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Simultaneous time and frequency transfer over 100 km optical fiber based on sub-carrier modulation
Optics Communications 427 (2018) 335–340
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Simultaneous time and frequency transfer over 100 km optical fiber based on sub-carrier modulation Longqiang Yu a, *, Lin Lu b, *, Lei Shi a , Zhiyan Xu a , Jiahua Wei a , Chuanxin Wu b , Yimei Wei b , Heng Wei b a b
Information and Navigation College, Air Force Engineering University, Xi’an, Shanxi, 710000, China Communication Engineering College, Army Engineering University of PLA, Nanjing, Jiangsu, 210007, China
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Keywords: Time and frequency transfer Optical fiber Sub-carrier modulation
ABSTRACT In this paper a novel scheme is proposed to realize the simultaneous transfer of precise time and frequency signals. By performing sub-carrier modulation to the time signal, the time and frequency signals can be directly transferred in the same optical channel without causing mutual interference. The remote user does not need a slave oscillator to clear up the frequency signal and therefore can maintain a simple structure. We test the scheme in the proof-of-concept experiment, in which the 50 MHz modulated time signal and 400 MHz frequency signal are transferred together over 100 km optical fiber link. Good signal compatibility and system performance is observed in the experimental results.
1. Introduction Fiber optic time and frequency transfer has drawn considerable interest during the past decade because they are capable of providing accurate and stable access to high-level atomic clocks or realizing ultra-precision time and frequency comparison. Presently, great system performance has been achieved for frequency dissemination both in point-to-point systems [1–6] and point-to-multipoint networks [7–15], which deeply facilitates their applications in scientific projects, such as the well-known Square Kilometer Array (SKA) [16] and Acatama Large Millimeter Wave Array (ALMA) telescope [17]. On the other hand, various fiber optic time synchronization systems were also demonstrated by two-way clock comparison or round-trip transfer [18–21], making the technique more closer to be widely used in navigation, guidance, security, et al. However, still it should be noted that sometimes exclusive time or frequency transfer cannot meet the demand of particular applications, such as the deep space exploration, coherent radar array and communication systems for which both time and frequency synchronization is indispensable. Therefore simultaneous time and frequency transfer is needed for such applications. One technical issue in simultaneous time and frequency transfer is how to avoid the interference between the time signal (TS) and the frequency signal (FS). Some groups use the wavelength division multiplexing technique to distinguish them in the optical domain [14,22]. The method is straightforward, but in fact it is just the direct combination *
of two independent systems. Also this will lead to relative phase shift between TS and FS when the transmission delay varies, which may be a problem in applications where mutual calibration of the TS and FS is needed. A better choice is to transfer them by a common optical carrier. In [13], Z. Jiang et al. try to reduce the interference by modulating FS and TS on two individual Mach–Zehnder modulators. Though obvious suppression of the interference is observed in the report, unavoidable interference is still expected because two signals will beat with each other in photon detector, and one may have to use a clear-up oscillator to purify the FS at the remote end. L. Sliwczynski et al. [6,11] design a special structure to combine two signals. They mark the TS by introducing phase change to one of the falling edges of the 10 MHz square signal, so that the FS and TS can be recovered respectively with reference to the rising and the falling edges. The scheme is quite effective, however, a slave oscillator is still indispensable to extract the FS from the rising edges, which also increases the structural and technical complexity of the remote user. In this manuscript, we present a new solution to simultaneously transfer the TS and FS. The solution is based on sub-carrier modulation in which the base-band TS is shifted to intermediate frequency. It not only realizes the joint transfer of TS and FS in common optical channels, but also eliminates the interference on FS without additional clear-up slave oscillator. Experiment is performed to transfer a 50 MHz modulated TS and a 400 MHz radio frequency (RF) signal. Stabilization
Corresponding authors. E-mail addresses: [email protected] (L. Yu), [email protected] (L. Lu).
https://doi.org/10.1016/j.optcom.2018.06.043 Received 29 March 2018; Received in revised form 23 May 2018; Accepted 16 June 2018 0030-4018/© 2018 Elsevier B.V. All rights reserved.
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Optics Communications 427 (2018) 335–340
Fig. 1. Sketch of the spectra of (a) 1PPS and RF before modulation, (b) 1PPS and RF after joint transfer, (c) MTS and RF after sub-carrier modulation, (d) MTS and RF after joint transfer.
all the residual interfering components will remain outside the passband of the filter. Then the FS can be extracted without deterioration. To stabilize the FS, we make some improvement over the passive hybrid frequencies transfer scheme proposed in our previous research [25], shown in Fig. 2. The FS, 𝑽𝑹 ∝ cos 𝜔0 𝒕, is bidirectionally transferred over the optical fiber, indicated by the blue path. 𝜑 is the phase change ( ) over single trip. By mixing the round-trip FS, 𝑽𝑹 ∝ cos 𝜔0 𝒕 + 2𝜑 , with the frequency-tripled local reference, 𝑽𝑻 ∝ cos 3𝜔0 𝒕, we get the phase( ) conjugated signal, 𝑽𝑰 ∝ cos 2𝜔0 𝒕 − 2𝜑 , which could counteract the phase change of the optical fiber. Here instead of directly mixing 𝑉𝑅 and 𝑉𝑇 , we use the dual-mixer time-difference (DMTD) method to avoid the crosstalk from the second harmonics of 𝑉𝑅 , which is also adopted in [26]. An auxiliary frequency, 𝑽𝑨 ∝ cos 𝜔𝑨 𝒕, is introduced to premix with the two signals. They can do either sum-frequency mixing or beat-frequency mixing. Here we choose the latter. Then the outputs, [( ) ] ( ) 𝑽𝒙 ∝ cos 𝜔0 − 𝜔𝑨 𝒕 + 2𝜑 and 𝑽𝒚 ∝ cos 3𝜔0 − 𝜔𝑨 𝒕, are mixed again to get the beat signal 𝑉𝐼 . It is critical that 𝜔𝐴 should be properly chosen so that no crosstalk will arise in three mixing procedures. The stability of the auxiliary signal is insignificant since its phase terms are canceled eventually. Then after frequency conversion with a coefficient ( ) of 0.5m, the phase-conjugated signal cos 𝒎 𝜔0 𝒕 − 𝜑 is transferred with the original FS and serves the remote user as a stable frequency standard, illustrated by the red path. We developed a large-dynamic-range compensation scheme to compensate the true time delay of TS [27]. The scheme runs by resolving the compensation time according to the period of a precise clock into the integral-multiples part and fractional part. Fig. 3 illustrates the compensation procedure. The total compensation time is 1−𝜏 = 𝑛𝑇 +𝛥T, where 𝜏 is the single-trip time delay, T the clock period, and 𝛥T the fractional part after resolution. At the beginning, TS triggers the counter to count the rising edges of the clock. Then it is regenerated when the counting reaches n, amounting to a true time delay of nT. After subcarrier modulation the MTS is delayed 𝛥T by an electronic variable delay line (EVDL), accomplishing the whole time compensation.
