Abstract

Fiber-optic time and frequency synchronization technology demonstrates ultra-high synchronization performance and has been gradually applied in various fields. Based on frequency synchronization, this study addressed the problems of period ambiguity and initial phase uncertainty of the phase signal to realize the coherent transmission of the phase. An absolute phase marking technology was developed based on high-speed digital logic with zero-crossing detection and an optimized control strategy. It can realize picosecond-level absolute phase marking and provide a picosecond-level ultra-low peak-to-peak jitter pulse marking signal to eliminate phase period ambiguity and determine initial phase and transmission delay. Thus, by combining the high-precision phase measurement capability of the synchronized frequency signal and long-distance ambiguity elimination capability of the pulse-per-second signal, a high-precision remote coherent phase transmission over an optical fiber is realized. After frequency synchronization, the peak-to-peak jitter between the local and remote phase-marking signals can be only 3.3 ps within 10,000 s measurement time. The uncertainty of the coherent phase transmission is 2.577 ps. This technology can significantly improve the phase coherence of fiber-optic time and frequency transmission and provide a new approach to achieve peak-to-peak picosecond-level reference phase marking and high-precision fiber-optic remote coherent phase transmission. This demonstrates broad application prospects in coherence fields such as radar networking.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Time and frequency, which are considered to be among the basic physical quantities, are the basis in many application fields, including precise navigation and timing, clock-based geodesy, and fundamental constant measurement [16]. Time and frequency can be measured with the highest measurement and transmission accuracy using methods such as measurement via an optical clock [57] and fiber-based time and frequency transmission [813]. Fiber-based time and frequency transfer technology has been widely used since its inception. Fields, such as very long-baseline interference [14] and square kilometer array telescopes [15], use optical fibers to achieve radio frequency (RF) and time synchronization by modulating the RF signal and time signal (pulse-per-second, PPS) to continuous lasers [9,10,1619]. Applications such as comparing optical clocks between different laboratories [20] use optical fibers to transmit ultra-stable optical frequency Refs. [11,2022]. In addition, many large-scale scientific devices [23,24] use optical fibers to transfer femtosecond mode-locked laser pulses and achieve femtosecond-level time synchronization inside the system. Femtosecond laser pulse transmission can simultaneously provide stable optical frequency references, RF references, and ultra-low jitter time pulse information [12,25,26].

These applications predominantly focus on the transmission and synchronization of the time and frequency signals. The time and frequency references require to be distributed to the remote site separately or simultaneously, and recovered or synchronized at the remote site with high precision; that is, the phase difference between the frequency signals can remain stable. However, an increasing number of coherence applications have established the requirements for reference phase synchronization, such as radar networking [27,28] and distributed antenna interference [29]. They require stabilizing the phase difference, overcoming the phase period ambiguity with both transmission and generation, eliminating the initial phase uncertainty, and calibrating the transmission delay. Thus, the differences between frequency synchronization and coherent phase transmission are mainly reflected in two aspects. First, frequency synchronization does not consider the period ambiguity problem; second, the initial phase after frequency synchronization is uncertain, and must be resolved in coherent phase transmission. By marking the phase with a lower frequency (longer period) signal, the period ambiguity can be eliminated, and initial phase can be determined accurately.

In this paper, an absolute phase marking technology is proposed. It is realized by a high-speed digital logic circuit based on zero-crossing detection and an optimized control strategy. A marking pulse signal can be generated at the zero phase points of the frequency signal, and its generation position and repeat frequency can be selected by a coarse control signal. Hence, the phase-marking points strictly correspond to the pulse edges of the mark signal. Then, a fiber-optic remote coherent phase transmission scheme is proposed. It uses the absolute phase marking technology, which can not only overcome the phase ambiguity of the signal generation and transmission process, but also provide time reference signals with picosecond-level jitter, stabilize the phase difference, eliminate the initial phase uncertainty, and calibrate the transmission delay. Furthermore, all these processes are performed in the picosecond-level uncertainty. This paper provides an in-detail description regarding the principles and results. Section 2 explains the principle of absolute phase marking technology and provides experimental verification. The general principle of fiber-optic remote coherent phase transmission based on absolute phase marking is described in Section 3.1. The experiments for coherent phase transmission are designed in Section 3.2. The relative stability and uncertainty results of the coherent phase transmission are provided in Sections 3.3 and 3.4, respectively. In particular, the aspects of coherent phase transmission, which include providing a time reference signal with picosecond-level jitter, stabilizing the phase difference, eliminating the initial phase uncertainty, and calibrating the transmission delay, are realized step-by-step through the sections. Section 4 presents the conclusions of the study.

2. Absolute phase marking technology

The principle of the proposed absolute phase marking technology is illustrated in Fig. 1. First, we consider zero phase points of the continuous frequency signal (denoted by F) as the mark points. Then, F is converted into a square-wave signal with high-speed edges according to the mark points. Because every two mark points correspond to one period of F (denoted by Tf), the duration time of both the high and low levels of the square wave (denoted by Wm) is equal to Tf. If a certain period of F corresponds to a high level of the square wave, the next period corresponds to the low level of the square wave, and the third period corresponds to the high level. Therefore, the repeated period of the square wave was twice that of Tf. This indicates that the phase evolution law of F has a one-to-one correspondence with the square wave. The phase has been marked completely, but arbitrary marking cannot be performed. Finally, a control signal (denoted by C) was used to achieve arbitrary phase marking. The phase of F is marked only when the rising edge of C arrives, and the phase-marking operation stops with the arrival of the falling edge of C. The trigger level of the edges is equal to a 50% voltage difference between the high and low levels. The edge position, pulse width (denoted by Wc), and repetition period (denoted by Tc) of C directly determine the phase-marking points and marking period (denoted by Tm) in the result. Therefore, the absolute phase marking was completed, and the marking result can be described by the mark signal (denoted by M) generated by the marking process.

 figure: Fig. 1.

Fig. 1. Principle of the proposed absolute phase marking technology. C, control signal; F, frequency signal; M, mark signal; Tc, repetition period of C; Wc, pulse width of C; Tf, period of F; Tm, repetition period of M; Wm, pulse width of M; τcf, transmission delay from C to F; τfm, transmission delay from F to M.

Download Full Size | PPT Slide | PDF

Figure 1 also shows a type of phase-marking process. Three period phase changes of F is marked during the first Tc (denoted by p1, p2, and p3), and the output M contains two sections of high level and one section of low level (denoted by m1, m2, and m3). Their duration time (denoted by Wm) is equal to Tf. While going to the second Tc, another three continuous period phase changes are marked (denoted by p4, p5, and p6). The output M is a double-pulse composite signal with a repetition period of Tm, which is equal to the delay between the two sections marked phase points. Figure 1 further shows the transmission delay between the three signals. The transmission delay from C to F (denoted by τcf) is determined by the relative position of the rising edges of C and F, which is a variable reflecting the phase-marking startup delay. The transmission delay from F to M (denoted by τfm) is determined by the technical principle, which is a constant reflecting the phase-marking output delay. When the control signal properties are modified, such as changing the position of the rising edge (that is, changing τcf), narrowing the pulse width, and increasing the repetition period, the phase-marking process and result may change accordingly.

We used the measurement system shown in Fig. 2 to verify the absolute phase marking technique. A high-precision frequency reference (Stanford Research Systems, FS725 Rubidium Frequency Standard) with 10 MHz outputs was used as the frequency source of the entire system. A digital pulse generator (Stanford Research Systems, DG645 and SRD1) was used to generate the control signal. A phase-locked frequency multiplier, mainly consisting of a 100 MHz oven controlled crystal oscillator (OCXO), phase-locked loop circuit, and 10-multiplier circuit, was used to generate a frequency signal of 1 GHz. Then, we used a high-speed logic module (HSLM) to perform the absolute phase-marking process. The HSLM is a T flip-flop with a reset function. When the reset pin is at a high level, it operates in a normal state, and its output switches to the opposite of its previous state according to the rising edge of the input clock. When the reset pin level is low, its output directly becomes low, regardless of the clock edge state. Therefore, we can use F as the clock input of the HSLM and C as the reset input of the HSLM to achieve the absolute phase-marking function and obtain M from the output of the HSLM. Finally, an oscilloscope (Keysight Technologies, MSOV334A) was used to test and analyze the frequency signal, control signal, and mark signal simultaneously, and was locked to the uniform 10 MHz frequency reference to decrease measurement errors. In addition, all cables used were fixed to avoid introducing additional delays during the entire measurement.

 figure: Fig. 2.

Fig. 2. Measurement setup of the absolute phase marking technology.

Download Full Size | PPT Slide | PDF

First, we set the properties of C as follows: Tc = 1 µs, Wc = 1.75 ns, and τcf = 0.39 ns. The waveform traces of the three signals were simultaneously collected using the oscilloscope, as shown in Fig. 3. The marking period is 1 µs, which is equal to Tc. Special observations were made at the X position from −4 ns to 5 ns and from 1996 ns to 2005 ns. F is a continuous sine signal with a frequency equal to 1 GHz, and C is an irregular pulse signal with a pulse width of approximately 1.75 ns and rise time of approximately 100 ps (from 10% to 90%). Only one regular pulse of M is included in these two X position ranges, which has a high level of 0.6 V, low level of 0 V, rise time of 30 ps, and pulse width of 1 ns equal to Tf. In addition, the relative positions of the three signals in the two X position ranges are the same. The transmission delay can be accurately measured as τcf = 390.1 ps and τfm = 544.7 ps, which were mainly caused by the inherent delay of the HSLM and cables. Furthermore, we used the oscilloscope to measure Tf, Tc, Tm, and Wm over a long time. The average value and P-P jitter of Tf are 999.8 ps and 1.1 ps, respectively, which indicate good phase properties of F. The results of Tc and Tm are shown in Fig. 4 (a). The average value of Tc and Tm are both 1 µs, but the P-P jitter of the former is as high as 129.2 ps and that of the latter is 3.5 ps. Hence, M shows a significantly precise repetition period, which benefits from the precise phase repetitiveness of F (the precise Tf). Figure 4 (b) shows the measured Wm. The P-P jitter of Wm is 3.3 ps, and the average value is 1.0005 ns, close to Tf. These results demonstrate that the control signal strictly marks the phase of the frequency signal, and the phase-marking results can be accurately determined by measuring the properties of the mark signal.

 figure: Fig. 3.

Fig. 3. Waveform traces when Tc = 1 µs, Wc = 1.75 ns, and τcf = 0.39 ns. X position from (a) −1.5 µs to 2.5 µs, (b) −4 ns to 5 ns, and (c) 1996 ns to 2005 ns.

Download Full Size | PPT Slide | PDF

 figure: Fig. 4.

Fig. 4. (a) Period of the control signal and mark signal and (b) pulse width of the mark signal.

