1 s and 7.8 × 10^-18/1000 s at the intermediate node. The similar performance is shown at the other node. Hence, the system has the potential application in high-precision frequency transmission system via a long-haul multi-access loop link.

Stable radio frequency dissemination via a 1007 km fiber link based on a high-performance phase lock loop

In this paper, we propose an active-compensation stable radio frequency (RF) transmission scheme based on a high-performance phase lock loop (PLL). In our PLL, a new structure for phase-detection is designed with only one standard RF signal to obtain a simple structure with no interference from other signals. In addition, different optical wavelengths carrying the same RF signal are utilized in the two directions to suppress Rayleigh scattering. The low phase noise homemade bi-directional erbium doped fiber amplifier (EDFA) module is used to reduce signal-to-noise ratio (SNR) deterioration. Hence, the transmission distance is greatly improved. The effects of polarization mode dispersion and phase noise produced by the EDFA on the transmission distance are discussed. Ultimately, a stable RF signal with 2.4 GHz transmitted over a 1007 km fiber link is obtained. The experimental results demonstrate that frequency instabilities of 1.2×10^{- 13} at 1s and 5.1×10^{- 16} at 20000s. Therefore, the system can be used for atomic clocks comparisons and provides frequency standard for time transfer systems over a long-haul fiber.

Simple-structured, subfemtosecond-resolution optical-microwave phase detector

We demonstrate a simple all-fiber photonic phase detector that can measure the phase (timing) difference between an optical pulse train and a microwave signal with subfemtosecond resolution and -60  dB-level amplitude-to-phase conversion coefficient. It is based on passive phase biasing of a Sagnac loop by the intrinsic phase shift of a symmetric 3×3 fiber coupler. By eliminating the necessity of magneto-optic components or complex radio frequency (RF) electronics for phase biasing of the Sagnac loop, this phase detector has potential to be implemented as an integrated photonic device as well. When using this device for synchronization between a 250 MHz mode-locked Er-fiber laser and an 8 GHz microwave oscillator, the minimum residual phase noise floor reaches <-154  dBc/Hz (at 8 GHz carrier) with integrated root mean square (rms) timing jitter of 0.97 fs [1 Hz-1 MHz]. The long-term rms timing drift and frequency instability are 0.92 fs (over 5000 s) and 4×10^-19 (at 10,000 s averaging time), respectively.

Ultrasensitive, high-dynamic-range and broadband strain sensing by time-of-flight detection with femtosecond-laser frequency combs

Ultrahigh-resolution optical strain sensors provide powerful tools in various scientific and engineering fields, ranging from long-baseline interferometers to civil and aerospace industries. Here we demonstrate an ultrahigh-resolution fibre strain sensing method by directly detecting the time-of-flight (TOF) change of the optical pulse train generated from a free-running passively mode-locked laser (MLL) frequency comb. We achieved a local strain resolution of 18 pε/Hz^1/2 and 1.9 pε/Hz^1/2 at 1 Hz and 3 kHz, respectively, with large dynamic range of >154 dB at 3 kHz. For remote-point sensing at 1-km distance, 80 pε/Hz^1/2 (at 1 Hz) and 2.2 pε/Hz^1/2 (at 3 kHz) resolution is demonstrated. While attaining both ultrahigh resolution and large dynamic range, the demonstrated method can be readily extended for multiple-point sensing as well by taking advantage of the broad optical comb spectra. These advantages may allow various applications of this sensor in geophysical science, structural health monitoring, and underwater science.

10-fs-level synchronization of photocathode laser with RF-oscillator for ultrafast electron and X-ray sources

Ultrafast electron-based coherent radiation sources, such as free-electron lasers (FELs), ultrafast electron diffraction (UED) and Thomson-scattering sources, are becoming more important sources in today's ultrafast science. Photocathode laser is an indispensable common subsystem in these sources that generates ultrafast electron pulses. To fully exploit the potentials of these sources, especially for pump-probe experiments, it is important to achieve high-precision synchronization between the photocathode laser and radio-frequency (RF) sources that manipulate electron pulses. So far, most of precision laser-RF synchronization has been achieved by using specially designed low-noise Er-fibre lasers at telecommunication wavelength. Here we show a modular method that achieves long-term (>1 day) stable 10-fs-level synchronization between a commercial 79.33-MHz Ti:sapphire laser oscillator and an S-band (2.856-GHz) RF oscillator. This is an important first step toward a photocathode laser-based femtosecond RF timing and synchronization system that is suitable for various small- to mid-scale ultrafast X-ray and electron sources.