schemes are also applied to counteract the variation of the transmission delay. 2. Principle The spectra of TS and FS, as well as their interactions after transfer, are shown in Fig. 1. The TS is usually in form of one pulse per second (1 PPS) and its Fourier spectrum is composed of discrete points with the absolute envelop of a sinc function, while FS is a continuous sinusoidal wave and its spectrum is a single point, denoted by 𝑓0 in Fig. 1(a). Fig. 1(b) shows the spectra when FS and TS are directly combined and transferred together. It is expected that around 𝑓0 there will be dense interfering components whose spectrum is identical to that of the 1 PPS. This is also the case reported in [23], indicating that the FS is interfered by the TS. There are two reasons for the illustrated interference. One is that the TS and FS, when received by the remote user, will mutually beat with each other in photon detector, obeying square law. Moreover, because neither the direct modulation nor external modulation is ideally linear, the TS will be modulated on the FS in the local modulation procedure, known as cross modulation. As the 1 PPS can be regarded as a square wave of 1 Hz, the spacing of its spectrum components is 1 Hz too. Therefore it will be impossible for ordinary electronic filters to clear up the interfering frequencies around 𝑓0 . Even if in some schemes the timing signal is in form of pseudo-random code with frequency of several kilohertz [24], it is still too harsh for the filtering. In such case additional clear-up oscillator with locking bandwidth <1 Hz is needed to perform narrow-band filtering to purify the FS. Here we propose a solution to combine the FS and TS, which can relieve FS from the interference of TS when they are simultaneously transferred in the same transmission channel. To start with, we modulate the TS on an intermediate-frequency sub-carrier, 𝑓𝑠𝑐 , as is shown in Fig. 1(c). Then when the modulated TS (MTS) is transferred with the FS, the center frequency of the interfering signals will shift from 𝑓0 to 𝑓0 ±𝑓𝑠𝑐 . However, since the spectrum of the MTS is similar to that of the TS, the interfering frequency components still exist. So we use a bandpass filter to limit the bandwidth of the MTS within 2𝑓𝑏1 before it is combined with FS. As a result, the bandwidth of the interfering signal is also limited. Then after the MTS and FS are detected at the remote end, we use another ordinary bandpass filter, whose center frequency and bandwidth is respectively 𝑓0 and 2𝑓 𝑏2 , to clear up the side bands. As long as the condition 𝑓𝑠𝑐 >𝑓𝑏1 + 𝑓𝑏2 is satisfied like the case in Fig. 1(d),
3. Experimental results To test the proposed scheme, we simultaneously transfer 50 MHz MTS, 400 MHz and 1 GHz FS over 100 km optical fiber using the same laser diode (LD). The setup of the proof-of-concept experiment is illustrated in Fig. 4 and elaborated below. We first focus on the frequency transfer subsystem, as shown in the left part of the schematic. 336
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Fig. 2. Sketch of the frequency stabilization scheme. DMTD: dual-mixer time-difference.
Fig. 3. Sketch of the time compensation scheme. EVDL: electronic variable delay line.
A signal generator is referred to the 10 MHz frequency standard of a rubidium atomic clock to generate a 1 GHz FS, 𝑉0 . It is fed to one ports of the RF combiner and modulated on a distributed feedback (DFB) LD at 1547.7 nm. Then the optical signal is sent into the optical fiber via an optical circulator. At the remote end, the optical signal is amplified by an erbium-doped fiber amplifier (EDFA), filtered by an optical band-pass filter (BPF), and detected by a photon detector. After relevant electronic filtering and combination, the 1 GHz FS is transferred back by another LD. We choose a different wavelength at 1546.9 nm in the backward transmission in order to eliminate the impact of Rayleigh scattering. At the local end, we use a crystal oscillator to generate a 100 MHz auxiliary signal 𝑉𝐴 , and perform DMTD mixing with the round-trip FS (𝑉𝑅 ) and the triple-frequency signal (𝑉𝑇 ). That means the 1 GHz and 3 GHz signals are first shifted respectively to 900 MHz (𝑉𝑥 ) and 2.9 GHz (𝑉𝑦 ), and then they are mixed again to gain a 2 GHz phase-conjugated FS, 𝑉𝐼 . Considering that the frequencies of 𝑉𝑅 and 𝑉𝑇 are at least ten times higher than that of 𝑉𝐴 , the crosstalk in the pre-mixing from the 9th and 29th harmonics of 𝑉𝐴 could be ignored. But certainly it will be better if auxiliary frequencies like 700 MHz are used in DMTD mixing. Then we convert 𝑉𝐼 to 400 MHz, whose phase is also conjugate to the phase change of the optical link. After combined with 𝑉0 , it is transferred to the remote end. In this way the remote user can extract a stable 400
MHz FS using an electronic BPF. Both the remotely received 400 MHz FS and the local 1 GHz reference signal (𝑉0 ) are down-converted to 200 MHz to perform phase comparison. The outputs of the mixer are steadily measured by a digital multimeter, then converted to relative phase fluctuations for performance characterization. The time transfer subsystem is shown in the right part of the schematic. By referring to the 10 MHz frequency standard of atomic clock, a 50 MHz FS is generated as the intermediate-frequency subcarrier. After sub-carrier modulation, the MTS is filtered by a BPF, whose passband is 40 MHz centering at 50 MHz. Then it is also combined by the RF combiner with the FSs and modulated on the same LD. At the remote end, part of the received MTS is detected to regenerate the 1 PPS for the user, and the other part is amplified and sent back to the local end. The round-trip transmission delay of the MTS is measured by a time interval counter (TIC) and the results are sent to a time delay control module to perform time compensation. Based on a precise 100 MHz clock, the compensation time is divided into the multiple-of −10 ns part and fractional part. The compensation of the former part is realized by a clock counter, which starts the counting when triggered by the source 1 PPS and regenerates the 1 PPS when corresponding time is up. Then the regenerated 1 PPS is modulated on the sub-carrier and filtered. Finally the MTS is delayed by an EVDL with 10 ps resolution and 337
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Fig. 4. Experimental setups of the time and frequency transfer system. Syn.: frequency synthesizer, CC: clock counter, Mod.: modulator, EVDL: electronic variable delay line, TIC: time interval counter, LD: laser diode, PD: photon detector, OBPF: optical bandpass filter, EDFA: erbium doped fiber amplifier, TC: temperature control, BPF: (electronic) bandpass filter, Time Reg.: time regenerator.