Download Full Size | PPT Slide | PDF

Now, we set the other two different groups of the properties of C as follows: (a) Tc = 1 s, Wc = 4.52 ns, τcf = 0.39 ns, and (b) Tc = 1 s, Wc = 5.22 ns, τcf = 0.85 ns. Figure 5 shows the waveform traces acquired under the two settings. Currently, the marking period is 1 s, and the mark signal contains three pulses in one marking period. The first two pulse widths are 1 ns, but the third pulse width is less than 1 ns because the falling edge of C arrives and stops the marking process. As observed from the figure, the delay from the falling edge of C to the falling edge of the current pulse of M (denoted by τcm) represents the phase-marking shutoff delay, which is also constant owing to the technical principle. The waveform data shows that τfm = 544.7 ps and τcm = 875.4 ps for both the settings, and the third pulse width of (a) is 461.9 ps, but the third pulse width of (b) is 695.3 ps. These results demonstrate that modifying the properties of the control signal can achieve arbitrary phase marking effects.

 figure: Fig. 5.

Fig. 5. Waveform traces when (a) Tc = 1 s, Wc = 4.52 ns, τcf = 0.39 ns, and (b) Tc = 1 s, Wc = 5.22 ns, τcf = 0.85 ns.

Download Full Size | PPT Slide | PDF

Therefore, we conclude that the properties of the control signal play a decisive role in the phase-marking process, and the phase-marking result can be determined by accurately measuring the mark signal. The pulse edges of the mark signal and marked phase zero points of the frequency signal strictly correspond. The measurements show that the period and pulse width of the mark signal have less than 3.5 ps P-P jitter for a measurement duration of more than 10,000 s. Therefore, the proposed absolute phase marking technology can achieve picosecond-level phase marking, and the generated mark signal with ultra-low time jitter can be used as a suitable time reference.

3. Fiber-optic remote coherent phase transmission based on absolute phase marking

3.1 General principle

Based on the aforementioned absolute phase marking technology, we propose a fiber-optic remote coherent phase transmission system scheme. Figure 6 illustrates the general principle of the proposed scheme. To facilitate the analysis, we divided the system process into two steps. The first step, based on the existing fiber-optic joint time and frequency transfer technology, is the stable distribution of the signals. At the local site, the signal source outputs a frequency reference signal (continuous sine wave) and a control signal (PPS), which undergo electro-optical conversion (E/O) to form a modulated optical signal. The optical signal passes through a delay stabilization device and is sent to a remote site over the fiber. The modulated optical signal is demodulated at the remote site through opto-electrical conversion (O/E) to recover the frequency signal and control signal, which is used as the signal source of the remote site. The round-trip noise compensation method should be used to obtain stable signals. Therefore, the E/O/E method is also used to transmit the frequency and control signals back to the local site along the same fiber route. A delay measurement device was used to measure the delay change between the source and return signals at the local site. Half of the round-trip phase difference of the frequency signal (denoted by Δφfr) is used as an error signal to drive the delay stabilization device in real time, making its delay change offset the delay fluctuation of the fiber link. Thus, a stable fiber transmission link was established. The frequency signals between both sites can have the same frequency and a stable phase difference, and the control signals can have a stable time delay. Thus, the signal distribution process is completed.

 figure: Fig. 6.

Fig. 6. Schematic diagram of the proposed coherent phase transmission system. E/O, electro-optical conversion; O/E, opto-electrical conversion; HSLM, high-speed logic module; CL, control signal of local site; FL, frequency signal of local site; CR, control signal of remote site; Crt, round-trip control signal; Frt, round-trip frequency signal; CLd, delayed control signal of local site; FLd, delayed frequency signal of local site; ML, mark signal of local site; MR, mark signal of remote site; Δφfr, round-trip phase difference; Δtfr, round-trip link delay.

Download Full Size | PPT Slide | PDF

The second step, based on the absolute phase marking technology, is coherent phase transmission. After the first step, the two sites had relatively delay-stabilized frequency and control signals. We denote the control signal and frequency signal as CL and FL at the local site, and CR and FR at the remote site. Two HSLMs are installed in each site to perform the phase-marking process and generate mark signals (denoted by ML and MR). By appropriately setting the initial control signal, ML and MR can be both 1 PPS, indicating that one phase period is marked within 1 s. Additionally, the mark signals can be used as time reference signals at the two sites. The reference plane of the coherent phase transmission is defined on the input location of the HSLMs at local and remote sites, as shown in Fig. 6. Owing to the physical time delay, synchronization can only occur between a certain period and other periods for the frequency signal. Figure 7 (a) shows the timing relationships between these signals. The marked phase points of FL and FR (denoted by φL and φR) are not yet synchronized, and ML and MR are not synchronized accordingly. The delay between CL and CR (denoted by Δtc), φL and φR (denoted by Δtf), and ML and MR (denoted by Δtm), respectively, are theoretically equal. CL and CR must be synchronized first to eliminate the large delay between φL and φR. The delay measurement device at the local site measures the delay between the source control signal (CL) and round-trip control signal (Crt in Fig. 6) to obtain the absolute round-trip link delay (denoted by Δtcr). Further, Δtc = Δtcr/2 under the assumption that the forward and backward transmission delays are the same. The delay control device then applies a delay of Δtcr/2 to CL such that the delayed local control signal (CLd in Fig. 6) and CR are synchronized. The timing relationships are shown in Fig. 7 (b). φL has moved N periods when compared to Fig. 7 (a), where $N=\left\lfloor\Delta t_{c} / T_{f}\right]$, and “⌊ ⌋” is the round down operation. Therefore, Δtf has been significantly eliminated, and only a small delay (denoted by τf, equals the phase time difference between FL and FR) remains, where τf = ΔtcNTf < Tf, and Δtm = τf. If τf is eliminated, coherent phase transmission can be achieved. According to the measured Δtcr, τf can be calculated theoretically as

$$\left\{ \begin{array}{l} {\tau_f} = \Delta {t_c} - N{T_f}\\ \Delta {t_c} = \Delta {t_{cr}}/2\\ N = \lfloor{\Delta {t_c}/{T_f}} \rfloor \end{array} \right..$$
However, owing to the limited accuracy of the time measurement, we used the measured round-trip phase difference (Δφfr) as an auxiliary to improve the calculation accuracy of τf. Owing to the period ambiguity problem during phase measurement, the phase difference between FL and FR can be calculated according to Δφfr as
$$2\mathrm{\pi }{v_0}{\tau _f} = (\Delta {\varphi _{fr}}\textrm{/2) or (}\mathrm{\pi } + \Delta {\varphi _{fr}}\textrm{/2),}$$
where ν0 is the frequency of FL and FR. Therefore, the true value of τf must be determined using the measured Δtcr and Eq. (1). After the delay control device applies a delay of τf to FL, the delayed local frequency signal (FLd in Fig. 6) and FR are phase-synchronized. Hence, φL and φR, and ML and MR are synchronized, as shown in Fig. 7 (c). Thus, the coherent phase transmission processes are completed, and the time interval between ML and MR can reflect the coherent phase transmission performance.

 figure: Fig. 7.

Fig. 7. Timing relationships between these signals in coherent transmission process when (a) only the transmission delay is stabilized, (b) the control signals are synchronized, and (c) both the control signals and frequency signals are synchronized.

Download Full Size | PPT Slide | PDF

3.2 Experimental setup

The experimental setup for the fiber-optic remote coherent phase transmission is shown in Fig. 8. First, a frequency reference (REF), phase-locked frequency multiplier (PLM), and digital pulse generator (DPG) constitute the signal source of the entire system, which mainly outputs a 1 GHz frequency signal and 1 PPS control signal. Then, we adopt the time and frequency simultaneous transmission method based on dense wavelength division multiplexing over the optical fiber to transmit frequency and control signals. At the local site, the frequency signal (FL) is amplitude-modulated to laser diode-1 (LD-1) (internally modulated distributed feedback (DFB) laser, wavelength λ1 = 1548.51 nm), and the control signal (CL) is amplitude-modulated to LD-2 (electro-absorption modulated DFB laser, wavelength λ2 = 1550.12 nm). The two modulated optical signals are combined by an optical coupler (OC) and then pass through a polarization scrambler (PS), circulator (CIR), and an optical delay line (ODL), and finally input to the fiber link. The PS is used to eliminate the influence of the polarization mode dispersion [9]. At the remote site, the optical signal is sent from another CIR into a dense wavelength division multiplexer (DWDM) to separate two optical signals with different wavelengths. Then, the modulated signals are detected by two photodetectors (PDs). The PD-1 (New Focus 1611, bandwidth 1 GHz) demodulates the frequency signal (FR), while the PD-2 (New Focus 1811, bandwidth 100 MHz) demodulates the control signal (CR). After optical fiber transmission, the phase noise of the frequency signal is degraded [8,9,16]. However, phase noise is the fundamental factor causing timing jitter in high-speed digital devices and systems [30,31]. To achieve the best phase-marking performance, the phase noise must be cleaned, which is often achieved by phase-locking the transmitted frequency signal to an oscillator with ultra-low phase noise [8,9,16]. Therefore, the frequency signal output by PD-1 is sent to a phase noise cleanup device (the cleaner in Fig. 8). The cleaner is composed of a ten frequency divider, phase detector, an OCXO, and a ten frequency multiplier. The OCXO outputs a 100 MHz signal with ultra-low phase noise, and the phase lock bandwidth is approximately 50 Hz. Thus, phase noise above 50 Hz is cleaned, and outputs the phase-noise-cleaned 1 GHz frequency signal (FR). Then, FR is modulated to LD-3 (internal modulation DFB laser, wavelength λ3 = 1547.72 nm), and CR is modulated to LD-4 (electro-absorption modulated DFB laser, wavelength λ4 = 1549.32 nm) and sent back to the local site along the same fiber link. The local site detects the round-trip signal by another DWDM and two PDs, where PD-3 (same as PD-1) demodulates the frequency signal (Frt) and PD-4 (same as PD-2) demodulates the control signal (Crt). The phase frequency detector (PFD, Analog Devices, HMC439) measures the phase difference between FL and Frt (round-trip phase difference, Δφfr). Then, a proportion integration differentiation controller (PID) generates an error signal and feeds it back to the ODL to cancel the fluctuation of Δφfr (with the same feedback bandwidth of the cleaner). Therefore, the transmission delay of the link is stabilized. Next, the delay between CL and Crt (round-trip time delay, Δtcr) is measured by a time interval counter (TIC, Stanford Research Systems, SR620), and the local DPG generates CLd according to Δtcr. According to Δtcr and Δφfr, the electrical delay line (EDL) delays FL to generate FLd. Finally, the local HSLM completes the phase-marking process and generates the mark signal ML. At the remote site, another DPG reshapes the control signal to adapt CR to the marking condition, and then the remote HSLM completes the phase-marking process and generates the mark signal MR.

 figure: Fig. 8.

Fig. 8. Experimental setup. REF, reference frequency; PLM, phase-locked multiplier; DPG, digital pulse generator; LD, laser diode; PD, photodetector; DWDM, dense wavelength division multiplex; OC, optical coupler; PS, polarization scrambler; CIR, circulator; ODL, optical delay line; Bi-EDFA, bidirectional erbium-doped fiber amplifier; PFD, phase frequency detector; TIC, time interval counter; PID, proportion integration differentiation controller; EDL, electrical delay line; HSLM, high-speed logic module; ÷10, 10 frequency divider; ×10, 10 frequency multiplier; OCXO, oven controlled crystal oscillator.

