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Abstract
Free-space optical time transfer that features high precision will act as a crucial role in near-future outdoor timing service and ground-to-satellite/inter-satellite clock networks. Here we propose a free-space optical two-way time transfer method using flexible binary offset carrier modulation. The alternative method could yield a comparative precision compared to optical binary phase-shift keyed modulation. For verification, a time transfer experiment with our home-built system between two sites separated by a 30-m free-space path outside the laboratory was conducted. Over a 15 h period, the time deviation is 2.3 ps at 1-s averaging time, and averages down to 1.1 ps until ∼30 s. The fractional frequency instability exhibits 4.0×10−12 at a gate time of 1 s, and approaches to 1.3×10−15 at 10000 s.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Nowadays, free-space optical time transfer has been in rapid development, and shown a potential in near-future high-precision ground-to-satellite/inter-satellite clock networks and outdoor timing services.
Recently, comb-based optical two-way time and frequency transfer over a 2-km free-space link has demonstrated femtosecond-level synchronization with time-of-flight method [1–4], and further achieved attosecond-level transfer via carrier-phase technique [5]. This performance allows precise intercomparisons between optical lattice clocks. Nevertheless, as put in the Ref [6], such a high precision is not always required in general applications at present. Free-space optical two-way time synchronization with digital coherent communication based on binary phase-shift keyed (BPSK) modulation is proposed and achieves sub-picosecond timing precision across a 4-km turbulent range [6]. Besides, several ground-to-satellite optical time transfer base on time-of-flight measurement, such as time transfer by laser link (T2L2) [7] and European laser timing (ELT) [8], have realized picosecond precision.
Here we propose an alternative optical two-way time transfer method in free space using flexible binary offset carrier (FlexBOC) modulation. Compared with the existing optical two-way time transfer based on BPSK modulation [6], it achieves a comparative precision via comprehensive analysis of the pseudorandom noise (PN) code and sub-carrier within FlexBOC signal. Since FlexBOC-based microwave satellite transfer has been maturely developed right now [9,10], this sort of system combining optical technique could be simply established, and would be applicable in the near-future high-precision timing service.
2. Principle
Due to effective suppression of time delay fluctuation along the link, two-way methodology is widely used in precision time transfer [11]. In a two-way transfer configuration, Site A and B send their waveforms at global timestamps: TAT and TBT, respectively. The waveforms reciprocally propagate along a common path, and are received in the opposite sites at global timestamps: TBR and TAR, respectively. As illustrated in Fig. 1(a), the time intervals between sending local waveform and receiving remote waveform in Site A and B, ΔTA and ΔTB, could be described as [9]
Fig. 1. Principle of optical two-way time transfer. (a) Timing diagram; (b) System architecture. TX, transmitter; RX, receiver; E/O, electronic-to-optical converter; O/E, optical-to-electronic converter; CLK, clock.
3. Experimental setup and module design
According to the principle, a free-space optical time transfer system using FlexBOC modulation was established, as shown in Fig. 2. The transceivers in Sites A and B were co-located, but not necessarily, to share a Rubidium frequency standard for the convenience of verification. Each FlexBOC transceiver is in the identical design including an optical module and a modem, and fulfills both time interval measurement and data interaction in full duplex mode. A free-space optical communication link between both sites was built via C-band laser lights encoded by FlexBOC modulation. The reciprocity of the atmosphere was fully exploited by two-way transfer to suppress the air turbulence along the traversing path. The differential length variations of fiber-coupled circulators are passively temperature-controlled.
Fig. 2. (a) Schematic of the free-space optical time transfer system using FlexBOC modulation. (b) Top-level design of the FlexBOC transceiver. (c) Snapshot of the experimental system. syn, synthesizer; gen., generator; ADC, analog-to-digital converter; DAC, digital-to-analog converter; PD, photodiode; PN, pseudorandom noise; TI, Time interval; Time diff., Time difference.
3.1 Optical module
In Fig. 3(a), the home-built optical module contains a frequency-tunable diode laser and a photodiode to achieve electrical-to-optical (E/O) and optical-to-electrical (O/E) conversion, respectively. The diode laser emits 4-mW optical light at ∼1550 nm, and the photodiode is optimized to allow a broadband photodetection. Within the E/O part, the laser diode operates in constant-current mode to realize a broadband modulation. The DC operating current is regulated by a feedback loop, while the AC modulation input is coupled through the capacitor to modulate the power of laser light. Within the O/E part, the input laser light is converted to electronic signal by photodiode. Then, two stages of broadband amplifiers followed by signal conditioners boost the power of electronic signal. The modulation bandwidth of the optical module was tested by a microwave network analyzer and presented in Fig. 3(b). It shows that the optical module supports an analog modulation up to ∼3.5 GHz, which is capable to high-fidelity E/O and O/E conversion.
Fig. 3. (a) Functional architecture of optical module. (b) Bandwidth test. Mod, modulation input; deMod, demodulation output; I-V, current-to-voltage conversion; VR, voltage regulator; C, capacitor; LD, laser diode; PD, photodiode; AMP, amplifier; SC, signal conditioner.
