Frequency transfer via a two-way optical phase comparison on a multiplexed fiber network

High-Precision Fiber Noise Detection and Comparison over a 260 km Field Fiber Link

In this paper, we present a high-precision optical frequency noise detection and comparison technique using a two-way transfer method over a 260 km field fiber link. This method allows for the comparison of optical frequencies between remote optical references without the need for data transfer through communication. We extend a previously established two-way comparison technique to obtain all data at the local site. Two optical carrier signals are injected into the bidirectional fiber from both ends, and one carrier is reflected back from the remote end. This enables the phase comparison of the two carrier signals at a single site without the need to transmit experimental data. The common-mode frequency noise induced by the bidirectional fiber link is detected and effectively suppressed without the need for sophisticated active fiber noise control. Our demonstration system, which uses a 260 km field fiber link and a common laser source, achieves a fractional instability of 2.5×10-17 at 1 s averaging time and scales down to 3.5×10-21 at 8000 s. This scheme offers the distinct advantage of completing the comparison at a single site, eliminating the need for remote data transfer via communication. This method is expected to enhance reliability for high-precision frequency comparisons between remote optical clocks and advanced atomic clocks.

Optical Multiplexing of Metrological Time and Frequency Signals in a Single 100-GHz-Grid Optical Channel

In this article, the concept of co-locating all metrological time and frequency signals in a single optical channel of a standard, 100-GHz-spaced optical grid is presented and evaluated. The solution is intended for situations where only a narrow optical bandwidth is available in a fiber heavily loaded with standard data traffic. We localized the optical reference signals in the middle of the channel, with signals related to RF reference and time tags shifted ±12.5 GHz apart. In the experimental evaluation with a 260-km-long fiber, we demonstrate that the stability of frequency signals and the calibration of time tags remained at the very same level of stability and accuracy as for systems utilizing separate channels: the fractional long-term instability for the optical frequency reference was below 5 ×10^-20 , that for the RF reference at the level of 10^-17, and the mismatch of the time tag calibration was not more than 10 ps. We also identify possible issues, mainly related to a risk of unwanted Brillouin amplification and scattering.

Non-reciprocity in optical fiber links: experimental evidence

Fundamental limits of fiber link are set by non-reciprocal effects that violate the hypothesis of equality between forward and backward path. Non-reciprocal noise arises technically from the set-up asymmetry, and fundamentally by the Sagnac effect when the fiber link encloses a non-zero area. As a pre-requisite for observation of Sagnac effect in fiber links, we present a study on phase noise and frequency stability contributions affecting coherent optical frequency transfer in bi-directional fiber links. Both technical and fundamental limitations of Two-Way optical frequency transfer are discussed. Our model predicts and our experiments substantially verify that the dominant noise mechanism at low Fourier frequencies is the polarization asymmetry induced by the temperature and relative humidity variations impacted on fiber links. The flicker noise floor due to the non-reciprocal noise arising from polarization mode dispersion is evidenced for the first time. We perform a post-processing approach which enables us to remove this polarization noise, improve the long-term stability and remove a frequency bias. We evaluate the uncertainty contributions of all the effects discussed for our 50 km spooled fiber link, dominated by its non-reciprocal noise induced by polarization mode dispersion with uncertainty of 1.9( ± 0.8)( ± 1.2) × 10^-20. After correction, the linear drift of the residual phase is as low as 27 yoctosecond/s, leading to an uncertainty of the frequency transfer of 2.6 ( ± 39) × 10^-22, confirming its potential for searching for more fundamental effects such as Sagnac effect or transient frequency variation due to dark matter.

Performance of digital servos in an optical frequency transfer network

We demonstrate the use of three kinds of flexible digital servos for the stabilization of the optical fiber link, the interferometer temperature, and the polarization of the transmitted light at the remote site, respectively. The main fiber noise cancellation digital servo provides a large phase detection range (∼2¹⁰π radians), automatic relock function, and low cycle-slip rate over a 62 km field-deployed fiber link achieved by utilizing a feedback optical actuator of an acousto-optic modulator fed by a voltage-controlled oscillator. The temperature control and polarization control digital servos enable that the temperature of the interferometer can be stabilized at a stability of 0.01 K and the data uptime is enhanced from 85.5% to 99.9% by implementing the polarization controller. The results demonstrate that the performance of the three digital servos is sufficient for high-precision optical frequency transfer applications and indicates comparable performance to existing analog optical frequency control systems. The full digital controlled optical frequency transfer method demonstrated here provides guidance for the development of a low-cost, low-complexity, and high-reliability optical frequency transfer system.