10.24 ns adjustment range, finishing the rest of the time compensation. The regenerated 1 PPS at the remote end is compared with the local one by a TIC apparatus, whose noise floor is about 63 ps (peak to peak). To reduce the impact of the high-order harmonics of MTS, we use direct intensity modulation and properly adjust the DFB in order to gain better modulation linearity. Meanwhile the passband of the filters used to extract the 1 GHz and 400 MHz FS are limited within 20 MHz, so that the condition 𝑓𝑠𝑐 >𝑓𝑏1 + 𝑓𝑏2 is satisfied. The effectiveness of the design is first tested by a simple experiment. We modulate the 1 GHz FS on LD with 1 PPS or MTS and unidirectionally transfer them to the remote end. The spectra of the detected 1 GHz FS are measured by an electronic spectrum analyzer, and the results are shown in Fig. 5. Fig. 5(a) is the spectrum of the 1 GHz FS when it is transferred alone. The center frequency in the view is 1 GHz, the span is 1 kHz, and the resolution bandwidth is 10 Hz. The spectrum of the received signal when FS is combined with 1 PPS is shown in Fig. 5(b). Under the same test condition, dense frequency components are clearly observed on both sides of the 1 GHz FS, indicating the severe interference from TS. The result when we transfer 50 MHz MST instead of 1 PPS is demonstrated in Fig. 5(c). It is apparent that the interfering components are well suppressed and the purity of spectrum in the view shows no observable degradation compared with that in Fig. 5(a). Thus the proposed design is proved to be capable of eliminating the interference on FS in the simultaneous time and frequency transfer. Some calibrations for the time transfer subsystem are needed before the systematic experiment. The local and remote setups are connected by a 1 m optical fiber. Based on the results of this back-to-back test we calibrate the intrinsic timing offset induced by terminal setups, including the asymmetric optical and electronic lines, the phase mismatch between the source 1 PPS and the counting clock, and the envelop distortion of the MST. The other concern is the transmission asymmetry caused by chromatic dispersion. For specific link it can be measured in advance by dispersion analyzer [6,14]. However, considering that perfect calibration of chromatic dispersion has not been achieved yet and this is also not the focus of this paper, we just directly do the co-location calibration by replacing the 1 m optical fiber with 100 km experimental fiber spools. After the calibrations we run the time and frequency transfer system and do continuous measurements to test the proposed scheme. Fiber
Fig. 5. The normalized spectrum of the received 1 GHz FS when (a) 1 GHz FS, (b) 1 GHz FS+1 PPS TS, (c) 1 GHz FS+50 MHz MTS, are transferred together.
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Fig. 6. Results of the proof-of-concept experiment. (a) The single-trip transmission delay of the 100 km optical fiber. (b) The timing errors of the time transfer. (c) The relative phase fluctuations of the 400 MHz FS. (d) The Allan deviation of the 400 MHz FS.
stabilization is activated, 6.85 × 10−17 /104 s. Compared with the noise floor measured in the back-to-back test, the performance around 200 s shows a degree of degradation, corresponding to the quasi-periodic phase fluctuations in Fig. 6(c). Limited by our technical merit, the proof-of-concept experiment has not been performed with the best configuration. We think better performance is expected if the following two aspects are improved. One immediate way is to upgrade the hardware of the setups and bring down the noise floor. The other one is the further elimination of the interference between the combined signals. Although the 8th and 20th harmonics of 50 MHz MTS are relative weak, still they may remain as interference to the 400 MHz and 1 GHz FSs. For our consideration this residual crosstalk can be eliminated if a more proper sub-carrier, e.g. 300 MHz, could be generated. Such a higher frequency also allows a larger bandwidth for MTS, so that lower time jitter could be maintained [28]. Hopefully we think the proposed scheme will be also effective in the real field. In such cases, the Sagnac effect should be taken into consideration when the link lays across different longitudes [29]. For longer transfer link, it is also necessary to use bidirectional amplifiers to compensate the loss of the optical fiber.
spools are placed in a temperature-controlled oven to change the transmission delay of the signals. Fig. 6(a) gives the variation of the singletrip transmission delay, which also indicates the time and frequency asynchronization in the unstabilized link. We lower the temperature by about 13 ◦ C in 40 000 s measurement time, and the transmission delay also decreases accordingly by 44.27 ns from 496.14236 μs to 496.09809 μs. The timing errors of the stabilized link are also simultaneously recorded in Fig. 6(b). During the measurement time the mean time difference between the local and remote ends is 9.1 ps, with root mean square (RMS) value of 50.2 ps. Such performance is comparable with our previous experiment in which the 1 PPS is exclusively transferred with 54.4 ps (RMS) uncertainty [27], showing that the time transfer scheme based on MTS is effective. For our point of view several factors lead to the obtained results. The noise floor revealed in the back-to-back test, as one of the major factors, is about 41.8 ps (RMS) which is mainly decided by the art of the devices and circuits [27]. The resolution of the TIC we use is 100 ps, and this is expected to introduce 25 ps timing uncertainty after 16-point averaging. Other possible trivial factors include the temperature dependent variation of chromatic dispersion, the polarization mode dispersion (PMD) and the amplitude-to-phase jitter, which could respectively contribute 0.8 ps [15], 1 ps (PMD coefficient of 0.1 ps km−1∕2 ), and 0.9 ps [28] to the total uncertainty. In addition, the instability of the terminal equipment may account for the time drift. Under the same variation of the transmission delay, the relative phase fluctuations of the received 400 MHz FS are shown in Fig. 6(c). The fluctuations are well stabilized within 2.1 ps in the measurement time, which also indicates that the FS is not interfered by MTS. Based on the phase data we also calculate the Allan deviation of the FS and the curves are displayed in Fig. 6(d). It shows that the Allan deviation in the free-running case is larger than 1.5 × 10−14 during the whole measurement time. While this improves by three orders when the
4. Conclusion In this paper we propose a new scheme to simultaneously transfer the time and frequency signals, in which TS is modulated on an intermediate-frequency sub-carrier and followed by a BPF to limit its bandwidth. The proposed scheme has two significant advantages. The first is that TS and FS share the same optical channels and as a result their coherence could be better preserved. The other one is that the scheme is free from the mutual interference among signals and no slave oscillator is needed to regenerate the FS in the remote end. In the proofof-concept experiment, the 50 MHz MTS and the 400 MHz FS are transferred over 100 km optical fiber spools. Respectively, the FS is stabilized 339
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by passive phase conjugation, while the MTS is compensated by clock counting and EVDL, achieving fractional instability of 6.85 × 10−17 /104 s and timing errors of 50.2 ps (RMS). The results demonstrate that the proposed scheme is a viable solution to simultaneously disseminate the time and frequency signals.
