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Abstract
Time transfer based on phase modulation schemes has attracted extensive attention in recent years. We propose and experimentally demonstrate an adjustable and stable Michelson interferometer (MI) with a DC phase tracking algorithm for two-way time transfer. Time signal with one pulse per second (1 PPS) is loaded on an optical carrier modulated in phase and demodulated by a Michelson interferometer. The whole compact and cost-effective demodulator is symmetrical with a single coupler to split and recombine optical waves, flexible with one photodetector and a bias tee to separate the DC signal and recovery pulses and stable with a phase modulator to compensate for the drift-phase noise. We show the implementation of modulation and demodulation of the time signal and obtain the stability of 2.31 × 10−11 at 1000 s averaging time. We then demonstrate two-way time transfer over 1556 km lab fibers. The experimental result shows time interval stability of 1 PPS with 5.62 × 10−11 at 1000 s averaging time. It has the potential to transfer time signals in long-distance fiber optic links.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The synchronization of time between different locations plays an important role in many applications, such as deep-space network and antenna arrays [1–3]. Compared with the traditional two-way satellite time and frequency transfer (TWSTFT) [4,5], optical fiber links are considered a promising alternative medium for high-stability and long-distance time transmission [6–10], owing to the advantages of low attenuation, large bandwidth, and immunity to electromagnetic interference. However, the time delay of fiber-optic links is drifting, mainly resulting from mechanical perturbation and temperature variation [11,12]. One of the classic methods to overcome this problem is to setup the bidirectional (two-way) transmission of time signals in two participating sites [13–15]. Another way is to redirect the signal arriving at the remote site back to the local site [16–18]. Both solutions are necessary to compare the local signal with the received signal of each site. According to the comparison result, propagation delay fluctuation is dynamically compensated and calibrated to improve the stability of the time transfer system [19,20].
In recent years, people prefer phase modulator rather than intensity modulator for time transmission due to its simple structure and stable performance [21–26]. Phase modulator eliminates the bias drifting problem, which usually occurs in a traditional Mach-Zehnder modulator. Time signal can be directly encoded as the binary phase shift key (BPSK) format to the optical carrier in a phase modulator [22,23]. However, phase-modulated information cannot be directly detected by a photodetector at the receiver. The optical interferometer is a typical way to achieve phase demodulation. In 2020, a Mach-Zehnder interferometer (MZI) is utilized as a phase demodulator, which contains an optical coupler, an optical hybrid, two photodetectors and a piezo-driver fiber phase shifter [23]. The complexity of these components makes the demodulator bulky and expensive.
In this paper, a novel phase demodulator for two-way time transfer based on Michelson interferometer (MI) is proposed and demonstrated. This polarization-maintaining MI demodulator has low complexity, cost-effectiveness and high reliability. In this phase demodulator, a commercial optical coupler, a variable optical attenuator, two Faraday rotator mirrors, and a phase modulator are utilized. The phase-modulated signal light goes through the MI and then detected by a photodetector. The DC error signal and recovered pulses are separated by a bias tee. To stabilize the amplitude of recovery pulses, a phase tracking algorithm based on DC error signal is designed to compensate the drift-phase noise. A two-way time transmission link with different fiber lengths is created and a proof-of-concept experiment is carried out. The experimental results show that the stability of time transfer is 5.62 $\times$ 10$^{-11}$ at 1000 s averaging time over a 1556 km fiber link.
2. Principle
Figure 1 illustrates the schematic diagram of the proposed phase modulation delivery scheme. The pulse amplitude is chosen in such a way that a ${\pi }$-phase step is imprinted at the phase modulator output. Time signal with 1 PPS is then encoded as BPSK format to the optical carrier from the continue-wave (CW) laser source by a phase modulator. After propagation through a single-mode fiber, we obtain the photoelectric field ${E_1 }$ arriving at the input of the demodulation module:
Fig. 1. Experimental setup of 1 PPS time signal modulation and demodulation system. LD, laser diode; PG, digital delay pulse generator; 1 PPS, one-pulse-per-second; PM, phase modulator; SMF, single-mode fiber; ISO, isolator; MI, Michelson interferometer; OC, optical coupler; VOA, variable optical attenuator; FRM, Faraday rotator mirror; PD, photodetector; TIC, time interval counter.
Fig. 2. (a) the 1 PPS generated by a pulse generator; (b) Response curve of ${V_2}$ with fast scan ${V_3}$ while ${\Delta \varphi }$ is in little change; (c) the demodulation of the phase-modulated light with 1 PPS in a one-way system; (d) the demodulation of the phase-modulated light with 1 PPS in the two-way system over 1556 km fiber link.
