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Abstract
An absolute phase synchronization method based on phase-conjugation scheme is demonstrated. A repeatable phase difference regardless of restart operation and fiber route changing between the phase standard at local site and the recovered signal at the intermediate-access node is achieved. This indicates that absolute phase synchronization to arbitrary nodes along the fiber link is feasible. At the intermediate-access node, this phase difference is highly stable with a fluctuation of ±0.014 rad over 10000s. And this phase difference shows consistency within 2% of the full cycle under different situations such as restart operation and fiber route changing.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The rapid development of frequency standards [1–4] has driven continuous improvement of time and frequency synchronization technology. For instance, time synchronization between distant optical clocks has reached femtosecond level [5,6] and frequency synchronization technologies now allow for remote comparison between the most stable and accurate frequency standards [7,8]. However, the requirement for absolute phase synchronization over long range has long been ignored and unsatisfied. Absolute phase synchronization should deliver exactly in-phase frequency signals to remote sites. The synchronized signals “tick as one” and serve as the phase reference of each remote site. It has promising applications in distributed phased array radar [9–11] and radio telescope array [12].
For RF-over-fiber frequency transfer methods, once the frequency transfer link is established, the reference frequency will be recovered at the remote site. In this way, the phase difference of these two signals remains constant. But for most methods, due to the existence of the phase-locked-loop, this phase difference constant is not repeatable. That is to say, if the system experiences restart operation or the fiber route is changed, this phase difference constant changes accordingly.
An absolute phase synchronization method over the fiber link is proposed. Based on this method, multi-access absolute phase synchronization along the fiber link is also demonstrated. The phase differences among the local site, the remote site and the intermediate-access node are independent of the fiber route, and are only determined by accumulated phase delay of the out-of-loop part at each site, which can be precisely calibrated in advance. Experiment results verify the feasibility of the proposed method. At the intermediate-access node, highly stable phase difference is achieved with a fluctuation of ±0.014 rad over 10000s. When system is restarted under different conditions, the mean values of phase difference at the access node show consistency within 0.006 rad. And for cases that the fiber route changes, the mean values of phase difference at the access site remain within 0.098 rad with each other.
2. Experiment setup
Figure 1 shows the principle of the proposed phase synchronization method. The main idea is to deliver the phase of reference signal 2 to arbitrary nodes along the fiber link. It is based on phase conjugation scheme. The following discussion ignores the amplitude item of the signals. The frequency of reference signal 1 is ideally half of that of reference signal 2. Part of the reference signal 1, expressed as $\cos (\omega t + {\phi _{r1}})$, is split out, modulates a laser light and transfers over the fiber link, as shown by the red dashed line. The accumulated phase delay of the forward signal during the transmission is denoted by ${\phi _p}$. The forward signal can be expressed as $\cos (\omega t + {\phi _{r1}} + {\phi _p})$. It is then mixed with a stable reference signal 2, denoted by $\cos (2\omega t + {\phi _{r2}})$, to generate a phase-conjugated intermediate RF signal $\cos (\omega t + {\phi _{r2}} - {\phi _{r1}} - {\phi _p})$. This output signal then modulates a laser light and back-propagates the same fiber link, as shown by the blue dashed line. The forward and backward optical carriers are tuned to the same wavelength. In this way, the accumulated phase delay of the backward signal during transmission over the fiber link is also ${\phi _p}$. The backward signal, written as $\cos (\omega t + {\phi _{r2}} - {\phi _{r1}})$, is mixed with the other part of the reference signal 1, $\cos (\omega t + {\phi _{r1}})$. The up-conversion output frequency signal, $\cos (2\omega t + {\phi _{r2}})$, is theoretically phase stabilized. And its phase difference with the reference signal 2 is a repeatable constant value, and is independent of the values of ${\phi _{r1}}$, ${\phi _p}$ and ${\phi _{r2}}$. In the actual system, this phase difference is decided by accumulated phase delay of the out-of-loop part, denoted as phase offset ${\phi _1}$. Therefore absolute phase synchronization can be achieved by measuring the value of ${\phi _1}$ in advance.