[13] Z. Jiang, Y. Dai, A. Zhang, F. Yin, J. Li, K. Xu, Q. Lv, T. Ren, G. Tang, Precise time delay sensing and stable frequency dissemination on arbitrary intermediate point along fiber-optic loop link with rf phase locking assistance, IEEE Photonics J. 7 (2015) 7200809. [14] W. Chen, Q. Liu, N. Cheng, D. Xu, F. Yang, Y. Gui, H. Cai, Joint time and frequency dissemination network over delay-stabilized fiber optic links, IEEE Photonics J. 7 (2015) 7901609. [15] L. Yu, R. Wang, L. Lu, Y. Zhu, J. Zheng, C. Wu, B. Zhang, P. Wang, WDM-based radio frequency dissemination in a tree-topology fiber optic network, Opt. Express 23 (2015) 19783–19792. [16] B. Wang, X. Zhu, C. Gao, Y. Bai, J. Dong, L. Wang, Square kilometre array telescopeprecision reference frequency synchronisation via 1f-2f dissemination, Sci. Rep. 5 (2015) 13851. [17] J.F. Cliche, B. Shillue, Precision timing control for radioastronomy: maintaining femtosecond synchronization in the atacama large millimeter array, IEEE Control Syst. 26 (2006) 19–26. [18] S.M.F. Raupach, G. Grosche, Chirped frequency transfer: a tool for synchronization and time transfer, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 61 (2014) 920– 929. [19] J. Kodet, P. Panek, I. Prochazka, Two-way time transfer via optical fiber providing subpicosecond precision and high temperature stability, Metrologia 53 (2015) 18– 26. [20] V. Smotlacha, J. Vojtech, Accurate time distribution using optical fiber, in: IEEE 2015 International Association of Institutes of Navigation World Congress (IAIN), 2015, pp. 1–5. [21] P. Krehlik, L. Sliwczynski, L. Buczek, J. Kolodziej, M. Lipinski, Ultrastable longdistance fibre-optic time transfer: active compensation over a wide range of delays, Metrologia 52 (2015) 82–88. [22] B. Wang, C. Gao, W. Chen, J. Miao, X. Zhu, Y. Bai, J. Zhang, Y. Feng, T. Li, L. Wang, Precise and continuous time and frequency synchronisation at the 5×10−19 accuracy level, Sci. Rep. (2012) 00556. [23] F. Yin, Z. Wu, Y. Dai, T. Ren, K. Xu, J. Lin, G. Tang, Stable fiber-optic time transfer by active radio frequency phase locking, Opt. Lett. 39 (2014) 3054–3057. [24] O. Lopez, A. Kanj, P.E. Pottie, D. Rovera, J. Achkar, C. Chardonnet, A. Amy-Klein, G. Santarelli, Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network, Appl. Phys. B 110 (2013) 3–6. [25] L. Yu, R. Wang, L. Lu, Y. Zhu, C. Wu, B. Zhang, P. Wang, Stable radio frequency dissemination by simple hybrid frequency modulation scheme, Opt. Lett. 39 (2014) 5255–5258. [26] F. Yin, A. Zhang, Y. Dai, T. Ren, K. Xu, J. Li, J. Lin, G. Tang, Phase-conjugation-based fast rf phase stabilization for fiber delivery, Opt. Express 22 (2014) 878–884. [27] L. Yu, R. Wang, L. Lu, Y. Zhu, C. Wu, B. Zhang, Y. Wei, Large-dynamic-range time pre-compensation scheme for fiber optic time transfer, Appl. Opt. 56 (2017) 1757– 1762. [28] Ł. Sliwczynski, J. Kolodziej, Bidirectional optical amplification in long-distance twoway fiber-optic time and frequency transfer systems, IEEE Trans. Instrum. Meas. 62 (2013) 253–262. [29] L. Yu, L. Lu, R. Wang, J. Jing, C. Wu, Y. Zhu, B. Zhang, Analysis of the sagnac effect on the accuracy of the long haul optical fiber time transfer system, in: European Frequency and Time Forum & International Frequency Control Symposium (EFTF/IFC), 2013, pp. 303–305.
Acknowledgments The work described in this manuscript was supported in part by the National Natural Science Foundation of China under Grant No. 61032005, 61177065, and 61673393 and the Jiangsu Province Natural Science Foundation under Grant No. BK20140069. References [1] S. Droste, T. Udem, R. Holzwarth, T.W. Hansch, Optical frequency dissemination for metrology applications, C.R. Phys. 16 (2015) 524–530. [2] S.M.F. Raupach, A. Koczwara, G. Grosche, Brillouin amplification supports 1 × 10−20 uncertainty in optical frequency transfer over 1400 km of underground fiber, Phys. Rev. A 92 (2015) 41–58. [3] O. Lopez, F. Kefelian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.E. Pottie, A. Amy-Klein, G. Santarelli, Frequency and time transfer for metrology and beyond using telecommunication network fibres, C.R. Phys. 16 (2015) 531–539. [4] C.E. Calosso, E.K. Bertacco, D. Calonico, C. Clivati, G.A. Costanzo, M. Frittelli, F. Levi, S. Micalizio, A. Mura, A. Godone, Doppler-stabilized fiber link with 6 db noise improvement below the classical limit, Opt. Lett. 40 (2015) 131–134. [5] J. Kim, H. Schnatz, D.S. Wu, G. Marra, D.J. Richardson, R. Slavik, Optical injection locking-based amplification in phase-coherent transfer of optical frequencies, Opt. Lett. 40 (2015) 4198–4201. [6] L. Sliwczynski, P. Krehlik, A. Czubla, L. Buczek, M. Lipinski, Dissemination of time and rf frequency via a stabilized fibre optic link over a distance of 420 km, Metrologia 50 (2013) 133–145. [7] G. Grosche, Eavesdropping time and frequency: phase noise cancellation along a time-varying path, such as an optical fiber, Opt. Lett. 39 (2014) 2545–2548. [8] A. Bercy, S. Guellati-Khelifa, F. Stefani, G. Santarelli, C. Chardonnet, P.E. Pottie, O. Lopez, A. Amy-Klein, In-line extraction of an ultrastable frequency signal over an optical fiber link, J. Opt. Soc. Am. B 31 (2014) 678–685. [9] S.W. Schediwy, D. Gozzard, K.G. Baldwin, B.J. Orr, R.B. Warrington, G. Aben, A.N. Luiten, High-precision optical-frequency dissemination on branching optical-fiber networks, Opt. Lett. 38 (2013) 2893–2896. [10] C. Gao, B. Wang, W. Chen, Y. Bai, J. Miao, X. Zhu, T. Li, L. Wang, Fiber-based multiple-access ultrastable frequency dissemination, Opt. Lett. 37 (2012) 4690– 4692. [11] L. Sliwczynski, P. Krehlik, Multipoint joint time and frequency dissemination in delay-stabilized fiber optic links, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 62 (2015) 412–420. [12] S. Zhang, J. Zhao, Frequency comb-based multiple-access ultra-stable frequency dissemination with 7 × 10−17 instability, Opt. Lett. 40 (2015) 37–40.