Download Full Size | PPT Slide | PDF

In the experiment, we set up optical fiber links of different lengths to study the performance of the coherent phase transmission system. The shortest link is a 1 m fiber patch cord, and the longest link consists of 150 km cascaded fiber spools. When the fiber length increases, the attenuation of the optical power also increases. Particularly, when the fiber link is longer than 90 km, a bidirectional erbium-doped fiber amplifier (Bi-EDFA) is added to compensate for the power loss. Here, the ODL length is 10 km (with 18 ns dynamic range). Hence, the Bi-EDFA is placed at half the total length of the fiber link and ODL to compensate for the power loss in both directions symmetrically. When the fiber link is shorter than 40 km, the ODL length is 5 km (with a dynamic range of 9 ns). The entire system was situated in an ordinary laboratory environment without an enclosed control. The performance was evaluated at the reference plane via phase analysis (phase difference measurement and phase noise measurement) and time analysis (time interval measurement), and the measurement equipment uniformly used the frequency reference of the REF to reduce measurement errors.

3.3 Phase marking and its relative stability between local and remote sites

When the system reaches the closed-loop state, where the propagation delay is stabilized, we first evaluated the relative stability of the phase marking between local and remote sites. Based on previous studies [13,32], the relative stability of frequency synchronization (commonly expressed through Allan deviation) can reach the order of 10−14 at 1 s and 10−17 at 10,000 s, and the P-P jitter of the relative delay between local and remote control signals can be stabilized on the order of 100 ps. To facilitate the evaluation of relative phase-marking stability, we delayed CL appropriately (the delay parameters are discussed in the calibration section) such that the time interval between ML and MR (called the marking time difference) is within 1 ns. We used an oscilloscope (MSOV334A) to measure the marking time difference under different fiber lengths, with a 1 s measurement interval and more than 10,000 s measurement duration. Figure 9 (a) shows the statistical analysis results of the obtained marking time difference data, which reflects the relative stability of the phase marking between local and remote sites, including the P-P jitter, time deviation (TDEV) at an averaging time of 1 s, and root-mean-square (RMS) jitter. The abscissa represents the total length of the fiber link and ODL; for example, 10 km indicates that the optical fiber link is 5 km and the ODL is 5 km. Under different fiber lengths, the P-P jitter does not exceed 3.5 ps, and the TDEV at 1 s and RMS jitter do not exceed 500 fs, showing ultra-high and consistent stability. The inset in Fig. 9 (a) shows the marking time difference fluctuation under the longest 150 km fiber link and 10 km ODL, with only a 3.3 ps P-P jitter within 10,000 s measurement time. Moreover, we used a signal source analyzer (AnaPico, APPH40G) to measure the absolute phase noise of the frequency signals under a 100 km fiber link and 10 km ODL, as shown in Fig. 9 (b). When compared with the source signal (FL), the phase noise of the frequency signal detected by PD-1 has significantly deteriorated at frequency offsets greater than 1 kHz, while the phase noise is significantly optimized after cleaner. This indicates the influence of optical fiber transmission on the phase noise of the frequency signal and cleanup effect of the cleaner. The inset in Fig. 9 (b) shows the relative stability of the 1 GHz frequency signal after cleaner, with 2.2×10−14 at 1 s and 1.6×10−17 at 10,000 s, proving a fine closed-loop state. The results also show that the mark signals can be used as ultra-low jitter time references in a time-frequency system.

 figure: Fig. 9.

Fig. 9. (a) Relative stabilities of the marking time difference under different fiber lengths (the inset shows the result of a 150 km fiber link and 10 km ODL) and (b) absolute phase noise of frequency signals under a 100 km fiber link and 10 km ODL (the inset shows relative stability of frequency signal after cleaner).

Download Full Size | PPT Slide | PDF

3.4 Calibration and the uncertainty of coherent phase transmission

To achieve a high-precision coherent phase transmission, a further calibration procedure is required to eliminate period ambiguity and initial phase uncertainty. According to the general principle, the time delay between CL and CR must be calibrated first. Owing to the system asymmetry and influence of the external components located outside the entire loop, the time delay between CL and CR (called the control time difference) should be

$$\Delta {t_c} = \Delta {t_{cr}}/2 + \Delta {t_\lambda } + \Delta {t_0},$$
where Δtλ is the group delay difference caused by chromatic dispersion, and Δt0 is the inherent delay caused by the inconsistent devices and cables at the two sites. The two terms are almost unchanged when the environmental temperature of the system changes relatively slowly. In the system experiment of a 25 km optical fiber link and 5 km ODL, the system is switched off and restarted, and the time intervals from shutdown to restart range from 2 to 30 min. We measured the round-trip delay Δtcr and control time difference Δtc under each closed-loop state, with a measurement time interval of 1 s and a duration longer than 300 s. After calculating the average values of each measurement, we calculated the difference between the mean values of Δtc and Δtcr/2, and the results are shown in Table 1. In 10 measurements, the value of Δtc−Δtcr/2 is between 104749 and 104788 ps, which is mainly due to the trigger delay of the DPG outside the loop located at the remote site. The trigger delay was approximately 98 ns. The results represent the range of Δtλt0. Because the maximum difference between these measurements is 39 ps, we may consider the average of the fourth column of the table as the value of Δtλt0; thus, Eq. (3) becomes
$$\Delta {t_c} = \Delta {t_{cr}}/2 + 104768,$$
where Δtc and Δtcr are given in units of ps. By calculating this delay value and using the DPG to apply it to CL, CLd and CR will be synchronized. The calculated delay value is denoted by dc. The calibration uncertainty is the uncertainty of Δtλt0. This calibration is insufficient for high-precision time synchronization. However, because of the principle of phase marking technology, the control signal’s rising edge position only needs to be ensured between the two phase zero points of the frequency signal. Hence, the synchronization between CLd and CR allowed is relatively rough here. The maximum allowable synchronization uncertainty was 500 ps (or the allowable time difference was 0 ± 500 ps) with the appropriate setting.

 figure: Fig. 10.

Fig. 10. (a) Measured mean values of the control time difference and marking time difference under different delay settings in local DPG and (b) time fluctuation of the control time difference.

Download Full Size | PPT Slide | PDF

Tables Icon

Table 1. Average delay values under system multiple shutdowns and restartsa

Table 1 also shows the round-trip phase time difference (τfr), phase time difference between FL and FR (τf), and marking time difference (Δtm). The phase time difference is calculated as

$$\tau = \frac{{\Delta \varphi }}{{2\mathrm{\pi }{v_0}}},$$
where Δφ is the phase difference measured by the PFD, and v0 = 1 GHz. According to the 6×10−5 rad resolution of Δφ, the resolution of the phase time difference measured indirectly by Eq. (5) is approximately 10 fs, which is much higher than the 100 fs resolution of direct measurement by the oscilloscope. Owing to the principle of the “round-trip phase stabilization method,” τfr is almost unchanged. However, τf and Δtm sometimes change by approximately 500 ps, which can be determined from the value of Δtcr. As shown in Table 1, the value of Δtcr increases by 999 ps from measurement 4 to 5, indicating that the round-trip delay of the system only increases one period of the frequency signal. Hence, τfr remains unchanged, but Δtc increases by 510 ps, τf increases by 499.71 ps, and Δtm increases by 499.1 ps, indicating that the one-way delay of the system increases by half a period. From measurement 5 to 6, the value of Δtcr increases by 1004 ps, while Δtc increases by 509 ps, τf decreases by 499.90 ps, and Δtm increases by 499.9 ps. When compared with measurement 4, the round-trip delay increases by two periods, while τf returns to the state of measurement 4, and other one-way parameters increase one period because they do not exhibit period ambiguity problem. The results show that the two round-trip parameters Δtcr and τfr can be combined for coherent phase transmission.

The control signal was calibrated and verified under the 25 km optical fiber link. In a calibration experiment, the measured Δtcr = 290506136 ps, Δtc = 145357907 ps, and Δtm = 145357408 ps before calibration. At the local site, the delay value that the DPG applies to CL is dc = 290506136÷2 + 104768 = 145357836 ps, 71 ps smaller than Δtc. In practice, because the resolution of the DPG was 5 ps, the delay was set to 145357835 ps. After calibration, the measured Δtc = 487 ps and Δtm = 405.4 ps. The large time delay between the mark signals is eliminated after the calibration, and the remaining small delay is determined by the phase difference between the frequency signals. However, the value of Δtc here is different from the expected value, which is theoretically equal to 71 ps. This is because of a certain error between the DPG delay control and true delay value described in its manual. As aforementioned, the synchronization accuracy of the control signals need not to be very high. To analyze the allowable range of the control time difference in reality, we set the delay value with a step of 100 ps based on dc, and then measured the Δtc and Δtm calibrated according to each delay value. As shown in Fig. 10 (a), Δtm remains approximately 405 ps when the setting delay is from dc−500 ps to dc+300 ps. Correspondingly, the control time difference is from 232 ps to 1012 ps, and when the setting delay is out of that range, the value of Δtm changes. Figure 10 (b) shows the time fluctuation data of Δtc within 20,000 s of the measurement time. Its P-P jitter is 217 ps; hence, the allowable control time difference at any time should be from 232−217÷2 ps to 1012 + 217÷2 ps, that is, from 123.5 ps to 1120.5 ps, and the range size is 997 ps. Therefore, the actual allowable range of the control time difference is close to 1 ns, but the center is not at zero time difference. According to the phase-marking principle, this phenomenon is caused by a delay between the control signal and frequency signal (τcf). First, τcf at the local site is not equal to Tf/2. The transmission delays of the control signal and frequency signal are not equal, and thus, τcf at the remote site changes by a certain delay value. Therefore, Δtc is limited to 0 ± 500 ps, but adjusting τcf by the DPGs at both sites can change the range of Δtc. Thus, the calibration of the control signal is relatively rough. At a later stage, we operate according to Eq. (4) and do not establish strict requirements regarding the control time difference after calibration to be close to zero.

According to the above calibration method of the control signal, delays before and after calibration under 10 times system shutdown and restart operations are measured, and the results are shown in Table 2. The difference between the calculated dc and measured Δtc before calibration was less than 100 ps. The Δtc after calibration was between 480 ps and 539 ps, indicating good synchronization consistency of the control signals. A comparison of the marking time difference before and after calibration is observed, proving the validity of the calibration. After calibration, Δtm is close to two values, 400 ps and 900 ps, which is approximately half the period of the frequency signal, and its variation law strictly corresponds to the variation of τf. However, because of the inconsistency delay of the cable and instrument between the PFD-based measurement and oscilloscope-based measurement, the absolute values of τf and Δtm are not equal, and can be calibrated by uniformly using the oscilloscope. Moreover, τf has several ps deviations between different measurements with similar values, resulting in the deviation of Δtm, while τfr does not change more than 100 fs, which is the asymmetry problem caused by inconsistent system states. The problem occurred in all time and frequency transfer systems based on the round-trip method [810,18].