As mentioned above, only when: (1) the wavelengths of forward and backward optical carriers are the same; (2) the frequency of the reference signal 1 is equal to half of that of the reference signal 2, the accumulated phase delay of counter-propagation signals in the fiber link are equal, i.e. ${\phi _p}(forward) = {\phi _p}(backward)$. Therefore, the proposed absolute phase synchronization method also relies on frequency synchronization between two ends of the fiber link. The one-way transmission time difference Δτ of the counter-propagation optical carriers in the fiber link is $\Delta \tau = D \cdot \Delta \lambda \cdot L$, here D is the dispersion coefficient, and is about 17 ps/km/nm for single-mode fiber at 1550 nm, Δλ is the offset of the two laser wavelengths at two sites, and L is the fiber link length. Thus, the accumulated phase delay difference of the counter-propagation signals is given by $\Delta \phi = {\phi _p}(forward) - {\phi _p}(backward) = 2\pi \cdot f \cdot \Delta \tau + 2\pi \cdot \Delta f \cdot \tau$, here $\Delta f$ is the frequency difference of the counter-propagation signals, and τ is the one-way transmission time in the fiber link. Therefore, for 40 km fiber link and 2 GHz reference signal 2, to guarantee that this accumulated phase delay difference is less than 0.125 rad (corresponding to ∼2% coherence loss for 2 GHz signal, which is acceptable for radio telescope application [13]), the wavelength offset of the two optical carriers should be less than 14.7 pm (corresponding to frequency offset of 1.84 GHz), and the frequency difference of the reference signal 1 from 1 GHz should be less than 50 Hz. It requires frequency synchronization between two ends of the fiber link of better than 10−8. A variety of approaches can achieve frequency synchronization with far better level [13–27]. To demonstrate the validity of the proposed method, the easiest and the most practical way is to put two ends of the fiber link at the same place and accessed to the same frequency reference. The fiber link is ring-like and multi-access absolute phase synchronization at an arbitrary point along the fiber link is demonstrated as following.
The multi-access absolute phase synchronization is based on multi-access frequency dissemination scheme [25]. As shown by the red and blue dotted lines in Fig. 1, part of the forward and backward transferred signals is coupled out at the access node by adding a 2×2 fiber coupler in the fiber link. The forward and backward out-coupled signals can be expressed as $\cos (\omega t + {\phi _{r1}} + {\phi _{p1}})$ and $\cos (\omega t + {\phi _{r2}} - {\phi _{r1}} - {\phi _p} + {\phi _{p2}})$, respectively. Here, ${\phi _{p1}}$ and ${\phi _{p2}}$ are the accumulated phase delay induced in the fiber link for the forward and backward signals, respectively, and they have the relationship of ${\phi _{p1}} + {\phi _{p2}} = {\phi _p}$. Mixing the two out-coupled signals, the up-conversion output signal can be denoted by $\cos (2\omega t + {\phi _{r2}})$. Its phase difference with the reference signal 2 is a repeatable constant, and is independent of the values of ${\phi _{r1}},\;{\phi _p},\;{\phi _{p1}},\;{\phi _{p2}}$ and ${\phi _{r2}}$, which means this value is independent of the fiber route. In the actual system, this phase difference is decided by accumulated phase delay of the out-of-loop part, denoted as phase offset ${\phi _2}$. Therefore multi-access absolute phase synchronization can be achieved by measuring the value of ${\phi _2}$ in advance.
Figure 2 shows the experimental setup of the absolute phase synchronization system. The fiber link is ring-like and consists of four fiber spools with length of 10 m, 10 km, 25 km and 2 km, respectively. The 25 km fiber spool is placed inside a temperature variation box. The output optical power of laser 1 and laser 2 are at relatively low level (+2.7 dBm and +3.7 dBm, respectively) to minimize the effect of Rayleigh backscattering. The phase offset ${\phi _1}$, decided by accumulated phase delay of the out-of-loop part, can serve as the status monitor of the whole link. Affected by the limited isolation and nonlinear performance of the frequency mixer [26], phase-conjugation mixing operation at the local site and up-conversion mixing operation at the access node are not ideal. An anti-nonlinear-effect (ANE) method is adopted to suppress the RF leakage and nonlinear effect. As shown in Fig. 2(b), at the local site, anti-nonlinear-effect phase-conjugation (ANEPC) mixing operation based on dual-frequency-mixing is employed [21,27]. The forward signal and reference signal 2 are both frequency shifted via up-conversion mixing with an assistance signal. After bandpass filtering operation, mixing these two frequency-up-conversion signals, the output down-conversion signal is the phase-conjugation signal we need. In Fig. 2(c), at the access node, ANE up-conversion mixing operation is taken. The assistance signal 2, generated by an independent signal generator, mixes with out-coupled counter-propagation signals by frequency-up-conversion operation. Then the output signal mixes with the assistance signal 2, the down-conversion signal is the target phase synchronized signal. The frequencies of reference signal 1, reference signal 2, assistance signal 1 and assistance signal 2 are 1 GHz, 2 GHz, 1.77 GHz and 1.77 GHz, respectively.
