In recent years, the use of optical frequency dissemination through telecommunication fibers has steadily grown both in the context of stateof-the-art metrology like optical clocks and in the use of ultrastable reference signals for precision measurements in other fields of physics or earth science.Evaluating the performance of the fiber link can be difficult, as outliers and dysfunctioning regions lead to missing data.In this article, we discuss these challenges and investigate three different approaches to dealing with the missing data of a 1410-km-long optical link.We find a benefit in replacing the missing data with simulated noise with a statistical behavior similar to that of the original signal.
In recent years, the use of optical frequency dissemination through telecommunication fibers has steadily grown both in the context of stateof-the-art metrology like optical clocks and in the use of ultrastable reference signals for precision measurements in other fields of physics or earth science.Evaluating the performance of the fiber link can be difficult, as outliers and dysfunctioning regions lead to missing data.In this article, we discuss these challenges and investigate three different approaches to dealing with the missing data of a 1410-km-long optical link.We find a benefit in replacing the missing data with simulated noise with a statistical behavior similar to that of the original signal.
Abstract Aiming at delivering a highly available service, the French national optical fiber link network is run mostly unmanned and automatically, with the help of a global supervision. However, at a year scale, missing data are seemingly unavoidable. Here, we present a first study of the uncertainty of coherent fiber links with missing data. We present the tools to assess statistical properties for processes which are not strictly stationary, and a simulation of optical fiber links depending only on a handful of parameters. We show how missing data affects the phase-coherent optical fiber links, and how to mitigate the issue with a fill-in procedure that preserves the statistical properties. We apply the method for a 5 years-long data set of a 1410 km long fiber link. Second, we apply the method to the case of optical clock comparisons, where the downtimes of the optical clocks degrade the coherence of the links. We show that our methodology of processing the missing data is robust and converges to consistent mean values, even with very low uptimes. We present an offset and uncertainty contribution from the French fiber network of 2.4 (9.0) × 10−20, that is an improvement by a factor 5 as compared to a processing without taking the effect of missing data into account.
The transfer of ultra-stable frequencies between distant laboratories is required by many applications from fundamental metrology to high-precision measurements. For that purpose, optical fibre links have been intensively studied over the last decade. They have demonstrated impressive results far beyond the GPS capabilities on distances up to 2000 km, thanks to an active compensation of the fiber propagation noise.Up to now, optical links has been mainly implemented between two labs, when future applications will require the development of metrological fiber networks. Towards this goal, we have developed a few techniques which allow us to distribute the ultrastable optical signal to many users simultaneously. We have designed repeater laser stations, which can be used to build a cascaded link or to distribute the ultrastable signal among two optical links [1]. These stations allow us also to compare the output end signals of two optical links. These versatile stations will be a key-component of the national metrological network currently being developed in France within the Refimeve+ project. To complete the network, we have demonstrated the extraction of the ultrastable signal from a main link and its seeding to a secondary link [2].Optical links are already been successfully used for clocks comparison. Recently we were able to compare the atomic clocks of the French and German National Metrology Institutes through two connected optical links of total length 1415-km [3]. We found that the two fully independent Sr lattice optical clocks at the two sites agreed to better than 5x10-17 limited only by the clocks uncertainties. A fractional statistical uncertainty of 3x10-17 was reached after only 1000 s averaging time, which is 10 times better, and more than four orders of magnitude faster than with any other existing frequency transfer method. The atomic fountain primary frequency standards from the two institutes were also compared and they were found to agree well within their combined uncertainties of a few 10-16 [4].