Tables Icon

Table 2. Average delay values before and after the control signal calibrationa

The final step is the calibration of the frequency signal to eliminate τf. This is for phase synchronization, and the mark signals are automatically synchronized through absolute phase marking. According to Eq. (1) and (2), we can calculate τf but require additional measurement and evaluation, making the calibration work complex. Based on the aforementioned experimental results, we can first observe the values of all delay parameters in a certain closed-loop system state and set them as the reference values. Then, we are required to calculate the round-trip delay variation relative to the reference value to obtain the present one-way values. If measurement 5 in Table 2 was used as the reference values, the Δtcr of measurement 1 increased by 3029 ps. That is, the delay was 3Tf longer. Hence, τf increases by 1.5Tf, and correspondingly, Δtm should also increase by the same amount, which should change from 900.8 ps to 2400.8 ps. However, the 2 ns increment is eliminated by the control signal calibration such that the expected Δtm is changed to 400.8 ps, which is 500 ps less than the reference value (900.8 ps). The actual measured value of the Δtm is 400.1 ps, which is only 0.7 ps less than the expected value. Measurement 2 was identical. In addition, the Δtcr of measurements 6, 7, 8, and 10 relatively decreases by approximately 1 ns, and thus, Δtm decreases by approximately 500 ps. While the relative change of Δtcr is an even multiple of Tf, Δtm is relatively unchanged, such as measurements 3, 4, and 9. Therefore, we monitored Δtcr and calculated the relative period change to identify whether to delay FL by half of Tf. The relative period change is calculated as

$$\Delta N = \left[ {\frac{{\Delta {t_{cr}} - \Delta {t_{ref}}}}{{{T_f}}}} \right],$$
where Δtref represents the reference value of Δtcr, “$[\; ]$” represents the rounding operation. This study uses measurement 5 in Table 2 as the reference values uniformly; hence, Δtref = 290507121 ps. When ΔN is odd, we delay FL by half of Tf, and when ΔN is even, we do not take any action.

According to the above calibration method of the frequency signal, the delays before and after the calibration under 12 times system shutdown and restart operation are measured, and the time interval between the last shutdown and the next restart is from 2 to 30 min. However, the interval between measurement 10 shutdown and measurement 11 restart reaches 10 h, and the next interval reaches 5 h. The results are shown in Table 3. When ΔN is even, EDL does not delay FL, and τf and Δtm remain unchanged; when ΔN is odd, EDL delays FL by 500 ps, and both τf and Δtm increase by approximately 500 ps. After calibration, the τf is between 660.80 ps to 666.73 ps; hence, the maximum difference between the 12 measurements is 5.93 ps, which corresponds to the maximum phase difference of 0.0373 rad. The Δtm is between 899.3 ps to 906.4 ps after calibration, and the maximum difference between the 12 measurements is 7.1 ps, indicating good coherent phase transmission consistency. To reflect the relationship between the marked phase difference and marking time difference, an oscilloscope was used to remeasure the calibrated τf, as shown in the last column of Table 3. Here, Δtmτf is between 4.4 ps to 5.5 ps. Because the HSLMs performing the phase-marking process at the two sites are not completely consistent, the phase-marking transmission delay τfm is different, which affects the consistency of Δtm and τf. The experimental device shown in Fig. 2 was used to measure the transmission delays of two HSLMs; τfmL = 544.7 ps (local HSLM) and τfmR = 549.3 ps (remote HSLM) were obtained. Therefore, according to the principle of phase marking, Δtmτf should be equal to τfmRτfmL = 4.6 ps, which is consistent with the data in the table.

Tables Icon

Table 3. Average delay values before and after the frequency signal calibrationa

After the above calibration, the marked phase difference between two sites is maintained to be approximately a constant value. The constant value can be eliminated or adjusted by applying an appropriate delay to the frequency signal according to the user requirements at any time. Therefore, we have achieved coherent phase transmission by applying absolute phase marking technology. We can evaluate the uncertainty of the coherent phase transmission based on the measured values in Table 3. The average values of the 12 measurements of τf (using the 7th column data measured by PFD for accurate evaluation) and Δtm are 662.96 ps and 902.6 ps, respectively. Under a confidence probability of 99.9%, the t-distribution factor is 4.318; hence, the calculated uncertainties of type A are 2.577 ps and 2.65 ps, respectively. Because the value of the measurement resolution is sufficiently small, type B uncertainty is negligible. Therefore, type A is the total uncertainty. The uncertainty of coherent phase transmission evaluated by phase time difference is approximately 2.577 ps, and the uncertainty of coherent phase transmission evaluated by marking time difference is approximately 2.65 ps. Thus, the measured τf and Δtm in Table 3 can be expressed as 662.96 ± 2.577 ps and 902.6 ± 2.65 ps, respectively. This indicates that the system achieved a satisfactory and consistent coherent transmission performance. Moreover, the measurement results of Δtm also show an excellent performance of the mark signals, which can be used as suitable time references. Thus, high-precision remote time synchronization over optical fiber can be realized simultaneously.

4. Conclusion

Reference phase synchronization is becoming increasingly significant in many applications. Therefore, we propose and demonstrate a technical scheme that can simultaneously achieve absolute phase marking and picosecond-level fiber-optic remote coherent phase transmission. The scheme uses the potential of high-speed digital communication circuits in high-precision analog information processing, and combines the characteristics of pulse time signal and continuous frequency signal. The former is used to eliminate long-distance ambiguity and the latter has high measurement control precision. First, through high-speed digital logic based on zero-crossing detection and optimized control, the absolute phase marking for the frequency signal is realized, transferring the excellent phase performances of the frequency signals to mark signals. After frequency synchronization and absolute phase marking, the relative frequency stability of the 1 GHz frequency signal can reach the order of 10−14 at 1 s and 10−17 at 10,000 s, and the relative phase-marking stability of picosecond-level P-P jitter is achieved under different fiber lengths. Particularly under a 150 km fiber link, the P-P jitter can be only 3.3 ps within 10,000 s measurement time, and TDEV can be as low as 438 fs at 1 s. Then, by measuring the round-trip time delay of the control signal, the periodic changes of the phase difference between the frequency signals are identified to eliminate the ambiguity of periodic signals. Combining with the phase difference measurement, the control signal calibration and frequency signal calibration are completed to remove the initial phase uncertainty. The coherent phase transmission over a 25 km fiber link is realized. The coherent transmission uncertainty evaluated by the phase time difference is approximately 2.577 ps, while the coherent transmission uncertainty evaluated by marking time difference is approximately 2.65 ps, indicating a fairly good coherent phase transmission consistency. The proposed scheme provides a new approach for realizing reference phase marking and remote coherent phase transmission. It can significantly improve the phase coherence of fiber-optic time-frequency transmission and has broad application prospects in fields such as radar networking and coherent array detection. It also demonstrates the excellent performance of the application of high-speed digital communication technology in high-precision analog signal transmission, and provides a method for simultaneous remote synchronization of time, frequency, and phase over optical fiber.

Funding

National Natural Science Foundation of China (61875214); Strategic Priority Research Program of the Chinese Academy of Sciences (XDB43000000); Youth Innovation Promotion Association of the Chinese Academy of Sciences (YIPA2019251); National Key Research and Development Program of China (2020YFC2200300).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

References

1. F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7(6), 434–438 (2013). [CrossRef]  

2. W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018). [CrossRef]  

3. R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113(21), 210801 (2014). [CrossRef]  

4. X. Li, M. Ge, X. Dai, X. Ren, M. Fritsche, J. Wickert, and H. Schuh, “Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo,” J. Geodesy 89(6), 607–635 (2015). [CrossRef]  

5. M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017). [CrossRef]  

6. A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015). [CrossRef]  

7. E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019). [CrossRef]  

8. S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007). [CrossRef]  

9. O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” Eur. Phys. J. D 48(1), 35–41 (2008). [CrossRef]  

10. L. Sliwczynski, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia 50(2), 133–145 (2013). [CrossRef]  

11. K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012). [CrossRef]  

12. M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, W. T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 6(1), e16187 (2017). [CrossRef]  

13. J. Wang, C. Yue, Y. Xi, Y. Sun, N. Cheng, F. Yang, M. Jiang, J. Sun, Y. Gui, and H. Cai, “Fiber-optic joint time and frequency transfer with the same wavelength,” Opt. Lett. 45(1), 208–211 (2020). [CrossRef]  

14. P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017). [CrossRef]  

15. D. R. Gozzard, S. W. Schediwy, R. Dodson, M. J. Rioja, M. Hill, B. Lennon, J. McFee, P. Mirtschin, J. Stevens, and K. Grainge, “Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array,” Astron. J. 154(1), 9 (2017). [CrossRef]  

16. C. Gao, B. Wang, X. Zhu, Y. B. Yuan, and L. J. Wang, “Dissemination stability and phase noise characteristics in a cascaded, fiber-based long-haul radio frequency dissemination network,” Rev. Sci. Instrum. 86(9), 093111 (2015). [CrossRef]  

17. P. Shi, G. Wu, L. Hu, Q. Li, and J. Chen, “Stable RF transfer over a fiber-optic ring with DSBCS modulation and a DSB RF signal,” Chin. Opt. Lett. 18(2), 020603 (2020). [CrossRef]  

18. J. Kodet, P. Panek, and I. Prochazka, “Two-way time transfer via optical fiber providing subpicosecond precision and high temperature stability,” Metrologia 53(1), 18–26 (2016). [CrossRef]  

19. X. Yuan and B. Wang, “Using single wavelength light to improve the synchronization accuracy of the White Rabbit system,” Chin. Opt. Lett. 15(10), 101202 (2017). [CrossRef]  

20. T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10(10), 662–666 (2016). [CrossRef]  

21. O. Lopez, A. Haboucha, B. Chanteau, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Ultra-stable long distance optical frequency distribution using the Internet fiber network,” Opt. Express 20(21), 23518–23526 (2012). [CrossRef]  

22. Z. Feng, F. Yang, X. Zhang, D. Chen, F. Wei, N. Cheng, Y. Sun, Y. Gui, and H. Cai, “Ultra-low noise optical injection locking amplifier with AOM-based coherent detection scheme,” Sci. Rep. 8(1), 13135 (2018). [CrossRef]  

23. P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010). [CrossRef]  

24. H. Yang, B. Han, J. Shin, D. Hou, H. Chung, I. H. Baek, Y. U. Jeong, and J. Kim, “10-fs-level synchronization of photocathode laser with RF-oscillator for ultrafast electron and X-ray sources,” Sci. Rep. 7(1), 39966 (2017). [CrossRef]  

25. K. Jung, J. Shin, J. Kang, S. Hunziker, C. K. Min, and J. Kim, “Frequency comb-based microwave transfer over fiber with 7×10−19 instability using fiber-loop optical-microwave phase detectors,” Opt. Lett. 39(6), 1577–1580 (2014). [CrossRef]  

26. J. D. Deschenes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X 6(2), 021016 (2016). [CrossRef]  

27. H. Godrich, A. M. Haimovich, and R. S. Blum, “Target localization accuracy gain in MIMO radar-based systems,” IEEE Trans. Inf. Theory 56(6), 2783–2803 (2010). [CrossRef]  

28. Y. Yang and R. S. Blum, “Phase synchronization for coherent MIMO radar: algorithms and their analysis,” IEEE Trans. Signal Process. 59(11), 5538–5557 (2011). [CrossRef]  

29. J. Yan, J. Li, L. Zhao, and R. Chen, “Robust joint transmit beamforming with QoS guarantees in time-asynchronous DAS,” IEEE Trans. Veh. Technol. 64(4), 1506–1518 (2015). [CrossRef]  

30. K. Bidaj, J. B. Begueret, and J. Deroo, “Jitter definition, measurement, generation, analysis, and decomposition,” Int. J. Circuit Theory Appl. 46(12), 2171–2188 (2018). [CrossRef]  

31. M. J. Underhill, “Time jitter and phase noise-now and in the future?” in 2012 IEEE International Frequency Control Symposium (IFCS) (2012), pp. 1–8.