Fig. 2. (a)Experimental setup of the absolute phase synchronization system. The local and remote sites locate at the same place. (b) Detailed setup of ANEPC mixing operation. (c) Detailed setup of ANE up-conversion mixing operation at the access node. ANE, anti-nonlinear-effect; ANEPC, anti-nonlinear-effect phase-conjugation; BPF, band-pass filter; PD, photodiode.
3. Results and discussions
Figure 3 shows the phase difference stability of the monitor item ${\phi _1}$ and the detection item ${\phi _2}$ over 10000s. As mentioned above, the 25 km fiber spool in the fiber link is placed in a temperature variation box. Figures 3(a) and 3(b) are the experimental results when the temperature variation box changes rapidly with a rate of 20°C per hour during the experiment. Considering the mechanical tension coefficients and refractive index, the effective temperature coefficient of phase time delay is 76 ps/km/°C [28]. For the reference signal 1 of 1 GHz and the 25 km fiber spool under this temperature condition, the corresponding one-way phase delay changing rate is 238.76 rad per hour. The mean values of monitor and detection phase difference are ${\phi _1}$=2.441 (∼0.777π) rad and ${\phi _2}$=5.460 (∼1.738π) rad, respectively. And we observed phase difference fluctuations of ±0.025 rad and ±0.014 rad over 10000s for the monitor item ${\phi _1}$ and the detection item ${\phi _2}$, corresponding to phase time of ±2.01 ps and ±1.13 ps, respectively. The rapid phase difference fluctuation might be caused by residual RF leakage and nonlinear effect of frequency mixing in the experiment. Figures 3(c) and 3(d) show the results at room temperature and the door of the temperature variation box is open. The mean values of monitor and detection phase difference are ${\phi _1}$=2.443 (∼0.778π) rad and ${\phi _2}$=5.460 (∼1.738π) rad, respectively. And we observed phase difference fluctuations of ±0.019 rad and ±0.014 rad over 10000s for the monitor item ${\phi _1}$ and the detection item ${\phi _2}$, corresponding to phase time of ±1.48 ps and ±1.13 ps, respectively. The above results show the validity of the ANE frequency mixing methods.
Fig. 3. The red line shows the phase difference of monitor item ${\phi _1}$ and the black line shows the phase difference of detection item ${\phi _2}$. The embedded graph in each figure shows enlarged details of the experiment results. (a) and (b): the temperature of the 25 km fiber spool changes rapidly; (c) and (d): under room temperature.
Next, the repeatability of the absolute phase synchronization method when the system is shut down and restarted under room temperature is demonstrated. Figure 4 shows the results of the phase differences of monitor item ${\phi _1}$ and detection item ${\phi _2}$. As shown in Figs. 4(a) and 4(b), the 100 MHz frequency standard is switched off and restarted 3 times. The values of monitor item ${\phi _1}$ are within ±0.017 rad around 2.428 (∼0.773π) rad, and the detection item ${\phi _2}$ are within ±0.002 rad around 5.469 (∼1.741π) rad. In Figs. 4(c) and 4(d), the assistance signal 1 is switched off and restarted 3 times. The values of monitor item ${\phi _1}$ is within ±0.014 rad around 2.428 (∼0.773π) rad, and the detection item ${\phi _2}$ are within ± 0.002 rad around 5.468 (∼1.741π) rad. And as expected, changing the phase of the assistance signal 1, the phase differences of the monitor item and the detection item do not change. Figures 4(e) and 4(f) show the experimental results when the power of the whole system is switched off and restarted. Before the power is switched off, the mean values of monitor item ${\phi _1}$ are within ±0.008 rad around 2.438 (∼0.776π) rad, and the detection item ${\phi _2}$ are within ±0.001 rad around 5.466 (∼1.740π) rad. For a cold start, it needs some time for reference signal 1 and 2 to lock onto the 100 MHz reference frequency signal completely. Thus, when the system is restarted, after about 20-minute “warm up”, the mean values of monitor item ${\phi _1}$ are within ±0.007 rad around 2.442 (∼0.777π) rad, and the detection item ${\phi _2}$ are within ±0.002 rad around 5.468 (∼1.741π) rad again. The phase differences of the monitor item ${\phi _1}$ and the detection item ${\phi _2}$ show good consistency (within ∼0.038 rad and ∼0.006 rad, respectively) before and after the system is restarted under different conditions.