3. Experiment setup and results
A two-way time system needs to exchange its own time signals. We design an experiment to focus on the performance of optical demodulation after short-distance (2 m) transmission, that is, a one-way system. The structure of the experiment is represented in Fig. 1. A laser source (Connet, CoSF-R-ER-M) emits a CW optical carrier. Its wavelength is 1550.12 nm, and its linewidth is less than 1 kHz. The time signal generated by a pulse generator (Stanford Research Systems, DG645) is then encoded as the BPSK format using a phase modulator ($\rm {PM_1}$) and loaded on the optical carrier. The $\rm {PM_1}$ (EOSPACE, ${{V_\pi }=4.3}$ V at 16 GHz) is a commercial product with a bandwidth of 20 GHz. The amplitude of the pulse corresponds to the ${V_\pi }$ of the $\rm {PM_1}$. After short propagation by a single fiber that is approximately 2 m and through an isolator (ISO), the modulated light arrived in the receiver is then demodulated by a MI. The MI is an optical instrument that splits a wave into two waves using an optical coupler (OC), delays them at unequal distances, redirects them using Faraday rotator mirrors ($\rm {FRM_1}$ and $\rm {FRM_2}$), and recombines them using the same coupler. To suppress the direct influence of environmental noise, the MI with two different optical directions is encapsulated in a simple box. The variable optical attenuator (VOA) in the one arm of the MI is designed to make the loss of the two arms approximately the same, which can obtain higher fringe visibility. The signal waves produce a destructive interference at the end of the MI, and recover new signals after recombination. The demodulated light is detected by a photodetector (KangGuan, KG-APR-200M). The converted electrical signal is separated into the DC error signal and the recovered pulse signal by a bias tee (Anritsu, G3N46).
However, the signal generated after interference demodulation is unstable and a phase controller is used to drive a phase modulator ($\rm {PM_2}$) for feedback. The controller consists of a data acquisition card and a computer. The $\rm {PM_2}$ (CETC, GC15PMTL5513) in the other arm of the MI acts as a phase shifter. It is a commercial product with a bandwidth of DC-300MHz. The DC signal from the bias tee is sampled by the data acquisition card as a feedback signal, which is analyzed by the designed algorithm program in the computer. The phase tracking algorithm [27–29] based on the DC error signal is designed to compensate the drift-phase noise. The DC error is expected to be locked at the minimum amplitude position. Figure 3(a) shows the simplified compensation curve of the normalized power at ${V_{2}}$ with modulation index ${\frac {V_3 }{{{V_\pi }}}}$ in one period of 2 ${V_{\pi }}$. The flow chart of the control process is shown in Fig. 3(b). The software reads the DC error voltage value ${V_{et} }$ in this loop, which represents point A or B as shown in Fig. 3(a), for example. Then it compares with the DC error voltage ${V_{el} }$ of the last loop. If ${V_{el} }$ is larger than the ${V_{et} }$ we get the point C or D in the last loop. Afterward, the software compares the compensation voltage ${V_{cl} }$ of the last loop and ${V_{cb} }$ before that. If ${V_{cb} }$ is larger than ${V_{cl} }$, it is concluded that point D is for the last loop and point B for this loop, and the software will decrease the compensation voltage for the next loop. There will be four results for these two parameters’ comparison, which determines whether to increase or decrease the driving voltage for the next loop. The DC phase tracking algorithm can effectively optimize the compensation signal and lock the phase in time. Figure 5(a) shows the fluctuation of the DC error signal with free running and after compensation. The recovered signal from the bias tee is directly sent to a time interval counter (TIC) (Keysight, 53230A) to evaluate the performance of the demodulator.
Fig. 3. (a) the normalized compensation curve of the demodulator in one period; (b) the flow chart of the algorithm.
In one-way system, the short-term stability is limited by the timing jitter between the 1 PPS signals generated from the pulse generator. We measure the noise floor of pluses from two channels of the pulse generator (blue line in Fig. 5(b)), which is approximately $9.72\times 10^{-12}$ at 1 s and $9.74\times 10^{-12}$ at 1000 s. The red line in Fig. 5(b) is the result of the modulation and demodulation system. It has short-term stability of $1.32\times 10^{-11}$ at 1 s. The long-term stability of $2.31\times 10^{-11}$ at 1000 s worsens mainly because of the fluctuation of the laboratory temperature during this period, which may make the compensation voltage controlled by the feedback algorithm incomplete. The amplitude of the demodulated signal may rise or fall slightly, affecting the position of the rising edge of the trigger signal and the time interval of pulses before and after demodulation. The whole demodulator thus requires a more stable external environment apart from the improvement of algorithm design. Taking the noise floor as a reference, the time deviation value of the system is further reduced if a better pulse source is used.