32. N. Cheng, W. Chen, Q. Liu, D. Xu, F. Yang, Y. Z. Gui, and H. W. Cai, “Joint transfer of time and frequency signals and multi-point synchronization via fiber network,” Chin. Phys. B 25(1), 014206 (2016). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7(6), 434–438 (2013).
    [Crossref]
  2. W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
    [Crossref]
  3. R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113(21), 210801 (2014).
    [Crossref]
  4. X. Li, M. Ge, X. Dai, X. Ren, M. Fritsche, J. Wickert, and H. Schuh, “Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo,” J. Geodesy 89(6), 607–635 (2015).
    [Crossref]
  5. M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
    [Crossref]
  6. A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
    [Crossref]
  7. E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
    [Crossref]
  8. S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007).
    [Crossref]
  9. O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” Eur. Phys. J. D 48(1), 35–41 (2008).
    [Crossref]
  10. L. Sliwczynski, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia 50(2), 133–145 (2013).
    [Crossref]
  11. K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
    [Crossref]
  12. M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, W. T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 6(1), e16187 (2017).
    [Crossref]
  13. J. Wang, C. Yue, Y. Xi, Y. Sun, N. Cheng, F. Yang, M. Jiang, J. Sun, Y. Gui, and H. Cai, “Fiber-optic joint time and frequency transfer with the same wavelength,” Opt. Lett. 45(1), 208–211 (2020).
    [Crossref]
  14. P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
    [Crossref]
  15. D. R. Gozzard, S. W. Schediwy, R. Dodson, M. J. Rioja, M. Hill, B. Lennon, J. McFee, P. Mirtschin, J. Stevens, and K. Grainge, “Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array,” Astron. J. 154(1), 9 (2017).
    [Crossref]
  16. C. Gao, B. Wang, X. Zhu, Y. B. Yuan, and L. J. Wang, “Dissemination stability and phase noise characteristics in a cascaded, fiber-based long-haul radio frequency dissemination network,” Rev. Sci. Instrum. 86(9), 093111 (2015).
    [Crossref]
  17. P. Shi, G. Wu, L. Hu, Q. Li, and J. Chen, “Stable RF transfer over a fiber-optic ring with DSBCS modulation and a DSB RF signal,” Chin. Opt. Lett. 18(2), 020603 (2020).
    [Crossref]
  18. J. Kodet, P. Panek, and I. Prochazka, “Two-way time transfer via optical fiber providing subpicosecond precision and high temperature stability,” Metrologia 53(1), 18–26 (2016).
    [Crossref]
  19. X. Yuan and B. Wang, “Using single wavelength light to improve the synchronization accuracy of the White Rabbit system,” Chin. Opt. Lett. 15(10), 101202 (2017).
    [Crossref]
  20. T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10(10), 662–666 (2016).
    [Crossref]
  21. O. Lopez, A. Haboucha, B. Chanteau, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Ultra-stable long distance optical frequency distribution using the Internet fiber network,” Opt. Express 20(21), 23518–23526 (2012).
    [Crossref]
  22. Z. Feng, F. Yang, X. Zhang, D. Chen, F. Wei, N. Cheng, Y. Sun, Y. Gui, and H. Cai, “Ultra-low noise optical injection locking amplifier with AOM-based coherent detection scheme,” Sci. Rep. 8(1), 13135 (2018).
    [Crossref]
  23. P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
    [Crossref]
  24. H. Yang, B. Han, J. Shin, D. Hou, H. Chung, I. H. Baek, Y. U. Jeong, and J. Kim, “10-fs-level synchronization of photocathode laser with RF-oscillator for ultrafast electron and X-ray sources,” Sci. Rep. 7(1), 39966 (2017).
    [Crossref]
  25. K. Jung, J. Shin, J. Kang, S. Hunziker, C. K. Min, and J. Kim, “Frequency comb-based microwave transfer over fiber with 7×10−19 instability using fiber-loop optical-microwave phase detectors,” Opt. Lett. 39(6), 1577–1580 (2014).
    [Crossref]
  26. J. D. Deschenes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X 6(2), 021016 (2016).
    [Crossref]
  27. H. Godrich, A. M. Haimovich, and R. S. Blum, “Target localization accuracy gain in MIMO radar-based systems,” IEEE Trans. Inf. Theory 56(6), 2783–2803 (2010).
    [Crossref]
  28. Y. Yang and R. S. Blum, “Phase synchronization for coherent MIMO radar: algorithms and their analysis,” IEEE Trans. Signal Process. 59(11), 5538–5557 (2011).
    [Crossref]
  29. J. Yan, J. Li, L. Zhao, and R. Chen, “Robust joint transmit beamforming with QoS guarantees in time-asynchronous DAS,” IEEE Trans. Veh. Technol. 64(4), 1506–1518 (2015).
    [Crossref]
  30. K. Bidaj, J. B. Begueret, and J. Deroo, “Jitter definition, measurement, generation, analysis, and decomposition,” Int. J. Circuit Theory Appl. 46(12), 2171–2188 (2018).
    [Crossref]
  31. M. J. Underhill, “Time jitter and phase noise-now and in the future?” in 2012 IEEE International Frequency Control Symposium (IFCS) (2012), pp. 1–8.
  32. N. Cheng, W. Chen, Q. Liu, D. Xu, F. Yang, Y. Z. Gui, and H. W. Cai, “Joint transfer of time and frequency signals and multi-point synchronization via fiber network,” Chin. Phys. B 25(1), 014206 (2016).
    [Crossref]

2020 (2)

2019 (1)

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

2018 (3)

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
[Crossref]

Z. Feng, F. Yang, X. Zhang, D. Chen, F. Wei, N. Cheng, Y. Sun, Y. Gui, and H. Cai, “Ultra-low noise optical injection locking amplifier with AOM-based coherent detection scheme,” Sci. Rep. 8(1), 13135 (2018).
[Crossref]

K. Bidaj, J. B. Begueret, and J. Deroo, “Jitter definition, measurement, generation, analysis, and decomposition,” Int. J. Circuit Theory Appl. 46(12), 2171–2188 (2018).
[Crossref]

2017 (6)

H. Yang, B. Han, J. Shin, D. Hou, H. Chung, I. H. Baek, Y. U. Jeong, and J. Kim, “10-fs-level synchronization of photocathode laser with RF-oscillator for ultrafast electron and X-ray sources,” Sci. Rep. 7(1), 39966 (2017).
[Crossref]

X. Yuan and B. Wang, “Using single wavelength light to improve the synchronization accuracy of the White Rabbit system,” Chin. Opt. Lett. 15(10), 101202 (2017).
[Crossref]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

D. R. Gozzard, S. W. Schediwy, R. Dodson, M. J. Rioja, M. Hill, B. Lennon, J. McFee, P. Mirtschin, J. Stevens, and K. Grainge, “Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array,” Astron. J. 154(1), 9 (2017).
[Crossref]

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, W. T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 6(1), e16187 (2017).
[Crossref]

2016 (4)

T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10(10), 662–666 (2016).
[Crossref]

J. Kodet, P. Panek, and I. Prochazka, “Two-way time transfer via optical fiber providing subpicosecond precision and high temperature stability,” Metrologia 53(1), 18–26 (2016).
[Crossref]

N. Cheng, W. Chen, Q. Liu, D. Xu, F. Yang, Y. Z. Gui, and H. W. Cai, “Joint transfer of time and frequency signals and multi-point synchronization via fiber network,” Chin. Phys. B 25(1), 014206 (2016).
[Crossref]

J. D. Deschenes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X 6(2), 021016 (2016).
[Crossref]

2015 (4)

J. Yan, J. Li, L. Zhao, and R. Chen, “Robust joint transmit beamforming with QoS guarantees in time-asynchronous DAS,” IEEE Trans. Veh. Technol. 64(4), 1506–1518 (2015).
[Crossref]

C. Gao, B. Wang, X. Zhu, Y. B. Yuan, and L. J. Wang, “Dissemination stability and phase noise characteristics in a cascaded, fiber-based long-haul radio frequency dissemination network,” Rev. Sci. Instrum. 86(9), 093111 (2015).
[Crossref]

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

X. Li, M. Ge, X. Dai, X. Ren, M. Fritsche, J. Wickert, and H. Schuh, “Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo,” J. Geodesy 89(6), 607–635 (2015).
[Crossref]

2014 (2)

R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113(21), 210801 (2014).
[Crossref]

K. Jung, J. Shin, J. Kang, S. Hunziker, C. K. Min, and J. Kim, “Frequency comb-based microwave transfer over fiber with 7×10−19 instability using fiber-loop optical-microwave phase detectors,” Opt. Lett. 39(6), 1577–1580 (2014).
[Crossref]

2013 (2)

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7(6), 434–438 (2013).
[Crossref]

L. Sliwczynski, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia 50(2), 133–145 (2013).
[Crossref]

2012 (2)

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref]

O. Lopez, A. Haboucha, B. Chanteau, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Ultra-stable long distance optical frequency distribution using the Internet fiber network,” Opt. Express 20(21), 23518–23526 (2012).
[Crossref]

2011 (1)

Y. Yang and R. S. Blum, “Phase synchronization for coherent MIMO radar: algorithms and their analysis,” IEEE Trans. Signal Process. 59(11), 5538–5557 (2011).
[Crossref]

2010 (2)

H. Godrich, A. M. Haimovich, and R. S. Blum, “Target localization accuracy gain in MIMO radar-based systems,” IEEE Trans. Inf. Theory 56(6), 2783–2803 (2010).
[Crossref]

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

2008 (1)

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” Eur. Phys. J. D 48(1), 35–41 (2008).
[Crossref]

2007 (1)

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007).
[Crossref]

Ablewski, P.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Akatsuka, T.

T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10(10), 662–666 (2016).
[Crossref]

Akre, R.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Alnis, J.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref]

Amy-Klein, A.

O. Lopez, A. Haboucha, B. Chanteau, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Ultra-stable long distance optical frequency distribution using the Internet fiber network,” Opt. Express 20(21), 23518–23526 (2012).
[Crossref]

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” Eur. Phys. J. D 48(1), 35–41 (2008).
[Crossref]

Arthur, J.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Baek, I. H.

H. Yang, B. Han, J. Shin, D. Hou, H. Chung, I. H. Baek, Y. U. Jeong, and J. Kim, “10-fs-level synchronization of photocathode laser with RF-oscillator for ultrafast electron and X-ray sources,” Sci. Rep. 7(1), 39966 (2017).
[Crossref]

Baumann, E.

J. D. Deschenes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X 6(2), 021016 (2016).
[Crossref]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7(6), 434–438 (2013).
[Crossref]

Begueret, J. B.

K. Bidaj, J. B. Begueret, and J. Deroo, “Jitter definition, measurement, generation, analysis, and decomposition,” Int. J. Circuit Theory Appl. 46(12), 2171–2188 (2018).
[Crossref]

Beloy, K.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
[Crossref]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

Bergeron, H.