Fig. 4. The red line shows the phase difference of monitor item and the black line shows the phase difference of detection item. The embedded graph in each figure shows enlarged details of the experiment results. (a) and (b): The 100 MHz frequency standard is switched off 3 times. Every switch-off operation lasts 30 seconds; (c) and (d): The assistance signal 1 is switched off 3 times. Every switch-off operation lasts 30 seconds; (e) and (f): The power of whole system is shut down and restarted after 30 minutes. “Warm-up” of the system can be observed from the phase differences.
Finally, the repeatability of the absolute phase synchronization method when the fiber route changes is tested. Figures 5(a) and 5(b) show changes of the monitor and detection items when the 10m-long fiber in Fig. 2(a) is removed from the fiber link. The phase differences of the monitor item ${\phi _1}$ change from within ±0.007 rad around 2.475 (∼0.788π) rad to within ±0.004 rad around 2.457 (∼0.782π) rad, and the detection item ${\phi _2}$ change from within ±0.003 rad around 5.472 (∼1.742π) rad to within ±0.003 rad around 5.439 (∼1.731π) rad. To further demonstrate the repeatability of the method when the fiber route changes, the 2-km fiber spool is removed. The phase differences of the monitor item ${\phi _1}$ change from within ±0.005 rad around 2.457 (∼0.782π) rad to within ±0.004 rad around 2.471 (0.787π) rad, and the detection item ${\phi _2}$ change from within ±0.003 rad around 5.438 (∼1.731π) rad to within ±0.0004 rad around 5.374 (∼1.711π) rad. Then, the access node changes to Point B in Fig. 2(a), and Figs. 5(e) and 5(f) show the experiment results. The phase differences of the monitor item ${\phi _1}$ change from within ±0.004 rad around 2.473 (∼0.787π) rad to within ±0.002 rad around 2.458 (∼0.782π) rad, and the detection item ${\phi _2}$ change from within ±0.001 rad around 5.381 (∼1.713π) rad to within ±0.002 rad around 5.413 (∼1.723π) rad. According to the above results, the fluctuations of the monitor and detection items are very small. The mean values of phase difference of the monitor item ${\phi _1}$ show consistency within 0.018 rad; and for the detection item ${\phi _2}$, they remain within 0.098 rad (smaller than 2% of one full cycle) with each other. The experiment results show good repeatability of the phase differences among the local, remote and intermediate-access sites.
Fig. 5. The red line shows the phase difference of monitor item and the black line shows the phase difference of detection item. The embedded graph in each figure shows enlarged details of the experiment results. (a) and (b): A 10m-long fiber is removed from the fiber link; (c) and (d): The 2km-long fiber spool is removed from the fiber link; (e) and (f): The access node is moved to point B in Fig. 2.
4. Conclusion
An absolute phase synchronization method based on phase-conjugation scheme is demonstrated. Using passive and multi-access transfer framework, repeatable phase difference between arbitrary node along the fiber link and the reference phase standard is achieved. At the intermediate-access node, highly stable phase difference is achieved with a fluctuation of ±0.014 rad over 10000s. When the system is restarted under different conditions, the mean values of phase difference at the access node show consistency within 0.006 rad. And for cases that the fiber route changes, the mean values of phase difference at the access node remain within 0.098 rad with each other.
Funding
National Natural Science Foundation of China (Grant No. 61971259, Grant No. 91836301); Ministry of Science and Technology of the People's Republic of China (No. 2016YFA0302102).
Disclosures
The authors declare no conflicts of interest.
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