Attosecond precision multi-kilometer laser-microwave network

Synchronous laser-microwave networks delivering attosecond timing precision are highly desirable in many advanced applications, such as geodesy, very-long-baseline interferometry, high-precision navigation and multi-telescope arrays. In particular, rapidly expanding photon-science facilities like X-ray free-electron lasers and intense laser beamlines require system-wide attosecond-level synchronization of dozens of optical and microwave signals up to kilometer distances. Once equipped with such precision, these facilities will initiate radically new science by shedding light on molecular and atomic processes happening on the attosecond timescale, such as intramolecular charge transfer, Auger processes and their impacts on X-ray imaging. Here we present for the first time a complete synchronous laser-microwave network with attosecond precision, which is achieved through new metrological devices and careful balancing of fiber nonlinearities and fundamental noise contributions. We demonstrate timing stabilization of a 4.7-km fiber network and remote optical-optical synchronization across a 3.5-km fiber link with an overall timing jitter of 580 and 680 attoseconds root-mean-square, respectively, for over 40 h. Ultimately, we realize a complete laser-microwave network with 950-attosecond timing jitter for 18 h. This work can enable next-generation attosecond photon-science facilities to revolutionize many research fields from structural biology to material science and chemistry to fundamental physics.

Dissemination of optical-comb-based ultra-broadband frequency reference through a fiber network

We disseminated an ultra-broadband optical frequency reference based on a femtosecond (fs)-laser optical comb through a kilometer-scale fiber link. Its spectrum ranged from 1160 nm to 2180 nm without additional fs-laser combs at the end of the link. By employing a fiber-induced phase noise cancellation technique, the linewidth and fractional frequency instability attained for all disseminated comb modes were of order 1 Hz and 10^-18 in a 5000 s averaging time. The ultra-broad optical frequency reference, for which absolute frequency is traceable to Japan Standard Time, was applied in the frequency stabilization of an injection-seeded Q-switched 2051 nm pulse laser for a coherent light detection and ranging LIDAR system.

Long-term phase-locking technique for locking the repetition rate of an optical frequency comb laser with 1.67 × 10-19 precision

An ultrahigh stable phase-locked loop system for synchronization of an optical frequency comb to a hydrogen maser has been proposed and experimentally demonstrated. A mathematical model has been set up to investigate the feasibility and steady state of the phase-locking system. The fractional frequency instability is evaluated by measuring the mixed-phase signal of an improved experimental system. Experimental results show that the fractional frequency instability of the phase-locked loop system lies from 8.83×10^-16 at 1 s to 1.67×10^-19 at 1000 s, which indicates our proposed phase-locking system possesses ultrahigh measurement precision with good long-term stabilization performance.

Polarization Drift Channel Model for Coherent Fibre-Optic Systems

A theoretical framework is introduced to model the dynamical changes of the state of polarization during transmission in coherent fibre-optic systems. The model generalizes the one-dimensional phase noise random walk to higher dimensions, accounting for random polarization drifts, emulating a random walk on the Poincaré sphere, which has been successfully verified using experimental data. The model is described in the Jones, Stokes and real four-dimensional formalisms, and the mapping between them is derived. Such a model will be increasingly important in simulating and optimizing future systems, where polarization-multiplexed transmission and sophisticated digital signal processing will be natural parts. The proposed polarization drift model is the first of its kind as prior work either models polarization drift as a deterministic process or focuses on polarization-mode dispersion in systems where the state of polarization does not affect the receiver performance. We expect the model to be useful in a wide-range of photonics applications where stochastic polarization fluctuation is an issue.