3.2 FlexBOC modem
Our homebuilt FlexBOC modems are originally developed for two-way satellite time and frequency transfer [12]. The transmitter generates local FlexBOC signal containing the following four components that are shown in Fig. 4(a). A 70-MHz sinusoidal intermediate frequency (IF) carrier is synthesized to shift the modulation away from DC. A 10-MHz sub carrier is generated for fine time interval measurement, while a PN code is used for coarse time interval measurement. One 125-kHz PN code sequence contains 125 chips with 8 µs chip duration. Therefore, the PN code sequences repeat every 1 ms and enable clock time difference measurement at a maximum rate of 1 kHz. Last, the interactive data including the measured local one-way time interval and other operating status is for exchanging information to the remote site. The four signal components are mixed together in time domain, and then used as AC modulation input of the frequency-tunable diode laser in the optical module. As illustrated in Fig. 4(b), due to the sub-carrier modulation, two sidebands around the IF carrier are generated at an offset of 10 MHz. The 125-kHz PN codes bring cascaded sidebands around the sub-carrier, which is illustrated in the inset of Fig. 4(b). The high-order harmonics of the PN code will be filtered out in the signal processing within the receiver. Only the fundamental component is remained for the phase analysis.
Fig. 4. (a) RF spectrum of FlexBOC signal; (b) Components of FlexBOC signal. The gray shadows mask the sidebands.
The receiver is used to find the time intervals between the events of sending and receiving FlexBOC signal. The principle has been well developed in satellite navigation [9], and the engineering prototype has been presented in [12]. Generally, the processing includes signal acquisition, tracking, and data decoding. First, the IF carrier, sub carrier and PN code are recovered and separated by quadrate signal release with each local template. After that, the resulting correlation signals of the sub carrier and PN code are comprehensively phase-discriminated to obtain local one-way time interval, and loop-filtered to regulate the internal numerically-controlled oscillators that is the references of the three signals’ local templates. Eventually, according to Eq. (5), the clock time difference is computed with the remote one-way time interval decoded from the interactive data. In this way, three digital lock loops are built in software and keep all the three signal components tracked in real time during the transfer. Figure 5 depicts the autocorrelation of FlexBOC signal, the triangular envelop generated by PN code supports a coarse precision of ∼10 ns, while the internal carrier resulted from the sub carrier holds a fine precision to sub-picosecond. Nevertheless, the utilized locking and tracking scheme does not mean that the system has to work in a continuous operating link, where is crucial for frequency comparison between distant sites. Time transfer can be autonomously recovered by executing the above processing after routine physical obstructions. In contrast, as illuminated in [6], since sending pseudorandom binary sequence (PRBS) and exchanging data are time-multiplexed, one-way time interval measurement is executed in an open-loop scheme. In addition, the autocorrelation waveform of the PRBS sampled at ADC clocking rate is low time-resolved. The following peak finding via parabolic fitting is necessary for subsample precision.
Fig. 5. Numerical simulation of the autocorrelation of FlexBOC signal (red line) and BPSK signal (black line). The top inset gives a clear view of the centerburst, and the bottom inset shows the center peak of the autocorrelation. In the simulation of FlexBOC modulation, the sub carrier frequency is 10 MHz, the chip rate of PN code is 125 kHz, the number of chips is 125. To compare with the work in Ref [6], in the simulation of BPSK modulation, the chip rate of PN code is 10 MHz, the number of chips is 10000. The sampling rate is 200 MHz.
4. Results
Figure 6 exhibits measured RF spectra of the FlexBOC signals in the modem. Although there is a ∼40-dB loss between the transmitter and receiver separated by a 30-m free-space path, picosecond-level transfer still maintained for a long period. The loss is mainly from the low efficiency of the fiber collimators due to mismatching of working distance and link path. However, the received weak FlexBOC signal could be extracted due to the autocorrelation in the signal processing, even if it is submerged in noise. Hence, a transmission power of –40 dBm could also support time transfer over a 30-m free-space link.
The carrier-to-noise ratios were simultaneously recorded and shown in Fig. 7(a). Their variations coincided with the environmental temperature change, which probably leads to mechanical creep, therefore laser beam misalignment. The measured one-way time interval fluctuations at both sites are also in a high agreement with ambient temperature variation during a 15-hour period, as depicted in Figs. 7(b) and 7(c). Small asymmetry of the both drifts was probably caused by differential time delay of fibers, cables and temperature-sensitive devices. Because of environmental turbulence across the free-space link, the peak-to-peak values were ∼170 ps. According to two-way transfer methodology, this environmental turbulence could be cancelled out in the assumption of the reciprocity of atmosphere. In Fig. 7(d), the clock difference is further corrected with temperature drift. We next analyze the clock difference in terms of Allan deviations.
Fig. 7. (a) Carrier-to-noise ratio; (b) and (c) Time delay fluctuations of one-way time intervals during a 15-h period over a 30 m free-space link in forward and backward directions, respectively; (d) Clock difference with temperature correction. Ambient temperature is repeatedly drawn in subplot (a)-(c) for clear view. C/N0, carrier-to-noise ratio; Clock Diff, Clock difference.