White Rabbit Time and Frequency Transfer Over Wireless Millimeter-Wave Carriers

We demonstrate time and frequency transfer using a White Rabbit (WR) time transfer system over millimeter-wave (mm-wave) 71-76 GHz carriers. To validate the performance of our system, we present overlapping Allan deviation (ADEV), time deviation (TDEV), and phase statistics. Over mm-wave carriers, we report an ADEV of 7.1×10^-12 at 1 s and a TDEV of <10 ps at 10 000 s. Our results show that after 4 s of averaging, we have sufficient precision to transfer a cesium atomic frequency standard. We analyze the link budget and architecture of our mm-wave link and discuss possible sources of phase error and their potential impact on the WR frequency transfer. Our data show that WR can synchronize new network architectures, such as physically separated fiber-optic networks, and support new applications, such as the synchronization of intermittently connected platforms. We conclude with recommendations for future investigation, including cascaded hybrid wireline and wireless architectures.

Reciprocity of propagation in optical fiber links demonstrated to 10-21

We present a study of the fundamental limit of fiber links using dedicated link architecture. We use an experimental arrangement that enables us to detect the forward and backward propagation noise independently and simultaneously in optical fiber and where the optical phase evolution is expected to be driven by the only contribution of the reference arms of the Michelson interferometer ensemble. In this article, we demonstrate indeed the high correlation between the optical phase evolution and the temperature variation of the interferometer ensemble, leading to a frequency offset of (4.4±2.3)×10^-21. Using a simple temperature model and a Bayesian analysis to evaluate the model parameters, we show that the temperature effect can be compensated with post-processing, removing the frequency offset down to (0.5±2.0)×10^-21. The residual slope of the optical phase evolution over 33 days is 350 yoctosecond/s. Using a global temperature parameter, we divide these 33 days dataset in four subsets and analyse their uncertainties. We show that they are self-consistent when the temperature is taken into account. This provides an alternative method to evaluate the accuracy of a fiber link, especially when the dataset includes large dead times. The result is finally interpreted as a test of the reciprocity of the propagation delay in an optical fiber. This unprecedented transfer capability could enable the comparisons of future optical clocks with expected performance at 10^-20 level and open new possibilities for stringent tests of special and general relativity.

Femtosecond time synchronization of optical clocks off of a flying quadcopter

Future optical clock networks will require free-space optical time-frequency transfer between flying clocks. However, simple one-way or standard two-way time transfer between flying clocks will completely break down because of the time-of-flight variations and Doppler shifts associated with the strongly time-varying link distances. Here, we demonstrate an advanced, frequency comb-based optical two-way time-frequency transfer (O-TWTFT) that can successfully synchronize the optical timescales at two sites connected via a time-varying turbulent air path. The link between the two sites is established using either a quadcopter-mounted retroreflector or a swept delay line at speeds up to 24 ms⁻¹. Despite 50-ps breakdown in time-of-flight reciprocity, the sites’ timescales are synchronized to < 1 fs in time deviation. The corresponding sites’ frequencies agree to ~ 10⁻¹⁸ despite 10⁻⁷ Doppler shifts. This work demonstrates comb-based O-TWTFT can enable free-space optical networks between airborne or satellite-borne optical clocks for precision navigation, timing and probes of fundamental science.

Optical clock networks have many applications from precision time keeping, sensing to fundamental physics. Here the authors demonstrate robust and free-space femtosecond time synchronization of optical clocks via a moving quadcopter.

Compensation of the Fluctuations of Differential Delay for Frequency Transfer in DWDM Networks

This paper investigates the possibility of improving the stability of radio-frequency transfer in telecommunication dense wavelength division multiplexing fiber-optic networks. As it has been identified, the dispersion compensation fibers (DCFs), frequently used in these networks, cause substantial differential delay, whose temperature-induced fluctuations have the most significant impact on the deterioration of the stability of the frequency transfer. The authors present a method that allows achieving significant improvement in the long-term stability of the frequency transfer. The developed method is based on modeling the impact of DCFs with the help of remotely accessible temperature sensors factory installed by the manufactures in DCF modules. The effectiveness of the proposed solution has been tested on three different long-haul routes (up to 1550 km), set up in the operational Polish National Research and Education Network.