340
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Optics Communications journal homepage: www.elsevier.com/locate/optcom
Simultaneous time and frequency transfer over 100 km optical fiber based on sub-carrier modulation Longqiang Yu a, *, Lin Lu b, *, Lei Shi a , Zhiyan Xu a , Jiahua Wei a , Chuanxin Wu b , Yimei Wei b , Heng Wei b a b
Information and Navigation College, Air Force Engineering University, Xi’an, Shanxi, 710000, China Communication Engineering College, Army Engineering University of PLA, Nanjing, Jiangsu, 210007, China
ARTICLE
INFO
Keywords: Time and frequency transfer Optical fiber Sub-carrier modulation
ABSTRACT In this paper a novel scheme is proposed to realize the simultaneous transfer of precise time and frequency signals. By performing sub-carrier modulation to the time signal, the time and frequency signals can be directly transferred in the same optical channel without causing mutual interference. The remote user does not need a slave oscillator to clear up the frequency signal and therefore can maintain a simple structure. We test the scheme in the proof-of-concept experiment, in which the 50 MHz modulated time signal and 400 MHz frequency signal are transferred together over 100 km optical fiber link. Good signal compatibility and system performance is observed in the experimental results.
1. Introduction Fiber optic time and frequency transfer has drawn considerable interest during the past decade because they are capable of providing accurate and stable access to high-level atomic clocks or realizing ultra-precision time and frequency comparison. Presently, great system performance has been achieved for frequency dissemination both in point-to-point systems [1–6] and point-to-multipoint networks [7–15], which deeply facilitates their applications in scientific projects, such as the well-known Square Kilometer Array (SKA) [16] and Acatama Large Millimeter Wave Array (ALMA) telescope [17]. On the other hand, various fiber optic time synchronization systems were also demonstrated by two-way clock comparison or round-trip transfer [18–21], making the technique more closer to be widely used in navigation, guidance, security, et al. However, still it should be noted that sometimes exclusive time or frequency transfer cannot meet the demand of particular applications, such as the deep space exploration, coherent radar array and communication systems for which both time and frequency synchronization is indispensable. Therefore simultaneous time and frequency transfer is needed for such applications. One technical issue in simultaneous time and frequency transfer is how to avoid the interference between the time signal (TS) and the frequency signal (FS). Some groups use the wavelength division multiplexing technique to distinguish them in the optical domain [14,22]. The method is straightforward, but in fact it is just the direct combination *
of two independent systems. Also this will lead to relative phase shift between TS and FS when the transmission delay varies, which may be a problem in applications where mutual calibration of the TS and FS is needed. A better choice is to transfer them by a common optical carrier. In [13], Z. Jiang et al. try to reduce the interference by modulating FS and TS on two individual Mach–Zehnder modulators. Though obvious suppression of the interference is observed in the report, unavoidable interference is still expected because two signals will beat with each other in photon detector, and one may have to use a clear-up oscillator to purify the FS at the remote end. L. Sliwczynski et al. [6,11] design a special structure to combine two signals. They mark the TS by introducing phase change to one of the falling edges of the 10 MHz square signal, so that the FS and TS can be recovered respectively with reference to the rising and the falling edges. The scheme is quite effective, however, a slave oscillator is still indispensable to extract the FS from the rising edges, which also increases the structural and technical complexity of the remote user. In this manuscript, we present a new solution to simultaneously transfer the TS and FS. The solution is based on sub-carrier modulation in which the base-band TS is shifted to intermediate frequency. It not only realizes the joint transfer of TS and FS in common optical channels, but also eliminates the interference on FS without additional clear-up slave oscillator. Experiment is performed to transfer a 50 MHz modulated TS and a 400 MHz radio frequency (RF) signal. Stabilization
Corresponding authors. E-mail addresses: [email protected] (L. Yu), [email protected] (L. Lu).
https://doi.org/10.1016/j.optcom.2018.06.043 Received 29 March 2018; Received in revised form 23 May 2018; Accepted 16 June 2018 0030-4018/© 2018 Elsevier B.V. All rights reserved.
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Optics Communications 427 (2018) 335–340
Fig. 1. Sketch of the spectra of (a) 1PPS and RF before modulation, (b) 1PPS and RF after joint transfer, (c) MTS and RF after sub-carrier modulation, (d) MTS and RF after joint transfer.
all the residual interfering components will remain outside the passband of the filter. Then the FS can be extracted without deterioration. To stabilize the FS, we make some improvement over the passive hybrid frequencies transfer scheme proposed in our previous research [25], shown in Fig. 2. The FS, 𝑽𝑹 ∝ cos 𝜔0 𝒕, is bidirectionally transferred over the optical fiber, indicated by the blue path. 𝜑 is the phase change ( ) over single trip. By mixing the round-trip FS, 𝑽𝑹 ∝ cos 𝜔0 𝒕 + 2𝜑 , with the frequency-tripled local reference, 𝑽𝑻 ∝ cos 3𝜔0 𝒕, we get the phase( ) conjugated signal, 𝑽𝑰 ∝ cos 2𝜔0 𝒕 − 2𝜑 , which could counteract the phase change of the optical fiber. Here instead of directly mixing 𝑉𝑅 and 𝑉𝑇 , we use the dual-mixer time-difference (DMTD) method to avoid the crosstalk from the second harmonics of 𝑉𝑅 , which is also adopted in [26]. An auxiliary frequency, 𝑽𝑨 ∝ cos 𝜔𝑨 𝒕, is introduced to premix with the two signals. They can do either sum-frequency mixing or beat-frequency mixing. Here we choose the latter. Then the outputs, [( ) ] ( ) 𝑽𝒙 ∝ cos 𝜔0 − 𝜔𝑨 𝒕 + 2𝜑 and 𝑽𝒚 ∝ cos 3𝜔0 − 𝜔𝑨 𝒕, are mixed again to get the beat signal 𝑉𝐼 . It is critical that 𝜔𝐴 should be properly chosen so that no crosstalk will arise in three mixing procedures. The stability of the auxiliary signal is insignificant since its phase terms are canceled eventually. Then after frequency conversion with a coefficient ( ) of 0.5m, the phase-conjugated signal cos 𝒎 𝜔0 𝒕 − 𝜑 is transferred with the original FS and serves the remote user as a stable frequency standard, illustrated by the red path. We developed a large-dynamic-range compensation scheme to compensate the true time delay of TS [27]. The scheme runs by resolving the compensation time according to the period of a precise clock into the integral-multiples part and fractional part. Fig. 3 illustrates the compensation procedure. The total compensation time is 1−𝜏 = 𝑛𝑇 +𝛥T, where 𝜏 is the single-trip time delay, T the clock period, and 𝛥T the fractional part after resolution. At the beginning, TS triggers the counter to count the rising edges of the clock. Then it is regenerated when the counting reaches n, amounting to a true time delay of nT. After subcarrier modulation the MTS is delayed 𝛥T by an electronic variable delay line (EVDL), accomplishing the whole time compensation.