The fractional frequency instability is given by the modified Allan deviation and exhibited in Fig. 8(a) for the data in Fig. 7(d). It reaches 4.0×10−12 at a gate time of 1 s, which is close to the performance of the frequency reference, and averages down as τ−1 within ∼30 s, where τ is averaging time. At 10000 s, the frequency stability approaches to 1.3×10−15. The time transfer stability is shown in Fig. 8(b) for the same data in Fig. 8(a). The time deviation at 1-s averaging time is 2.3 ps. It drops to 1.1 ps until ∼30 s and then reaches a floor. We could almost attribute the time deviation drift beyond an average time of ∼30 s to the differential time delay, which could be further reduced by active temperature control of the fibers, cables and transceivers.
5. Discussion
5.1 Accuracy
Right now, the temperature sensitivity is the main factor to the accuracy. It is resulted from differential path length of the circulators and electronic cables, and temperature-sensitive electronics in the modems. According to the temperature correction in Fig. 7(d) and additional temperature sensitivity test, where one-way time intervals over a short fiber link was recorded. Generally, the temperature-sensitivity is estimated at 30∼50 ps/K.
5.2 Precision
Beam misalignment caused by mechanical creep and beam wander due to air turbulence could lead to precision degradation. They directly bring drastic fluctuation of carrier-to-noise ratio that is obvious at the end of the 15-h time transfer in Fig. 7(a). According to the theoretical analysis in [13], timing precision is enhanced by one order of magnitude per decade of carrier-to-noise ratio. Next, High carrier-to-noise ratio during a long-term transfer will be maintained in real time by laser tracking with tip-tilt mirrors.
In each site, the performance metrics of FlexBOC signal synthesis in the transmitter and one-way time interval measurements in the receiver are limited by clock reference. Here we utilized a Rubidium frequency standard with a frequency stability of 3.3×10−12 at 1-s averaging time as the common reference. To some extent, one-way measurements are limited to few picoseconds by the noise from the Rubidium frequency standard. This random deviation cannot be cancelled in two-way methodology. It is verified that the measured clock deviation is very close to the frequency stability of the utilized Rubidium frequency standard. Nevertheless, the precision limit of the system should be ∼0.8 ps at 1 s in the case of the carrier-to-noise ratio of 80∼90 dBHz [13]. From this respect, a higher precision would be expected if a more stable frequency standard was employed, such as a Hydrogen maser or photonic microwave generated by a frequency comb referenced to a narrow-linewidth cavity-stabilized laser.
Another factor is the tracking bandwidths of the FlexBOC signal tracking loops. The FlexBOC modem is originally developed for microwave satellite transfer. The loops are optimized in the case of satellite motion. Over a certain stationary link, the tracking loops should be carefully optimized again.
Besides, the precision improvement could be made by adopting carrier-phase analysis of IF carrier [14,15]. In this scenario, frequency up-conversion of FlexBOC signal to microwave region and down-conversion are preferred to exploit the Doppler effect of microwave carrier. Referred to the current performance achieved by 70 MHz IF carrier, the frequency precision will be 40∼50-fold enhanced with the carrier converted to S-band. For higher precision, external Ku- or Ka-band modulation realized by electro-optical modulator will be adopted, and more attention should be paid on low-noise frequency converter, O/E and E/O modules.
5.3 Features
The combination of optical technology and BOC-modulated time and frequency transfer would push forward high-precision optical clock networks. It should be applicable in optical picosecond-precision timing service on the ground. Direct microwave time and frequency dissemination between distant sites in free space near the ground is one of technique backups during satellite navigation invalidation [16,17]. But, in urban area or non-open area, multi-path effect caused by the microwave reflection of buildings adjacent to the microwave link will blur the receiving signals, and thus significantly degrade the uncertainty. Due to excellent directivity, the employed laser light as carrier can eliminate the effect. In addition, the proposed method might be an alternative solution in ground-to-satellite/inter-satellite in the future. The one-way time intervals are obtained with the method of incoherent detection. Broad-linewidth diode laser and low atmospheric coherence are allowed in this solution. Although the precision will be partially degraded compared to coherent detection, it relaxes the prerequisites of atmospheric coherence and laser coherence in the case of coherent detection [6]. When traversing range is scaled up, a pair of telescope with a larger diameter is essential to decrease beam divergence, and thus to enlarge the receiving cross-section for high-efficiency power receiving [18].
6. Conclusion
We have demonstrated a free-space optical time transfer method using FlexBOC modulation. Over a 30-m free-space path outside the laboratory, our home-built system yields a time deviation of 2.3 ps at a gate time of 1 s, and averages down to 1.1 ps until ∼30 s. The fractional frequency instability is 4.0×10−12 at 1 s, and approaches to 1.3×10−15 at 10000 s. As discussed above, this alternative method could provide a comparative precision compared to optical binary phase-shift keyed modulation and show a potential in outdoor timing service and ground-to-satellite/inter-satellite clock networks in the future.
Funding
State Key Laboratory of Precision Measurement Technology and Instruments (DL18-02); National Natural Science Foundation of China (11704037).
Disclosures
The authors declare no conflicts of interest.
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