Modeling and Optimization of Bidirectional Fiber-Optic Links for Time and Frequency Transfer

In this paper, a bidirectional fiber-optic link is considered, composed of two end terminals, connected by a number of fiber spans and bidirectional optical amplifiers. The end terminals exchange time and frequency information by sending and receiving intensity modulated optical signals in both directions, which is required to compensate the fluctuation of the propagation delay of the transmission medium. In such a link for its optimal performance, the gains of the bidirectional optical amplifiers need to be adjusted to minimize the noise resulting from Rayleigh backscattering and amplified spontaneous emission. A model of the link is proposed using a transmission matrixes approach, which allows estimating the signal-to-noise ratio (SNR) at the ends of the main link (i.e., connecting the end terminals) and at the extraction (tapping) nodes located along the main link. The transmission matrixes of a fiber span and Er-doped fiber amplifier are presented and required formulas are derived. In addition, wavelength selective isolators are considered, which allow intentional breaking of the propagation of backscattered signals and are effective in improving the SNR when long fiber spans are involved. The model is experimentally verified in a laboratory link composed of four bidirectional amplifiers and five fiber spans of total length up to 420 km, showing the agreement between the measured and calculated SNRs not worse than 2 dB.

First industrial-grade coherent fiber link for optical frequency standard dissemination

We report on a fully bidirectional 680 km fiber link connecting two cities for which the equipment, the setup, and the characterization are managed for the first time by an industrial consortium. The link uses an active telecommunication fiber network with parallel data traffic and is equipped with three repeater laser stations and four remote double bidirectional erbium-doped fiber amplifiers. We report a short-term stability at 1 s integration time of 5.4×10^-16 in 0.5 Hz bandwidth and a long-term stability of 1.7×10^-20 at 65,000 s of integration time. The accuracy of the frequency transfer is evaluated as 3×10^-20. No shift is observed within the statistical uncertainty. We show a continuous operation over five days with an uptime of 99.93%. This performance is comparable with the state-of-the-art coherent links established by National Metrology Institutes in Europe. It is a first step in the construction of an optical fiber network for metrology in France, which will give access to an ultrahigh performance frequency standard to a wide community of scientific users.

An open and flexible digital phase-locked loop for optical metrology

This paper presents an open and flexible digital phase-locked loop optimized for laser stabilization systems. It is implemented on a cheap and easily accessible FPGA-based digital electronics platform (Red Pitaya) running a customizable open-source firmware. A PC-based software interface allows controlling the platform and optimizing the loop parameters remotely. Several tools are included to allow measurement of quantities of interest smoothly and rapidly. To demonstrate the platform's capabilities, we built a fiber noise canceller over a 400 m fiber link. Noise cancellation was achieved over a 30 kHz bandwidth, a value limited mainly by the delays introduced by the actuator and by the round-trip propagation over the fiber link. We measured a total latency of 565 ns for the platform itself, limiting the theoretically achievable control bandwidth to approximately 225 kHz.

Long Haul Time and Frequency Distribution in Different DWDM Systems

In this paper, we have presented the possibility of time and frequency (T&F) distribution in two generations of dense wavelength-division-multiplexing (DWDM) networks: the older one, equipped with dispersion compensation fiber (DCF) modules, and the newest, without in-line chromatic dispersion compensation (dedicated for coherent signals). The experiments were performed in a 1500-km loop arranged in the PIONIER production network, with T&F signals regarded as so-called "alien wavelength" network service. In the newest DWDM version, we observed very good stability of delivered signals: modified Allan deviation approach 10^-16 for averaging longer than 10⁴ s (for 10-MHz frequency signal), and time deviation below 15 ps for averaging up to 10⁵ s for 1 PPS time signal. These results show that the DWDM alien wavelength service can be used for high-demanding applications like cesium fountains comparisons. Results achieved for the former version of DWDM were about one magnitude worse for a long-term comparison, but it can still be useful for less demanding applications. We found that the main reason for relatively poor results observed in the older generation of DWDM is the impact of the DCFs used in this DWDM approach.