Optical clocks are considered as promising candidates for redefining the second in the International System of Units. Compared with microwave clocks, optical clocks are powerful tools for the fundamental research such as the constancy of the fundamental constants, the validity of Einstein’s theory of general relativity, and the predictions of quantum electrodynamics. Recently two research groups have demonstrated the optical clocks with an unprecedented precision level of 10-18, which is two orders better than the present primary frequency standard. Using two Sr optical clocks and three Cs fountain clocks, SYRTE group has demonstrated the definition of second with optical clocks.#br#For redefining the second with optical clocks in the future, the optical clocks from the remote laboratories should have a high precision and the frequency of the optical clocks need to be transferred over a long distance, with extremely high precision. Unfortunately the conventional means of frequency transfer such as two-way satellite time and frequency transfer can reach a 10-16 level in one day which is far below the requirement for an optical clocks. Various methods have been developed to transfer optical frequency signal via optical fibers. Especially a research group from Germany has achieved a frequency transfer stability of 10-19 level in hundreds of seconds with a fiber length of 1840 km.#br#We demonstrate the recent development of optical frequency transfer over a 70-km fiber spool at National Time Service Center. The measurement shows that the compensation for the fiber noise is close to the limitation induced by the fiber delay for the Fourier frequency from 1 Hz to 250 Hz. The transfer stability (Allan deviation) of the fiber link is 1.2×10-15 in 1 s averaging time, and 1.4×10-18 in 10000 s. A preliminary test of the optical frequency transfer over a 100-km spooled fiber is achieved with a stability of roughly one order worse than the 71 km result, 5×10-15 in 1 s.#br#We demonstrate a new scheme of remote compensation for optical frequency transfer via fibers against conventional local compensation method. This new scheme has the advantage of great simplification of the local site, which can find applications in massive extension of star network. The key feature is that we transfer the mixture of the round-trip signal and local reference to the remote user’s end via an auxiliary fiber. At remote site, the fiber noise is measured and compensated by AOM2 accordingly.#br#Transfer stabilities of 13×10-15 in 1 s averaging time and 4.8×10-18 in 10000 s are achieved with the remote fiber noise compensation via a 25 km fiber spool. The demonstrated transfer stability is comparable to that obtained by the local fiber noise compensation method.#br#The future star fiber network of optical frequency transfer can benefit from this method, because the simpler local setup is required and even can be shared in the central site for multitudinous remote users.
We transferred the frequency of an ultrastable laser over a 108-km-long urban fiber link comprising 22 km of an optical communication network fiber simultaneously carrying Internet data traffic. The metrological signal and the digital data signal were transferred over two different frequency channels in a dense wavelength-division multiplexing scheme. The metrological signal was inserted in and extracted from the communication network using bidirectional off-the-shelf optical add-drop multiplexers. The link-induced phase noise was measured and canceled with a round-trip technique using an all-fiber-based interferometer. The compensated link showed an Allan deviation of a few 10−16at one second and below 10−19at 10,000 s This work paves the way to a wide dissemination of ultrastable optical clock signals between distant laboratories via the Internet network.
In recent years, the dissemination of optical frequency signals along phase-stabilized fibers has allowed the comparison of optical clocks at unprecedented levels of accuracy. This has a strong relevance in frequency metrology and boosted the measurement capabilities also in other research fields such as radioastronomy [1], geodesy [2] and fundamental physics [3]. Fiber-based frequency dissemination relies on the transmission of a continuous-wave, narrow-linewidth laser whose frequency is accurately measured with an atomic clock at the National Metrology Institute (NMI) where it is generated. Specific techniques are used to compensate for the acoustic and seismic noise and temperature variations, which degrade the phase stability of the transmitted signal. However, in existing implementations, it is not possible to detect and compensate for the birefringence variations of the optical fiber. These can induce variations in the state of polarization (SOP) of the transmitted signal, affecting the optical beatnotes at the receiving end. This not only degrades the achievable performances in terms of phase stability of the metrological signal, but can also lead to beatnote fading, with consequent failure of the entire system. This problem currently represents one of the strongest limitations to the reliability of fiber-based frequency dissemination.
The transfer of ultra-stable frequencies between distant laboratories is required by many applications in time and frequency metrology, fundamental physics, particle accelerators and astrophysics. Optical fiber links have been intensively studied for a decade and brought the potential to transfer frequency with a very high accuracy and stability thanks to an active compensation of the propagation noise. We are currently developing an optical metrological network using the fibers of the French National Research and Education Network. Using the so-called dark-channel approach, the ultrastable signal is copropagating with data traffic using wavelength division multiplexing. Due to significant reflections and losses along the fibers, which cannot be compensated with amplifiers, we have developed some repeater stations for the metrological signal. These remotely-operated stations amplify the ultrastable signal and compensate the propagation noise. The link is thus composed of a few cascaded spans. It gives the possibility to increase the noise correction bandwidth, which is proportional to the inverse of the fiber length for each span. These stations are a key element for the deployment of a reliable and large scale metrological network. We report here on the implementation of a two-spans cascaded link of 740 km reaching a relative stability of a few 10-20 after 103 s averaging time. Extension to longer links and alternative transfer methods will be discussed.