J. D. Deschenes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X 6(2), 021016 (2016).
[Crossref]

Bidaj, K.

K. Bidaj, J. B. Begueret, and J. Deroo, “Jitter definition, measurement, generation, analysis, and decomposition,” Int. J. Circuit Theory Appl. 46(12), 2171–2188 (2018).
[Crossref]

Binczewski, A.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Bionta, R.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Blum, R. S.

Y. Yang and R. S. Blum, “Phase synchronization for coherent MIMO radar: algorithms and their analysis,” IEEE Trans. Signal Process. 59(11), 5538–5557 (2011).
[Crossref]

H. Godrich, A. M. Haimovich, and R. S. Blum, “Target localization accuracy gain in MIMO radar-based systems,” IEEE Trans. Inf. Theory 56(6), 2783–2803 (2010).
[Crossref]

Bober, M.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Bongs, K.

R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113(21), 210801 (2014).
[Crossref]

Bostedt, C.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Bothwell, T.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

Boyd, M. M.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

Bozek, J.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Brachmann, A.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Brown, R. C.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
[Crossref]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

Bucksbaum, P.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Buczek, L.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

L. Sliwczynski, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia 50(2), 133–145 (2013).
[Crossref]

Cai, H.

J. Wang, C. Yue, Y. Xi, Y. Sun, N. Cheng, F. Yang, M. Jiang, J. Sun, Y. Gui, and H. Cai, “Fiber-optic joint time and frequency transfer with the same wavelength,” Opt. Lett. 45(1), 208–211 (2020).
[Crossref]

Z. Feng, F. Yang, X. Zhang, D. Chen, F. Wei, N. Cheng, Y. Sun, Y. Gui, and H. Cai, “Ultra-low noise optical injection locking amplifier with AOM-based coherent detection scheme,” Sci. Rep. 8(1), 13135 (2018).
[Crossref]

Cai, H. W.

N. Cheng, W. Chen, Q. Liu, D. Xu, F. Yang, Y. Z. Gui, and H. W. Cai, “Joint transfer of time and frequency signals and multi-point synchronization via fiber network,” Chin. Phys. B 25(1), 014206 (2016).
[Crossref]

Campbell, R. M.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Cermak, M.

J. D. Deschenes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X 6(2), 021016 (2016).
[Crossref]

Chanteau, B.

Chardonnet, C.

O. Lopez, A. Haboucha, B. Chanteau, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Ultra-stable long distance optical frequency distribution using the Internet fiber network,” Opt. Express 20(21), 23518–23526 (2012).
[Crossref]

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” Eur. Phys. J. D 48(1), 35–41 (2008).
[Crossref]

Chen, D.

Z. Feng, F. Yang, X. Zhang, D. Chen, F. Wei, N. Cheng, Y. Sun, Y. Gui, and H. Cai, “Ultra-low noise optical injection locking amplifier with AOM-based coherent detection scheme,” Sci. Rep. 8(1), 13135 (2018).
[Crossref]

Chen, J.

Chen, R.

J. Yan, J. Li, L. Zhao, and R. Chen, “Robust joint transmit beamforming with QoS guarantees in time-asynchronous DAS,” IEEE Trans. Veh. Technol. 64(4), 1506–1518 (2015).
[Crossref]

Chen, W.

N. Cheng, W. Chen, Q. Liu, D. Xu, F. Yang, Y. Z. Gui, and H. W. Cai, “Joint transfer of time and frequency signals and multi-point synchronization via fiber network,” Chin. Phys. B 25(1), 014206 (2016).
[Crossref]

Cheng, N.

J. Wang, C. Yue, Y. Xi, Y. Sun, N. Cheng, F. Yang, M. Jiang, J. Sun, Y. Gui, and H. Cai, “Fiber-optic joint time and frequency transfer with the same wavelength,” Opt. Lett. 45(1), 208–211 (2020).
[Crossref]

Z. Feng, F. Yang, X. Zhang, D. Chen, F. Wei, N. Cheng, Y. Sun, Y. Gui, and H. Cai, “Ultra-low noise optical injection locking amplifier with AOM-based coherent detection scheme,” Sci. Rep. 8(1), 13135 (2018).
[Crossref]

N. Cheng, W. Chen, Q. Liu, D. Xu, F. Yang, Y. Z. Gui, and H. W. Cai, “Joint transfer of time and frequency signals and multi-point synchronization via fiber network,” Chin. Phys. B 25(1), 014206 (2016).
[Crossref]

Chung, H.

H. Yang, B. Han, J. Shin, D. Hou, H. Chung, I. H. Baek, Y. U. Jeong, and J. Kim, “10-fs-level synchronization of photocathode laser with RF-oscillator for ultrafast electron and X-ray sources,” Sci. Rep. 7(1), 39966 (2017).
[Crossref]

Ciurylo, R.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Coddington, I.

J. D. Deschenes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X 6(2), 021016 (2016).
[Crossref]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7(6), 434–438 (2013).
[Crossref]

Coffee, R.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Cygan, A.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Czubla, A.

L. Sliwczynski, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia 50(2), 133–145 (2013).
[Crossref]

Dai, X.

X. Li, M. Ge, X. Dai, X. Ren, M. Fritsche, J. Wickert, and H. Schuh, “Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo,” J. Geodesy 89(6), 607–635 (2015).
[Crossref]

Daussy, C.

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” Eur. Phys. J. D 48(1), 35–41 (2008).
[Crossref]

Decker, F. J.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Deroo, J.

K. Bidaj, J. B. Begueret, and J. Deroo, “Jitter definition, measurement, generation, analysis, and decomposition,” Int. J. Circuit Theory Appl. 46(12), 2171–2188 (2018).
[Crossref]

Deschenes, J. D.

J. D. Deschenes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X 6(2), 021016 (2016).
[Crossref]

Ding, Y.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Dodson, R.

D. R. Gozzard, S. W. Schediwy, R. Dodson, M. J. Rioja, M. Hill, B. Lennon, J. McFee, P. Mirtschin, J. Stevens, and K. Grainge, “Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array,” Astron. J. 154(1), 9 (2017).
[Crossref]

Dowell, D.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Droste, S.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref]

Edstrom, S.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Emma, P.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Fasano, R. J.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
[Crossref]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

Feng, Z.

Z. Feng, F. Yang, X. Zhang, D. Chen, F. Wei, N. Cheng, Y. Sun, Y. Gui, and H. Cai, “Ultra-low noise optical injection locking amplifier with AOM-based coherent detection scheme,” Sci. Rep. 8(1), 13135 (2018).
[Crossref]

Fisher, A.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Foreman, S. M.

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007).
[Crossref]

Frisch, J.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Fritsche, M.

X. Li, M. Ge, X. Dai, X. Ren, M. Fritsche, J. Wickert, and H. Schuh, “Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo,” J. Geodesy 89(6), 607–635 (2015).
[Crossref]

Galayda, J.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Gao, C.

C. Gao, B. Wang, X. Zhu, Y. B. Yuan, and L. J. Wang, “Dissemination stability and phase noise characteristics in a cascaded, fiber-based long-haul radio frequency dissemination network,” Rev. Sci. Instrum. 86(9), 093111 (2015).
[Crossref]

Ge, M.

X. Li, M. Ge, X. Dai, X. Ren, M. Fritsche, J. Wickert, and H. Schuh, “Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo,” J. Geodesy 89(6), 607–635 (2015).
[Crossref]

Gilevich, S.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Gill, P.

R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113(21), 210801 (2014).
[Crossref]

Giorgetta, F. R.

J. D. Deschenes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X 6(2), 021016 (2016).
[Crossref]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7(6), 434–438 (2013).
[Crossref]

Giunta, M.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

Goban, A.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

Godrich, H.

H. Godrich, A. M. Haimovich, and R. S. Blum, “Target localization accuracy gain in MIMO radar-based systems,” IEEE Trans. Inf. Theory 56(6), 2783–2803 (2010).
[Crossref]

Godun, R. M.

R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113(21), 210801 (2014).
[Crossref]

Gozzard, D. R.

D. R. Gozzard, S. W. Schediwy, R. Dodson, M. J. Rioja, M. Hill, B. Lennon, J. McFee, P. Mirtschin, J. Stevens, and K. Grainge, “Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array,” Astron. J. 154(1), 9 (2017).
[Crossref]

Grainge, K.

D. R. Gozzard, S. W. Schediwy, R. Dodson, M. J. Rioja, M. Hill, B. Lennon, J. McFee, P. Mirtschin, J. Stevens, and K. Grainge, “Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array,” Astron. J. 154(1), 9 (2017).
[Crossref]

Grosche, G.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref]

Gui, Y.

J. Wang, C. Yue, Y. Xi, Y. Sun, N. Cheng, F. Yang, M. Jiang, J. Sun, Y. Gui, and H. Cai, “Fiber-optic joint time and frequency transfer with the same wavelength,” Opt. Lett. 45(1), 208–211 (2020).
[Crossref]

Z. Feng, F. Yang, X. Zhang, D. Chen, F. Wei, N. Cheng, Y. Sun, Y. Gui, and H. Cai, “Ultra-low noise optical injection locking amplifier with AOM-based coherent detection scheme,” Sci. Rep. 8(1), 13135 (2018).
[Crossref]

Gui, Y. Z.

N. Cheng, W. Chen, Q. Liu, D. Xu, F. Yang, Y. Z. Gui, and H. W. Cai, “Joint transfer of time and frequency signals and multi-point synchronization via fiber network,” Chin. Phys. B 25(1), 014206 (2016).
[Crossref]

Haboucha, A.

Haensch, T. W.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref]

Haimovich, A. M.

H. Godrich, A. M. Haimovich, and R. S. Blum, “Target localization accuracy gain in MIMO radar-based systems,” IEEE Trans. Inf. Theory 56(6), 2783–2803 (2010).
[Crossref]

Han, B.

H. Yang, B. Han, J. Shin, D. Hou, H. Chung, I. H. Baek, Y. U. Jeong, and J. Kim, “10-fs-level synchronization of photocathode laser with RF-oscillator for ultrafast electron and X-ray sources,” Sci. Rep. 7(1), 39966 (2017).
[Crossref]

Hastings, J.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Hays, G.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Hering, P.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Hill, M.

D. R. Gozzard, S. W. Schediwy, R. Dodson, M. J. Rioja, M. Hill, B. Lennon, J. McFee, P. Mirtschin, J. Stevens, and K. Grainge, “Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array,” Astron. J. 154(1), 9 (2017).
[Crossref]

Hinkley, N.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
[Crossref]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

Holman, K. W.

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007).
[Crossref]

Holzwarth, R.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref]

Hou, D.

H. Yang, B. Han, J. Shin, D. Hou, H. Chung, I. H. Baek, Y. U. Jeong, and J. Kim, “10-fs-level synchronization of photocathode laser with RF-oscillator for ultrafast electron and X-ray sources,” Sci. Rep. 7(1), 39966 (2017).
[Crossref]

Hu, L.

Huang, Z.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Hudson, D. D.

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007).
[Crossref]

Hunziker, S.

Hutson, R. B.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

Iverson, R.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Jeong, Y. U.