A Sub-ps Stability Time Transfer Method Based on Optical Modems

Coherent optical fiber links recently demonstrate their ability to compare the most advanced optical clocks over a continental scale. The outstanding performances of the optical clocks are stimulating the community to build much more stable time scales, and to develop the means to compare them. Optical fiber link is one solution that needs to be explored. Here, we are investigating a new method to transfer time based on an optical demodulation of a phase step imprint onto the optical carrier. We show the implementation of a proof-of-principle experiment over 86-km urban fiber, and report time interval transfer stability of 1 pulse per second signal with sub-ps resolution from 10 s to one day of measurement time. Prospects for future development and implementation in active telecommunication networks, not only regarding performance but also compatibility, conclude this paper.

Studying the fundamental limit of optical fiber links to the 10-21 level

We present a hybrid fiber link combining effective optical frequency transfer and evaluation of performances with a self-synchronized two-way comparison. It enables us to detect the round-trip fiber noise and each of the forward and backward one-way fiber noises simultaneously. The various signals acquired with this setup allow us to study quantitatively several properties of optical fiber links. We check the reciprocity of the accumulated noise forth and back over a bi-directional fiber to the level of 3.1(±3.9) × 10^-20 based on a 160000s continuous data. We also analyze the noise correlation between two adjacent fibers and show the first experimental evidence of interferometric noise at very low Fourier frequency. We estimate redundantly and consistently the stability and accuracy of the transferred optical frequency over 43 km at 4 × 10^-21 level after 16 days of integration and demonstrate that a frequency comparison with instability as low as 8 × 10^-18 would be achievable with uni-directional fibers in urban area.

Comparing Optical Oscillators across the Air to Milliradians in Phase and 10^{-17} in Frequency

We demonstrate carrier-phase optical two-way time-frequency transfer (carrier-phase OTWTFT) through the two-way exchange of frequency comb pulses. Carrier-phase OTWTFT achieves frequency comparisons with a residual instability of 1.2×10^{-17} at 1 s across a turbulent 4-km free space link, surpassing previous OTWTFT by 10-20 times and enabling future high-precision optical clock networks. Furthermore, by exploiting the carrier phase, this approach is able to continuously track changes in the relative optical phase of distant optical oscillators to 9 mrad (7 as) at 1 s averaging, effectively extending optical phase coherence over a broad spatial network for applications such as correlated spectroscopy between distant atomic clocks.

A Hybrid Solution for Simultaneous Transfer of Ultrastable Optical Frequency, RF Frequency, and UTC Time-Tags Over Optical Fiber

We describe a fiber-optic solution for simultaneous distribution of all signals generated at today's most advanced time and frequency laboratories, i.e., an ultrastable optical reference frequency derived from an optical atomic clock, a radio frequency precisely linked to a realization of the SI-Second, and a realization of an atomic timescale, being the local representation of the virtual, global UTC timescale. In our solution both the phase of the optical carrier and the delay of electrical signals (10-MHz frequency reference and one-pulse-per-second time tags) are stabilized against environmental perturbations influencing the fiber link instability and accuracy. We experimentally demonstrate optical transfer stabilities of and for 100 s averaging period, for optical carrier and 10-MHz signals, respectively.

Low-loss reciprocal optical terminals for two-way time-frequency transfer

We present the design and performance of a low-cost, reciprocal, compact free-space terminal employing tip/tilt pointing compensation that enables optical two-way time-frequency transfer over free-space links across the turbulent atmosphere. The insertion loss of the terminals is ∼1.5  dB with total link losses of 15 dB, 24 dB, and 50 dB across horizontal, turbulent 2-km, 4-km, and 12-km links, respectively. The effects of turbulence on pointing control and aperture size, and their influence on the terminal design, are discussed.

Characterization of optical frequency transfer over 154 km of aerial fiber

We present measurements of the frequency transfer stability and analysis of the noise characteristics of an optical signal propagating over aerial suspended fiber links up to 153.6 km in length. The measured frequency transfer stability over these links is on the order of 10^-11 at an integration time of 1 s dropping to 10^-12 for integration times longer than 100 s. We show that wind-loading of the cable spans is the dominant source of short-timescale noise on the fiber links. We also report an attempt to stabilize the optical frequency transfer over these aerial links.