schemes are also applied to counteract the variation of the transmission delay. 2. Principle The spectra of TS and FS, as well as their interactions after transfer, are shown in Fig. 1. The TS is usually in form of one pulse per second (1 PPS) and its Fourier spectrum is composed of discrete points with the absolute envelop of a sinc function, while FS is a continuous sinusoidal wave and its spectrum is a single point, denoted by 𝑓0 in Fig. 1(a). Fig. 1(b) shows the spectra when FS and TS are directly combined and transferred together. It is expected that around 𝑓0 there will be dense interfering components whose spectrum is identical to that of the 1 PPS. This is also the case reported in [23], indicating that the FS is interfered by the TS. There are two reasons for the illustrated interference. One is that the TS and FS, when received by the remote user, will mutually beat with each other in photon detector, obeying square law. Moreover, because neither the direct modulation nor external modulation is ideally linear, the TS will be modulated on the FS in the local modulation procedure, known as cross modulation. As the 1 PPS can be regarded as a square wave of 1 Hz, the spacing of its spectrum components is 1 Hz too. Therefore it will be impossible for ordinary electronic filters to clear up the interfering frequencies around 𝑓0 . Even if in some schemes the timing signal is in form of pseudo-random code with frequency of several kilohertz [24], it is still too harsh for the filtering. In such case additional clear-up oscillator with locking bandwidth <1 Hz is needed to perform narrow-band filtering to purify the FS. Here we propose a solution to combine the FS and TS, which can relieve FS from the interference of TS when they are simultaneously transferred in the same transmission channel. To start with, we modulate the TS on an intermediate-frequency sub-carrier, 𝑓𝑠𝑐 , as is shown in Fig. 1(c). Then when the modulated TS (MTS) is transferred with the FS, the center frequency of the interfering signals will shift from 𝑓0 to 𝑓0 ±𝑓𝑠𝑐 . However, since the spectrum of the MTS is similar to that of the TS, the interfering frequency components still exist. So we use a bandpass filter to limit the bandwidth of the MTS within 2𝑓𝑏1 before it is combined with FS. As a result, the bandwidth of the interfering signal is also limited. Then after the MTS and FS are detected at the remote end, we use another ordinary bandpass filter, whose center frequency and bandwidth is respectively 𝑓0 and 2𝑓 𝑏2 , to clear up the side bands. As long as the condition 𝑓𝑠𝑐 >𝑓𝑏1 + 𝑓𝑏2 is satisfied like the case in Fig. 1(d),
3. Experimental results To test the proposed scheme, we simultaneously transfer 50 MHz MTS, 400 MHz and 1 GHz FS over 100 km optical fiber using the same laser diode (LD). The setup of the proof-of-concept experiment is illustrated in Fig. 4 and elaborated below. We first focus on the frequency transfer subsystem, as shown in the left part of the schematic. 336
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Fig. 2. Sketch of the frequency stabilization scheme. DMTD: dual-mixer time-difference.
Fig. 3. Sketch of the time compensation scheme. EVDL: electronic variable delay line.
A signal generator is referred to the 10 MHz frequency standard of a rubidium atomic clock to generate a 1 GHz FS, 𝑉0 . It is fed to one ports of the RF combiner and modulated on a distributed feedback (DFB) LD at 1547.7 nm. Then the optical signal is sent into the optical fiber via an optical circulator. At the remote end, the optical signal is amplified by an erbium-doped fiber amplifier (EDFA), filtered by an optical band-pass filter (BPF), and detected by a photon detector. After relevant electronic filtering and combination, the 1 GHz FS is transferred back by another LD. We choose a different wavelength at 1546.9 nm in the backward transmission in order to eliminate the impact of Rayleigh scattering. At the local end, we use a crystal oscillator to generate a 100 MHz auxiliary signal 𝑉𝐴 , and perform DMTD mixing with the round-trip FS (𝑉𝑅 ) and the triple-frequency signal (𝑉𝑇 ). That means the 1 GHz and 3 GHz signals are first shifted respectively to 900 MHz (𝑉𝑥 ) and 2.9 GHz (𝑉𝑦 ), and then they are mixed again to gain a 2 GHz phase-conjugated FS, 𝑉𝐼 . Considering that the frequencies of 𝑉𝑅 and 𝑉𝑇 are at least ten times higher than that of 𝑉𝐴 , the crosstalk in the pre-mixing from the 9th and 29th harmonics of 𝑉𝐴 could be ignored. But certainly it will be better if auxiliary frequencies like 700 MHz are used in DMTD mixing. Then we convert 𝑉𝐼 to 400 MHz, whose phase is also conjugate to the phase change of the optical link. After combined with 𝑉0 , it is transferred to the remote end. In this way the remote user can extract a stable 400
MHz FS using an electronic BPF. Both the remotely received 400 MHz FS and the local 1 GHz reference signal (𝑉0 ) are down-converted to 200 MHz to perform phase comparison. The outputs of the mixer are steadily measured by a digital multimeter, then converted to relative phase fluctuations for performance characterization. The time transfer subsystem is shown in the right part of the schematic. By referring to the 10 MHz frequency standard of atomic clock, a 50 MHz FS is generated as the intermediate-frequency subcarrier. After sub-carrier modulation, the MTS is filtered by a BPF, whose passband is 40 MHz centering at 50 MHz. Then it is also combined by the RF combiner with the FSs and modulated on the same LD. At the remote end, part of the received MTS is detected to regenerate the 1 PPS for the user, and the other part is amplified and sent back to the local end. The round-trip transmission delay of the MTS is measured by a time interval counter (TIC) and the results are sent to a time delay control module to perform time compensation. Based on a precise 100 MHz clock, the compensation time is divided into the multiple-of −10 ns part and fractional part. The compensation of the former part is realized by a clock counter, which starts the counting when triggered by the source 1 PPS and regenerates the 1 PPS when corresponding time is up. Then the regenerated 1 PPS is modulated on the sub-carrier and filtered. Finally the MTS is delayed by an EVDL with 10 ps resolution and 337
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Fig. 4. Experimental setups of the time and frequency transfer system. Syn.: frequency synthesizer, CC: clock counter, Mod.: modulator, EVDL: electronic variable delay line, TIC: time interval counter, LD: laser diode, PD: photon detector, OBPF: optical bandpass filter, EDFA: erbium doped fiber amplifier, TC: temperature control, BPF: (electronic) bandpass filter, Time Reg.: time regenerator.