H. Yang, B. Han, J. Shin, D. Hou, H. Chung, I. H. Baek, Y. U. Jeong, and J. Kim, “10-fs-level synchronization of photocathode laser with RF-oscillator for ultrafast electron and X-ray sources,” Sci. Rep. 7(1), 39966 (2017).
[Crossref]

Jiang, M.

Johnson, L. A. M.

R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113(21), 210801 (2014).
[Crossref]

Jones, D. J.

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007).
[Crossref]

Jones, J. M.

R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113(21), 210801 (2014).
[Crossref]

Jung, K.

Kalaydzhyan, A.

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, W. T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 6(1), e16187 (2017).
[Crossref]

Kang, J.

Kärtner, F. X.

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, W. T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 6(1), e16187 (2017).
[Crossref]

Katori, H.

T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10(10), 662–666 (2016).
[Crossref]

Kedar, D.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

Kennedy, C. J.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

Kim, J.

H. Yang, B. Han, J. Shin, D. Hou, H. Chung, I. H. Baek, Y. U. Jeong, and J. Kim, “10-fs-level synchronization of photocathode laser with RF-oscillator for ultrafast electron and X-ray sources,” Sci. Rep. 7(1), 39966 (2017).
[Crossref]

K. Jung, J. Shin, J. Kang, S. Hunziker, C. K. Min, and J. Kim, “Frequency comb-based microwave transfer over fiber with 7×10−19 instability using fiber-loop optical-microwave phase detectors,” Opt. Lett. 39(6), 1577–1580 (2014).
[Crossref]

King, S. A.

R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113(21), 210801 (2014).
[Crossref]

Kodet, J.

J. Kodet, P. Panek, and I. Prochazka, “Two-way time transfer via optical fiber providing subpicosecond precision and high temperature stability,” Metrologia 53(1), 18–26 (2016).
[Crossref]

Kolodziej, J.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Krehlik, P.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

L. Sliwczynski, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia 50(2), 133–145 (2013).
[Crossref]

Kuroishi, Y.

T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10(10), 662–666 (2016).
[Crossref]

Lea, S. N.

R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113(21), 210801 (2014).
[Crossref]

Legero, T.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref]

Lennon, B.

D. R. Gozzard, S. W. Schediwy, R. Dodson, M. J. Rioja, M. Hill, B. Lennon, J. McFee, P. Mirtschin, J. Stevens, and K. Grainge, “Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array,” Astron. J. 154(1), 9 (2017).
[Crossref]

Li, J.

J. Yan, J. Li, L. Zhao, and R. Chen, “Robust joint transmit beamforming with QoS guarantees in time-asynchronous DAS,” IEEE Trans. Veh. Technol. 64(4), 1506–1518 (2015).
[Crossref]

Li, Q.

Li, X.

X. Li, M. Ge, X. Dai, X. Ren, M. Fritsche, J. Wickert, and H. Schuh, “Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo,” J. Geodesy 89(6), 607–635 (2015).
[Crossref]

Lipinski, M.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

L. Sliwczynski, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia 50(2), 133–145 (2013).
[Crossref]

Lisak, D.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Liu, Q.

N. Cheng, W. Chen, Q. Liu, D. Xu, F. Yang, Y. Z. Gui, and H. W. Cai, “Joint transfer of time and frequency signals and multi-point synchronization via fiber network,” Chin. Phys. B 25(1), 014206 (2016).
[Crossref]

Loos, H.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Lopez, O.

O. Lopez, A. Haboucha, B. Chanteau, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Ultra-stable long distance optical frequency distribution using the Internet fiber network,” Opt. Express 20(21), 23518–23526 (2012).
[Crossref]

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” Eur. Phys. J. D 48(1), 35–41 (2008).
[Crossref]

Lours, M.

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” Eur. Phys. J. D 48(1), 35–41 (2008).
[Crossref]

Ludlow, A. D.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
[Crossref]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

Marecki, A.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Margolis, H. S.

R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113(21), 210801 (2014).
[Crossref]

Marti, G. E.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

Maslowski, P.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Matei, D. G.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

McFee, J.

D. R. Gozzard, S. W. Schediwy, R. Dodson, M. J. Rioja, M. Hill, B. Lennon, J. McFee, P. Mirtschin, J. Stevens, and K. Grainge, “Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array,” Astron. J. 154(1), 9 (2017).
[Crossref]

McGrew, W. F.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
[Crossref]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

Messerschmidt, M.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Miahnahri, A.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Milani, G.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
[Crossref]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

Min, C. K.

Mirtschin, P.

D. R. Gozzard, S. W. Schediwy, R. Dodson, M. J. Rioja, M. Hill, B. Lennon, J. McFee, P. Mirtschin, J. Stevens, and K. Grainge, “Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array,” Astron. J. 154(1), 9 (2017).
[Crossref]

Miyahara, B.

T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10(10), 662–666 (2016).
[Crossref]

Moeller, S.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Morzynski, P.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Mücke, O. D.

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, W. T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 6(1), e16187 (2017).
[Crossref]

Munekane, H.

T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10(10), 662–666 (2016).
[Crossref]

Narbonneau, F.

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” Eur. Phys. J. D 48(1), 35–41 (2008).
[Crossref]

Nawrocki, J.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Newbury, N. R.

J. D. Deschenes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X 6(2), 021016 (2016).
[Crossref]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7(6), 434–438 (2013).
[Crossref]

Nicolodi, D.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
[Crossref]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

Nisbet-Jones, P. B. R.

R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113(21), 210801 (2014).
[Crossref]

Nogas, P.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Nuhn, H. D.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Oates, C. W.

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

Oelker, E.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

Ohmae, N.

T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10(10), 662–666 (2016).
[Crossref]

Panek, P.

J. Kodet, P. Panek, and I. Prochazka, “Two-way time transfer via optical fiber providing subpicosecond precision and high temperature stability,” Metrologia 53(1), 18–26 (2016).
[Crossref]

Pazderski, E.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Peik, E.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

Peng, M. Y.

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, W. T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 6(1), e16187 (2017).
[Crossref]

Phillips, N. B.

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

Pieczerak, J.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Pile, G.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Predehl, K.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref]

Prochazka, I.

J. Kodet, P. Panek, and I. Prochazka, “Two-way time transfer via optical fiber providing subpicosecond precision and high temperature stability,” Metrologia 53(1), 18–26 (2016).
[Crossref]

Ratner, D.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Raupach, S. M. F.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref]

Ren, X.

X. Li, M. Ge, X. Dai, X. Ren, M. Fritsche, J. Wickert, and H. Schuh, “Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo,” J. Geodesy 89(6), 607–635 (2015).
[Crossref]

Riehle, F.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

Rioja, M. J.

D. R. Gozzard, S. W. Schediwy, R. Dodson, M. J. Rioja, M. Hill, B. Lennon, J. McFee, P. Mirtschin, J. Stevens, and K. Grainge, “Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array,” Astron. J. 154(1), 9 (2017).
[Crossref]

Robinson, J. M.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

Rzepiela, J.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Safak, K.

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, W. T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 6(1), e16187 (2017).
[Crossref]

Sanner, C.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

Santarelli, G.

O. Lopez, A. Haboucha, B. Chanteau, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Ultra-stable long distance optical frequency distribution using the Internet fiber network,” Opt. Express 20(21), 23518–23526 (2012).
[Crossref]

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” Eur. Phys. J. D 48(1), 35–41 (2008).
[Crossref]

Schaffer, S. A.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
[Crossref]

Schediwy, S. W.

D. R. Gozzard, S. W. Schediwy, R. Dodson, M. J. Rioja, M. Hill, B. Lennon, J. McFee, P. Mirtschin, J. Stevens, and K. Grainge, “Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array,” Astron. J. 154(1), 9 (2017).
[Crossref]

Schioppo, M.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
[Crossref]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

Schmidt, P. O.

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

Schnatz, H.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref]

Schuh, H.

X. Li, M. Ge, X. Dai, X. Ren, M. Fritsche, J. Wickert, and H. Schuh, “Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo,” J. Geodesy 89(6), 607–635 (2015).
[Crossref]

Schultz, D.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Sherman, J. A.

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

Shi, P.

Shin, J.

H. Yang, B. Han, J. Shin, D. Hou, H. Chung, I. H. Baek, Y. U. Jeong, and J. Kim, “10-fs-level synchronization of photocathode laser with RF-oscillator for ultrafast electron and X-ray sources,” Sci. Rep. 7(1), 39966 (2017).
[Crossref]

K. Jung, J. Shin, J. Kang, S. Hunziker, C. K. Min, and J. Kim, “Frequency comb-based microwave transfer over fiber with 7×10−19 instability using fiber-loop optical-microwave phase detectors,” Opt. Lett. 39(6), 1577–1580 (2014).
[Crossref]

Sinclair, L. C.

J. D. Deschenes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X 6(2), 021016 (2016).
[Crossref]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7(6), 434–438 (2013).
[Crossref]

Sliwczynski, L.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

L. Sliwczynski, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia 50(2), 133–145 (2013).
[Crossref]

Smith, T.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Sonderhouse, L.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

Stefan, P.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Sterr, U.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

Stevens, J.

D. R. Gozzard, S. W. Schediwy, R. Dodson, M. J. Rioja, M. Hill, B. Lennon, J. McFee, P. Mirtschin, J. Stevens, and K. Grainge, “Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array,” Astron. J. 154(1), 9 (2017).
[Crossref]

Sun, J.

Sun, Y.

J. Wang, C. Yue, Y. Xi, Y. Sun, N. Cheng, F. Yang, M. Jiang, J. Sun, Y. Gui, and H. Cai, “Fiber-optic joint time and frequency transfer with the same wavelength,” Opt. Lett. 45(1), 208–211 (2020).
[Crossref]

Z. Feng, F. Yang, X. Zhang, D. Chen, F. Wei, N. Cheng, Y. Sun, Y. Gui, and H. Cai, “Ultra-low noise optical injection locking amplifier with AOM-based coherent detection scheme,” Sci. Rep. 8(1), 13135 (2018).
[Crossref]

Swann, W. C.

J. D. Deschenes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X 6(2), 021016 (2016).
[Crossref]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7(6), 434–438 (2013).
[Crossref]

Szymaniec, K.

R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113(21), 210801 (2014).
[Crossref]

Takamoto, M.

T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10(10), 662–666 (2016).
[Crossref]

Takano, T.

T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10(10), 662–666 (2016).
[Crossref]

Terra, O.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref]

Tompkins, H.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Turner, J.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Turza, K.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Udem, T.

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref]

Underhill, M. J.

M. J. Underhill, “Time jitter and phase noise-now and in the future?” in 2012 IEEE International Frequency Control Symposium (IFCS) (2012), pp. 1–8.

Ushijima, I.

T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10(10), 662–666 (2016).
[Crossref]

Wang, B.

X. Yuan and B. Wang, “Using single wavelength light to improve the synchronization accuracy of the White Rabbit system,” Chin. Opt. Lett. 15(10), 101202 (2017).
[Crossref]

C. Gao, B. Wang, X. Zhu, Y. B. Yuan, and L. J. Wang, “Dissemination stability and phase noise characteristics in a cascaded, fiber-based long-haul radio frequency dissemination network,” Rev. Sci. Instrum. 86(9), 093111 (2015).
[Crossref]

Wang, J.