Efficient carrier-envelope offset frequency stabilization through gain modulation via stimulated emission

A novel scheme for intracavity control of the carrier-envelope offset (CEO) frequency of a 100 MHz mode-locked Er:Yb:glass diode-pumped solid-state laser (DPSSL) based on the modulation of the laser gain via stimulated emission of the excited Er(3+) ions is demonstrated. This method allows us to bypass the ytterbium system few-kHz low-pass filter in the f(CEO) stabilization loop and thus to push the phase lock bandwidth up to a limit close to the relaxation oscillations frequency of the erbium system. A phase lock bandwidth above 70 kHz has been achieved with the fully stabilized laser, leading to an integrated phase noise [1 Hz-1 MHz] of 120 mrad.

300-MHz-repetition-rate, all-fiber, femtosecond laser mode-locked by planar lightwave circuit-based saturable absorber

We show the implementation of fiber-pigtailed, evanescent-field-interacting, single-walled carbon nanotube (CNT)-based saturable absorbers (SAs) using standard planar lightwave circuit (PLC) fabrication processes. The implemented PLC-CNT-SA device is employed to realize self-starting, high-repetition-rate, all-fiber ring oscillators at telecommunication wavelength. We demonstrate all-fiber Er ring lasers operating at 303-MHz (soliton regime) and 274-MHz (stretched-pulse regime) repetition-rates. The 303-MHz (274-MHz) laser centered at 1555 nm (1550 nm) provides 7.5 nm (19 nm) spectral bandwidth. After extra-cavity amplilfication, the amplified pulse train of the 303-MHz (274-MHz) laser delivers 209 fs (178 fs) pulses. To our knowledge, this corresponds to the highest repetition-rates achieved for femtosecond lasers employing evanescent-field-interacting SAs. The demonstrated SA fabrication method, which is based on well-established PLC processes, also shows a potential way for mass-producible and lower-cost waveguide-type SA devices suitable for all-fiber and waveguide lasers.

Few-femtosecond-resolution characterization and suppression of excess timing jitter and drift in indoor atmospheric frequency comb transfer

We characterize the timing jitter spectral density of the time-of-flight (TOF) in the indoor atmospheric transfer of optical pulse train over 10 decades of Fourier frequency range (10 μHz - 100 kHz) with sub-100-as resolution using a balanced optical cross-correlator (BOC). Based on the well-known theory for atmospheric transfer of a laser beam, we could fit the measured timing jitter power spectral density to the theory and analyze it with a fairly good agreement from 20 mHz to 10 Hz Fourier frequency range. Moreover, we demonstrate that the BOC-based timing stabilization method can suppress the excess fluctuations in timing from >200 fs (rms) to 2.6 fs (rms) maintained over 130 hours when an optical pulse train is transferred over a 76.2-m long free-space beam path in laboratory environment. The demonstrated stabilization result corresponds to 4 × 10(-20) overlapping Allan deviation at 117,000 s averaging time.

High-precision distribution of highly stable optical pulse trains with 8.8 × 10⁻¹⁹ instability

The high-precision distribution of optical pulse trains via fibre links has had a considerable impact in many fields. In most published work, the accuracy is still fundamentally limited by unavoidable noise sources, such as thermal and shot noise from conventional photodiodes and thermal noise from mixers. Here, we demonstrate a new high-precision timing distribution system that uses a highly precise phase detector to obviously reduce the effect of these limitations. Instead of using photodiodes and microwave mixers, we use several fibre Sagnac-loop-based optical-microwave phase detectors (OM-PDs) to achieve optical-electrical conversion and phase measurements, thereby suppressing the sources of noise and achieving ultra-high accuracy. The results of a distribution experiment using a 10-km fibre link indicate that our system exhibits a residual instability of 2.0 × 10⁻¹⁵ at1 s and8.8 × 10⁻¹⁹ at 40,000 s and an integrated timing jitter as low as 3.8 fs in a bandwidth of 1 Hz to 100 kHz. This low instability and timing jitter make it possible for our system to be used in the distribution of optical-clock signals or in applications that require extremely accurate frequency/time synchronisation.