10.24 ns adjustment range, finishing the rest of the time compensation. The regenerated 1 PPS at the remote end is compared with the local one by a TIC apparatus, whose noise floor is about 63 ps (peak to peak). To reduce the impact of the high-order harmonics of MTS, we use direct intensity modulation and properly adjust the DFB in order to gain better modulation linearity. Meanwhile the passband of the filters used to extract the 1 GHz and 400 MHz FS are limited within 20 MHz, so that the condition 𝑓𝑠𝑐 >𝑓𝑏1 + 𝑓𝑏2 is satisfied. The effectiveness of the design is first tested by a simple experiment. We modulate the 1 GHz FS on LD with 1 PPS or MTS and unidirectionally transfer them to the remote end. The spectra of the detected 1 GHz FS are measured by an electronic spectrum analyzer, and the results are shown in Fig. 5. Fig. 5(a) is the spectrum of the 1 GHz FS when it is transferred alone. The center frequency in the view is 1 GHz, the span is 1 kHz, and the resolution bandwidth is 10 Hz. The spectrum of the received signal when FS is combined with 1 PPS is shown in Fig. 5(b). Under the same test condition, dense frequency components are clearly observed on both sides of the 1 GHz FS, indicating the severe interference from TS. The result when we transfer 50 MHz MST instead of 1 PPS is demonstrated in Fig. 5(c). It is apparent that the interfering components are well suppressed and the purity of spectrum in the view shows no observable degradation compared with that in Fig. 5(a). Thus the proposed design is proved to be capable of eliminating the interference on FS in the simultaneous time and frequency transfer. Some calibrations for the time transfer subsystem are needed before the systematic experiment. The local and remote setups are connected by a 1 m optical fiber. Based on the results of this back-to-back test we calibrate the intrinsic timing offset induced by terminal setups, including the asymmetric optical and electronic lines, the phase mismatch between the source 1 PPS and the counting clock, and the envelop distortion of the MST. The other concern is the transmission asymmetry caused by chromatic dispersion. For specific link it can be measured in advance by dispersion analyzer [6,14]. However, considering that perfect calibration of chromatic dispersion has not been achieved yet and this is also not the focus of this paper, we just directly do the co-location calibration by replacing the 1 m optical fiber with 100 km experimental fiber spools. After the calibrations we run the time and frequency transfer system and do continuous measurements to test the proposed scheme. Fiber
Fig. 5. The normalized spectrum of the received 1 GHz FS when (a) 1 GHz FS, (b) 1 GHz FS+1 PPS TS, (c) 1 GHz FS+50 MHz MTS, are transferred together.
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Fig. 6. Results of the proof-of-concept experiment. (a) The single-trip transmission delay of the 100 km optical fiber. (b) The timing errors of the time transfer. (c) The relative phase fluctuations of the 400 MHz FS. (d) The Allan deviation of the 400 MHz FS.
stabilization is activated, 6.85 × 10−17 /104 s. Compared with the noise floor measured in the back-to-back test, the performance around 200 s shows a degree of degradation, corresponding to the quasi-periodic phase fluctuations in Fig. 6(c). Limited by our technical merit, the proof-of-concept experiment has not been performed with the best configuration. We think better performance is expected if the following two aspects are improved. One immediate way is to upgrade the hardware of the setups and bring down the noise floor. The other one is the further elimination of the interference between the combined signals. Although the 8th and 20th harmonics of 50 MHz MTS are relative weak, still they may remain as interference to the 400 MHz and 1 GHz FSs. For our consideration this residual crosstalk can be eliminated if a more proper sub-carrier, e.g. 300 MHz, could be generated. Such a higher frequency also allows a larger bandwidth for MTS, so that lower time jitter could be maintained [28]. Hopefully we think the proposed scheme will be also effective in the real field. In such cases, the Sagnac effect should be taken into consideration when the link lays across different longitudes [29]. For longer transfer link, it is also necessary to use bidirectional amplifiers to compensate the loss of the optical fiber.
spools are placed in a temperature-controlled oven to change the transmission delay of the signals. Fig. 6(a) gives the variation of the singletrip transmission delay, which also indicates the time and frequency asynchronization in the unstabilized link. We lower the temperature by about 13 ◦ C in 40 000 s measurement time, and the transmission delay also decreases accordingly by 44.27 ns from 496.14236 μs to 496.09809 μs. The timing errors of the stabilized link are also simultaneously recorded in Fig. 6(b). During the measurement time the mean time difference between the local and remote ends is 9.1 ps, with root mean square (RMS) value of 50.2 ps. Such performance is comparable with our previous experiment in which the 1 PPS is exclusively transferred with 54.4 ps (RMS) uncertainty [27], showing that the time transfer scheme based on MTS is effective. For our point of view several factors lead to the obtained results. The noise floor revealed in the back-to-back test, as one of the major factors, is about 41.8 ps (RMS) which is mainly decided by the art of the devices and circuits [27]. The resolution of the TIC we use is 100 ps, and this is expected to introduce 25 ps timing uncertainty after 16-point averaging. Other possible trivial factors include the temperature dependent variation of chromatic dispersion, the polarization mode dispersion (PMD) and the amplitude-to-phase jitter, which could respectively contribute 0.8 ps [15], 1 ps (PMD coefficient of 0.1 ps km−1∕2 ), and 0.9 ps [28] to the total uncertainty. In addition, the instability of the terminal equipment may account for the time drift. Under the same variation of the transmission delay, the relative phase fluctuations of the received 400 MHz FS are shown in Fig. 6(c). The fluctuations are well stabilized within 2.1 ps in the measurement time, which also indicates that the FS is not interfered by MTS. Based on the phase data we also calculate the Allan deviation of the FS and the curves are displayed in Fig. 6(d). It shows that the Allan deviation in the free-running case is larger than 1.5 × 10−14 during the whole measurement time. While this improves by three orders when the
4. Conclusion In this paper we propose a new scheme to simultaneously transfer the time and frequency signals, in which TS is modulated on an intermediate-frequency sub-carrier and followed by a BPF to limit its bandwidth. The proposed scheme has two significant advantages. The first is that TS and FS share the same optical channels and as a result their coherence could be better preserved. The other one is that the scheme is free from the mutual interference among signals and no slave oscillator is needed to regenerate the FS in the remote end. In the proofof-concept experiment, the 50 MHz MTS and the 400 MHz FS are transferred over 100 km optical fiber spools. Respectively, the FS is stabilized 339
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by passive phase conjugation, while the MTS is compensated by clock counting and EVDL, achieving fractional instability of 6.85 × 10−17 /104 s and timing errors of 50.2 ps (RMS). The results demonstrate that the proposed scheme is a viable solution to simultaneously disseminate the time and frequency signals.