Frequency Measurement System of Optical Clocks Without a Flywheel Oscillator

We developed a system for the remote frequency comparison of optical clocks. The system does not require a flywheel oscillator at the remote end, making it possible to evaluate optical frequencies even in laboratories, where no stable microwave reference, such as an Rb clock, a Cs clock, or a hydrogen maser exists. The system is established by the integration of several systems: a portable carrier-phase two-way satellite frequency transfer station and a microwave signal generation system by an optical frequency comb from an optical clock. The measurement was as quick as a conventional method that employs a local microwave reference. We confirmed the system uncertainty and instability to be at the low 10^-15 level using an Sr lattice clock.

A clock network for geodesy and fundamental science

Leveraging the unrivalled performance of optical clocks as key tools for geo-science, for astronomy and for fundamental physics beyond the standard model requires comparing the frequency of distant optical clocks faithfully. Here, we report on the comparison and agreement of two strontium optical clocks at an uncertainty of 5 × 10⁻¹⁷ via a newly established phase-coherent frequency link connecting Paris and Braunschweig using 1,415 km of telecom fibre. The remote comparison is limited only by the instability and uncertainty of the strontium lattice clocks themselves, with negligible contributions from the optical frequency transfer. A fractional precision of 3 × 10⁻¹⁷ is reached after only 1,000 s averaging time, which is already 10 times better and more than four orders of magnitude faster than any previous long-distance clock comparison. The capability of performing high resolution international clock comparisons paves the way for a redefinition of the unit of time and an all-optical dissemination of the SI-second.

Comparing the frequency of two distant optical clocks will enable sensitive tests of fundamental physics. Here, the authors compare two strontium optical-lattice clocks 690 kilometres apart to a degree of accuracy that is limited only by the uncertainty of the individual clocks themselves.

Avoiding Aliasing in Allan Variance: An Application to Fiber Link Data Analysis

Optical fiber links are known as the most performing tools to transfer ultrastable frequency reference signals. However, these signals are affected by phase noise up to bandwidths of several kilohertz and a careful data processing strategy is required to properly estimate the uncertainty. This aspect is often overlooked and a number of approaches have been proposed to implicitly deal with it. Here, we face this issue in terms of aliasing and show how typical tools of signal analysis can be adapted to the evaluation of optical fiber links performance. In this way, it is possible to use the Allan variance (AVAR) as estimator of stability and there is no need to introduce other estimators. The general rules we derive can be extended to all optical links. As an example, we apply this method to the experimental data we obtained on a 1284-km coherent optical link for frequency dissemination, which we realized in Italy.

In-field Raman amplification on coherent optical fiber links for frequency metrology

Distributed Raman amplification (DRA) is widely exploited for the transmission of broadband, modulated signals used in data links, but not yet in coherent optical links for frequency metrology, where the requirements are rather different. After preliminary tests on fiber spools, in this paper we deeper investigate Raman amplification on deployed in-field optical metrological links. We actually test a Doppler-stabilized optical link both on a 94 km-long metro-network implementation with multiplexed ITU data channels and on a 180 km-long dedicated fiber haul connecting two cities, where DRA is employed in combination with Erbium-doped fiber amplification (EDFA). The performance of DRA is detailed in both experiments, indicating that it does not introduce noticeable penalties for the metrological signal or for the ITU data channels. We hence show that Raman amplification of metrological signals can be compatible with a wavelength division multiplexing architecture and that it can be used as an alternative or in combination with dedicated bidirectional EDFAs. No deterioration is noticed in the coherence properties of the delivered signal, which attains frequency instability at the 10(-19) level in both cases. This study can be of interest also in view of the undergoing deployment of continental fiber networks for frequency metrology.