The experimental setup of two-way time transfer is shown in Fig. 4. A local site (LS) and a remote site (RS) are connected by single-mode fiber spools (SMF). The wavelengths of the optical carrier transmitted by two sites are 1550.12 nm and 1550.92 nm, respectively. Two different wavelengths are used to prevent Rayleigh scattering during fiber transmission and bi-directional erbium-doped fiber amplifier (Bi-EDFA) modules. Two DWDMs are used to separate the forward and backward optical carriers at the LS and RS. 1556 km fiber optic links set up in our laboratory are used for testing. There are twenty-one fiber spools placed in the link, which has a large loss. Table 1 shows the length distribution and loss of the fiber link, and the values indicated are close to those in a real buried environment. Twenty homemade low-noise Bi-EDFA modules are placed approximately every 77 km in our 1556 km fiber link. Each section of the 77 km fiber contains a dispersion compensation fiber in order to reduce the asymmetry of the optical path in both directions caused by the dispersion. The LS and RS use the same structure of modulation module to send time signals to each other and the same structure of demodulation module to recover the signals. In the experiment, the pulse generators from the LS and RS are locked to the same atomic clock (Quartzlock, A1000), which is to avoid the influence of the clock drift on the experiment test. We use two outputs of the pulse generator as initial time signals, which are set to synchronize. One output is used to send signals to the modulation module for transmission, and the other divides the power of signals into two channels for time interval counting. In particular, the pulse generator in the RS is not only used to generate time signals, but also as a pulse delayer to synchronize with the local time signals. The time interval counters ($\rm {TIC_1}$ and $\rm {TIC_2}$) in Fig. 4 are used to measure the time delay between the original pulse signals and demodulated signals. The computer (PC) reads and calculates these time delay data to feedback and adjusts the original pulse signals at remote site. Finally, we use the time interval counter ($\rm {TIC_3}$) to measure the delay jitter of the original pulses from the LS and RS to evaluate the performance of two-way time transfer system.
Fig. 4. Experimental setup of two-way time transmission system. LS, local site; RS, remote site; PG, digital delay pulse generator; EPD, electric power divider; DWDM, dense wavelength division multiplexer. SMF, single-mode fiber; Bi-EDFA, bi-directional erbium-doped fiber amplifier; PC, personal computer; 1 PPS, one-pulse-per-second; TIC, time interval counter.
Table 1. Length distribution and loss of the fiber link.
Fig. 5. (a) The fluctuation of the DC error signal with free running and after compensation. (b) Performance of 1 PPS time signal modulation and demodulation and stability of two-way time transfer over different fiber lengths.
Figure 5(b) shows the stabilities of fiber-optic time transfer over different fiber lengths. The TEDV of two-way time transfer over 2 m fiber link (green line) is less than $2.64\times 10^{-11}$ at 1 s and $2.57\times 10^{-11}$ at 1000 s. The TEDV of time transfer over 1556 km fiber link (black line) is less than $3.55\times 10^{-11}$ at 1 s and $5.62\times 10^{-11}$ at 1000 s. Based on phase modulation, the information of time signal with 1 PPS is attached to the optical carrier through the conversation of intensity to phase. The binary-phase-modulated CW laser light is simpler to amplify compared with intensity-modulated pulse light, which is important for long-distance transmission. Long-term stability is positively correlated with fiber’s chromatic dispersion [30,31], which is mainly due to the asymmetric transmission delay caused by different ambient temperature fluctuations during the test. Our system has similar performance [21–23], and our demodulator supports long distance transmission and takes advantage of the cost-effectiveness and high reliability.
4. Conclusion
In summary, we propose a cost-effective optical MI for phase-modulated time signal transmission. The time deviation of pulses before and after demodulation is $1.32\times 10^{-11}$ at 1 s and $2.31\times 10^{-11}$ at 1000 s averaging time in the one-way system. It is an effective method to demodulate and stabilize the phase-modulated time signal. The performance of the demodulator may be better if the algorithm is further optimized or if the whole interferometer is controlled within a more stable temperature range. The time deviation of pulses from the local and remote site is $3.55\times 10^{-11}$ at 1 s and $5.62\times 10^{-11}$ at 1000 s averaging time in the two-way time transfer system over 1556 km fiber links. It shows the potential to transfer 1 PPS time signals in long-distance fiber optic links for time synchronization.
Funding
National Natural Science Foundation of China (61690195, 61701040); Fund of Basic Scientific Research of Beijing University of Posts and Telecommunications (BUPT) (500419304); Youth Research and Innovation Program of BUPT (2019XDA18).
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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