[13] Z. Jiang, Y. Dai, A. Zhang, F. Yin, J. Li, K. Xu, Q. Lv, T. Ren, G. Tang, Precise time delay sensing and stable frequency dissemination on arbitrary intermediate point along fiber-optic loop link with rf phase locking assistance, IEEE Photonics J. 7 (2015) 7200809. [14] W. Chen, Q. Liu, N. Cheng, D. Xu, F. Yang, Y. Gui, H. Cai, Joint time and frequency dissemination network over delay-stabilized fiber optic links, IEEE Photonics J. 7 (2015) 7901609. [15] L. Yu, R. Wang, L. Lu, Y. Zhu, J. Zheng, C. Wu, B. Zhang, P. Wang, WDM-based radio frequency dissemination in a tree-topology fiber optic network, Opt. Express 23 (2015) 19783–19792. [16] B. Wang, X. Zhu, C. Gao, Y. Bai, J. Dong, L. Wang, Square kilometre array telescopeprecision reference frequency synchronisation via 1f-2f dissemination, Sci. Rep. 5 (2015) 13851. [17] J.F. Cliche, B. Shillue, Precision timing control for radioastronomy: maintaining femtosecond synchronization in the atacama large millimeter array, IEEE Control Syst. 26 (2006) 19–26. [18] S.M.F. Raupach, G. Grosche, Chirped frequency transfer: a tool for synchronization and time transfer, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 61 (2014) 920– 929. [19] J. Kodet, P. Panek, I. Prochazka, Two-way time transfer via optical fiber providing subpicosecond precision and high temperature stability, Metrologia 53 (2015) 18– 26. [20] V. Smotlacha, J. Vojtech, Accurate time distribution using optical fiber, in: IEEE 2015 International Association of Institutes of Navigation World Congress (IAIN), 2015, pp. 1–5. [21] P. Krehlik, L. Sliwczynski, L. Buczek, J. Kolodziej, M. Lipinski, Ultrastable longdistance fibre-optic time transfer: active compensation over a wide range of delays, Metrologia 52 (2015) 82–88. [22] B. Wang, C. Gao, W. Chen, J. Miao, X. Zhu, Y. Bai, J. Zhang, Y. Feng, T. Li, L. Wang, Precise and continuous time and frequency synchronisation at the 5×10−19 accuracy level, Sci. Rep. (2012) 00556. [23] F. Yin, Z. Wu, Y. Dai, T. Ren, K. Xu, J. Lin, G. Tang, Stable fiber-optic time transfer by active radio frequency phase locking, Opt. Lett. 39 (2014) 3054–3057. [24] O. Lopez, A. Kanj, P.E. Pottie, D. Rovera, J. Achkar, C. Chardonnet, A. Amy-Klein, G. Santarelli, Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network, Appl. Phys. B 110 (2013) 3–6. [25] L. Yu, R. Wang, L. Lu, Y. Zhu, C. Wu, B. Zhang, P. Wang, Stable radio frequency dissemination by simple hybrid frequency modulation scheme, Opt. Lett. 39 (2014) 5255–5258. [26] F. Yin, A. Zhang, Y. Dai, T. Ren, K. Xu, J. Li, J. Lin, G. Tang, Phase-conjugation-based fast rf phase stabilization for fiber delivery, Opt. Express 22 (2014) 878–884. [27] L. Yu, R. Wang, L. Lu, Y. Zhu, C. Wu, B. Zhang, Y. Wei, Large-dynamic-range time pre-compensation scheme for fiber optic time transfer, Appl. Opt. 56 (2017) 1757– 1762. [28] Ł. Sliwczynski, J. Kolodziej, Bidirectional optical amplification in long-distance twoway fiber-optic time and frequency transfer systems, IEEE Trans. Instrum. Meas. 62 (2013) 253–262. [29] L. Yu, L. Lu, R. Wang, J. Jing, C. Wu, Y. Zhu, B. Zhang, Analysis of the sagnac effect on the accuracy of the long haul optical fiber time transfer system, in: European Frequency and Time Forum & International Frequency Control Symposium (EFTF/IFC), 2013, pp. 303–305.
Acknowledgments The work described in this manuscript was supported in part by the National Natural Science Foundation of China under Grant No. 61032005, 61177065, and 61673393 and the Jiangsu Province Natural Science Foundation under Grant No. BK20140069. References [1] S. Droste, T. Udem, R. Holzwarth, T.W. Hansch, Optical frequency dissemination for metrology applications, C.R. Phys. 16 (2015) 524–530. [2] S.M.F. Raupach, A. Koczwara, G. Grosche, Brillouin amplification supports 1 × 10−20 uncertainty in optical frequency transfer over 1400 km of underground fiber, Phys. Rev. A 92 (2015) 41–58. [3] O. Lopez, F. Kefelian, H. Jiang, A. Haboucha, A. Bercy, F. Stefani, B. Chanteau, A. Kanj, D. Rovera, J. Achkar, C. Chardonnet, P.E. Pottie, A. Amy-Klein, G. Santarelli, Frequency and time transfer for metrology and beyond using telecommunication network fibres, C.R. Phys. 16 (2015) 531–539. [4] C.E. Calosso, E.K. Bertacco, D. Calonico, C. Clivati, G.A. Costanzo, M. Frittelli, F. Levi, S. Micalizio, A. Mura, A. Godone, Doppler-stabilized fiber link with 6 db noise improvement below the classical limit, Opt. Lett. 40 (2015) 131–134. [5] J. Kim, H. Schnatz, D.S. Wu, G. Marra, D.J. Richardson, R. Slavik, Optical injection locking-based amplification in phase-coherent transfer of optical frequencies, Opt. Lett. 40 (2015) 4198–4201. [6] L. Sliwczynski, P. Krehlik, A. Czubla, L. Buczek, M. Lipinski, Dissemination of time and rf frequency via a stabilized fibre optic link over a distance of 420 km, Metrologia 50 (2013) 133–145. [7] G. Grosche, Eavesdropping time and frequency: phase noise cancellation along a time-varying path, such as an optical fiber, Opt. Lett. 39 (2014) 2545–2548. [8] A. Bercy, S. Guellati-Khelifa, F. Stefani, G. Santarelli, C. Chardonnet, P.E. Pottie, O. Lopez, A. Amy-Klein, In-line extraction of an ultrastable frequency signal over an optical fiber link, J. Opt. Soc. Am. B 31 (2014) 678–685. [9] S.W. Schediwy, D. Gozzard, K.G. Baldwin, B.J. Orr, R.B. Warrington, G. Aben, A.N. Luiten, High-precision optical-frequency dissemination on branching optical-fiber networks, Opt. Lett. 38 (2013) 2893–2896. [10] C. Gao, B. Wang, W. Chen, Y. Bai, J. Miao, X. Zhu, T. Li, L. Wang, Fiber-based multiple-access ultrastable frequency dissemination, Opt. Lett. 37 (2012) 4690– 4692. [11] L. Sliwczynski, P. Krehlik, Multipoint joint time and frequency dissemination in delay-stabilized fiber optic links, IEEE Trans. Ultrason. Ferroelectr. Freq. Control 62 (2015) 412–420. [12] S. Zhang, J. Zhao, Frequency comb-based multiple-access ultra-stable frequency dissemination with 7 × 10−17 instability, Opt. Lett. 40 (2015) 37–40.
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