Doppler-stabilized fiber link with 6 dB noise improvement below the classical limit

It is known that temperature variations and acoustic noise affect ultrastable frequency dissemination along optical fiber. Active stabilization techniques are adopted to compensate for the fiber-induced phase noise. However, despite this compensation, the ultimate link performances are limited by the delay-unsuppressed noise that is related to the propagation delay of the light in the fiber. We demonstrate a post-processing approach which enables us to overcome this limit. We implement a subtraction algorithm between the optical signal delivered at the remote link end and the round-trip signal. In this way, a 6 dB improvement beyond the delay-unsuppressed noise is obtained. We confirm the prediction with experimental data obtained on a 47 km metropolitan fiber link and propose how to extend this method for frequency dissemination.

Transportable cavity-stabilized laser system for optical carrier frequency transmission experiments

We report the design and performance of a transportable laser system at 1543 nm, together with its application as the source for a demonstration of optical carrier frequency transmission over 118 km of an installed dark fiber network. The laser system is based around an optical reference cavity featuring an elastic mounting that bonds the cavity to its support, enabling the cavity to be transported without additional clamping. The cavity exhibits passive fractional frequency insensitivity to vibration along the optical axis of 2.0×10(-11)  m(-1) s(2). With active fiber noise cancellation, the optical carrier frequency transmission achieves a fractional frequency instability, measured at the user end, of 2.6×10(-16) at 1 s, averaging down to below 3×10(-18) after 20,000 s. The fractional frequency accuracy of the transfer is better than 3×10(-18). This level of performance is sufficient for comparison of state-of-the-art optical frequency standards and is achieved in an urban fiber environment.

Optical frequency transfer via a 660 km underground fiber link using a remote Brillouin amplifier

In long-distance, optical continuous-wave frequency transfer via fiber, remote bidirectional Er³ ⁺ -doped fiber amplifiers are commonly used to mitigate signal attenuation. We demonstrate for the first time the ultrastable transfer of an optical frequency using a remote fiber Brillouin amplifier, placed in a server room along the link. Using it as the only means of remote amplification, on a 660 km loop of installed underground fiber we bridge distances of 250 km and 160 km between amplifications. Over several days of uninterrupted measurement, we find an instability of the frequency transfer (Allan deviation of Λ-weighted data with 1 s gate time) of around 1 × 10(-19) and less for averaging times longer than 3000 s. The modified Allan deviation reaches 3 × 10(-19) at an averaging time of 100 s. Beyond 100 s it follows the interferometer noise floor, and for averaging times longer than 1000 s the modified Allan deviation is in the 10(-20) range. A conservative value of the overall accuracy is 1 × 10(-19)

Stable radio frequency dissemination by simple hybrid frequency modulation scheme

In this Letter, we propose a fiber-based stable radio frequency transfer system by a hybrid frequency modulation scheme. Creatively, two radio frequency signals are combined and simultaneously transferred by only one laser diode. One frequency component is used to detect the phase fluctuation, and the other one is the derivative compensated signal providing a stable frequency for the remote end. A proper ratio of the frequencies of the components is well maintained by parameter m to avoid interference between them. Experimentally, a stable 200 MHz signal is transferred over 100 km optical fiber with the help of a 1 GHz detecting signal, and fractional instability of 2×10(-17) at 10(5) s is achieved.

Chirped frequency transfer: a tool for synchronization and time transfer

We propose and demonstrate the phase-stabilized transfer of a chirped frequency as a tool for synchronization and time transfer. Technically, this is done by evaluating remote measurements of the transferred, chirped frequency. The gates of the frequency counters, here driven by a 10-MHz oscillation derived from a hydrogen maser, play a role analogous to the 1-pulse per second (PPS) signals usually employed for time transfer. In general, for time transfer, the gates consequently must be related to the external clock. Synchronizing observations based on frequency measurements, on the other hand, only requires a stable oscillator driving the frequency counters. In a proof of principle, we demonstrate the suppression of symmetrical delays, such as the geometrical path delay. We transfer an optical frequency chirped by around 240 kHz/s over a fiber link of around 149 km. We observe an accuracy and simultaneity, as well as a precision (Allan deviation, 18,000 s averaging interval) of the transferred frequency of around 2 × 10(-19). We apply chirped frequency transfer to remote measurements of the synchronization between two counters' gate intervals. Here, we find a precision of around 200 ps at an estimated overall uncertainty of around 500 ps. The measurement results agree with those obtained from reference measurements, being well within the uncertainty. In the present setup, timing offsets up to 4 min can be measured unambiguously. We indicate how this range can be extended further.