Wang, L. J.

C. Gao, B. Wang, X. Zhu, Y. B. Yuan, and L. J. Wang, “Dissemination stability and phase noise characteristics in a cascaded, fiber-based long-haul radio frequency dissemination network,” Rev. Sci. Instrum. 86(9), 093111 (2015).
[Crossref]

Wang, W. T.

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, W. T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 6(1), e16187 (2017).
[Crossref]

Wei, F.

Z. Feng, F. Yang, X. Zhang, D. Chen, F. Wei, N. Cheng, Y. Sun, Y. Gui, and H. Cai, “Ultra-low noise optical injection locking amplifier with AOM-based coherent detection scheme,” Sci. Rep. 8(1), 13135 (2018).
[Crossref]

Welch, J.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

White, W.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Wickert, J.

X. Li, M. Ge, X. Dai, X. Ren, M. Fritsche, J. Wickert, and H. Schuh, “Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo,” J. Geodesy 89(6), 607–635 (2015).
[Crossref]

Wu, G.

Wu, J.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Xi, Y.

Xin, M.

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, W. T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 6(1), e16187 (2017).
[Crossref]

Xu, D.

N. Cheng, W. Chen, Q. Liu, D. Xu, F. Yang, Y. Z. Gui, and H. W. Cai, “Joint transfer of time and frequency signals and multi-point synchronization via fiber network,” Chin. Phys. B 25(1), 014206 (2016).
[Crossref]

Yamaguchi, A.

T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10(10), 662–666 (2016).
[Crossref]

Yan, J.

J. Yan, J. Li, L. Zhao, and R. Chen, “Robust joint transmit beamforming with QoS guarantees in time-asynchronous DAS,” IEEE Trans. Veh. Technol. 64(4), 1506–1518 (2015).
[Crossref]

Yang, F.

J. Wang, C. Yue, Y. Xi, Y. Sun, N. Cheng, F. Yang, M. Jiang, J. Sun, Y. Gui, and H. Cai, “Fiber-optic joint time and frequency transfer with the same wavelength,” Opt. Lett. 45(1), 208–211 (2020).
[Crossref]

Z. Feng, F. Yang, X. Zhang, D. Chen, F. Wei, N. Cheng, Y. Sun, Y. Gui, and H. Cai, “Ultra-low noise optical injection locking amplifier with AOM-based coherent detection scheme,” Sci. Rep. 8(1), 13135 (2018).
[Crossref]

N. Cheng, W. Chen, Q. Liu, D. Xu, F. Yang, Y. Z. Gui, and H. W. Cai, “Joint transfer of time and frequency signals and multi-point synchronization via fiber network,” Chin. Phys. B 25(1), 014206 (2016).
[Crossref]

Yang, H.

H. Yang, B. Han, J. Shin, D. Hou, H. Chung, I. H. Baek, Y. U. Jeong, and J. Kim, “10-fs-level synchronization of photocathode laser with RF-oscillator for ultrafast electron and X-ray sources,” Sci. Rep. 7(1), 39966 (2017).
[Crossref]

Yang, Y.

Y. Yang and R. S. Blum, “Phase synchronization for coherent MIMO radar: algorithms and their analysis,” IEEE Trans. Signal Process. 59(11), 5538–5557 (2011).
[Crossref]

Ye, J.

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007).
[Crossref]

Yocky, G.

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

Yoon, T. H.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
[Crossref]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

Yuan, X.

Yuan, Y. B.

C. Gao, B. Wang, X. Zhu, Y. B. Yuan, and L. J. Wang, “Dissemination stability and phase noise characteristics in a cascaded, fiber-based long-haul radio frequency dissemination network,” Rev. Sci. Instrum. 86(9), 093111 (2015).
[Crossref]

Yue, C.

Zawada, M.

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Zhang, X.

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
[Crossref]

Z. Feng, F. Yang, X. Zhang, D. Chen, F. Wei, N. Cheng, Y. Sun, Y. Gui, and H. Cai, “Ultra-low noise optical injection locking amplifier with AOM-based coherent detection scheme,” Sci. Rep. 8(1), 13135 (2018).
[Crossref]

Zhao, L.

J. Yan, J. Li, L. Zhao, and R. Chen, “Robust joint transmit beamforming with QoS guarantees in time-asynchronous DAS,” IEEE Trans. Veh. Technol. 64(4), 1506–1518 (2015).
[Crossref]

Zhu, X.

C. Gao, B. Wang, X. Zhu, Y. B. Yuan, and L. J. Wang, “Dissemination stability and phase noise characteristics in a cascaded, fiber-based long-haul radio frequency dissemination network,” Rev. Sci. Instrum. 86(9), 093111 (2015).
[Crossref]

Astron. Astrophys. (1)

P. Krehlik, L. Buczek, J. Kolodziej, M. Lipinski, L. Sliwczynski, J. Nawrocki, P. Nogas, A. Marecki, E. Pazderski, P. Ablewski, M. Bober, R. Ciurylo, A. Cygan, D. Lisak, P. Maslowski, P. Morzynski, M. Zawada, R. M. Campbell, J. Pieczerak, A. Binczewski, and K. Turza, “Fibre-optic delivery of time and frequency to VLBI station,” Astron. Astrophys. 603, A48 (2017).
[Crossref]

Astron. J. (1)

D. R. Gozzard, S. W. Schediwy, R. Dodson, M. J. Rioja, M. Hill, B. Lennon, J. McFee, P. Mirtschin, J. Stevens, and K. Grainge, “Astronomical verification of a stabilized frequency reference transfer system for the Square Kilometer Array,” Astron. J. 154(1), 9 (2017).
[Crossref]

Chin. Opt. Lett. (2)

Chin. Phys. B (1)

N. Cheng, W. Chen, Q. Liu, D. Xu, F. Yang, Y. Z. Gui, and H. W. Cai, “Joint transfer of time and frequency signals and multi-point synchronization via fiber network,” Chin. Phys. B 25(1), 014206 (2016).
[Crossref]

Eur. Phys. J. D (1)

O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2×10−18 for RF frequency transfer,” Eur. Phys. J. D 48(1), 35–41 (2008).
[Crossref]

IEEE Trans. Inf. Theory (1)

H. Godrich, A. M. Haimovich, and R. S. Blum, “Target localization accuracy gain in MIMO radar-based systems,” IEEE Trans. Inf. Theory 56(6), 2783–2803 (2010).
[Crossref]

IEEE Trans. Signal Process. (1)

Y. Yang and R. S. Blum, “Phase synchronization for coherent MIMO radar: algorithms and their analysis,” IEEE Trans. Signal Process. 59(11), 5538–5557 (2011).
[Crossref]

IEEE Trans. Veh. Technol. (1)

J. Yan, J. Li, L. Zhao, and R. Chen, “Robust joint transmit beamforming with QoS guarantees in time-asynchronous DAS,” IEEE Trans. Veh. Technol. 64(4), 1506–1518 (2015).
[Crossref]

Int. J. Circuit Theory Appl. (1)

K. Bidaj, J. B. Begueret, and J. Deroo, “Jitter definition, measurement, generation, analysis, and decomposition,” Int. J. Circuit Theory Appl. 46(12), 2171–2188 (2018).
[Crossref]

J. Geodesy (1)

X. Li, M. Ge, X. Dai, X. Ren, M. Fritsche, J. Wickert, and H. Schuh, “Accuracy and reliability of multi-GNSS real-time precise positioning: GPS, GLONASS, BeiDou, and Galileo,” J. Geodesy 89(6), 607–635 (2015).
[Crossref]

Light: Sci. Appl. (1)

M. Xin, K. Şafak, M. Y. Peng, A. Kalaydzhyan, W. T. Wang, O. D. Mücke, and F. X. Kärtner, “Attosecond precision multi-kilometer laser-microwave network,” Light: Sci. Appl. 6(1), e16187 (2017).
[Crossref]

Metrologia (2)

L. Sliwczynski, P. Krehlik, A. Czubla, L. Buczek, and M. Lipinski, “Dissemination of time and RF frequency via a stabilized fibre optic link over a distance of 420 km,” Metrologia 50(2), 133–145 (2013).
[Crossref]

J. Kodet, P. Panek, and I. Prochazka, “Two-way time transfer via optical fiber providing subpicosecond precision and high temperature stability,” Metrologia 53(1), 18–26 (2016).
[Crossref]

Nat. Photonics (5)

P. Emma, R. Akre, J. Arthur, R. Bionta, C. Bostedt, J. Bozek, A. Brachmann, P. Bucksbaum, R. Coffee, F. J. Decker, Y. Ding, D. Dowell, S. Edstrom, A. Fisher, J. Frisch, S. Gilevich, J. Hastings, G. Hays, P. Hering, Z. Huang, R. Iverson, H. Loos, M. Messerschmidt, A. Miahnahri, S. Moeller, H. D. Nuhn, G. Pile, D. Ratner, J. Rzepiela, D. Schultz, T. Smith, P. Stefan, H. Tompkins, J. Turner, J. Welch, W. White, J. Wu, G. Yocky, and J. Galayda, “First lasing and operation of an angstrom-wavelength free-electron laser,” Nat. Photonics 4(9), 641–647 (2010).
[Crossref]

E. Oelker, R. B. Hutson, C. J. Kennedy, L. Sonderhouse, T. Bothwell, A. Goban, D. Kedar, C. Sanner, J. M. Robinson, G. E. Marti, D. G. Matei, T. Legero, M. Giunta, R. Holzwarth, F. Riehle, U. Sterr, and J. Ye, “Demonstration of 4.8×10−17 stability at 1s for two independent optical clocks,” Nat. Photonics 13(10), 714–719 (2019).
[Crossref]

M. Schioppo, R. C. Brown, W. F. McGrew, N. Hinkley, R. J. Fasano, K. Beloy, T. H. Yoon, G. Milani, D. Nicolodi, J. A. Sherman, N. B. Phillips, C. W. Oates, and A. D. Ludlow, “Ultrastable optical clock with two cold-atom ensembles,” Nat. Photonics 11(1), 48–52 (2017).
[Crossref]

F. R. Giorgetta, W. C. Swann, L. C. Sinclair, E. Baumann, I. Coddington, and N. R. Newbury, “Optical two-way time and frequency transfer over free space,” Nat. Photonics 7(6), 434–438 (2013).
[Crossref]

T. Takano, M. Takamoto, I. Ushijima, N. Ohmae, T. Akatsuka, A. Yamaguchi, Y. Kuroishi, H. Munekane, B. Miyahara, and H. Katori, “Geopotential measurements with synchronously linked optical lattice clocks,” Nat. Photonics 10(10), 662–666 (2016).
[Crossref]

Nature (1)

W. F. McGrew, X. Zhang, R. J. Fasano, S. A. Schaffer, K. Beloy, D. Nicolodi, R. C. Brown, N. Hinkley, G. Milani, M. Schioppo, T. H. Yoon, and A. D. Ludlow, “Atomic clock performance enabling geodesy below the centimetre level,” Nature 564(7734), 87–90 (2018).
[Crossref]

Opt. Express (1)

Opt. Lett. (2)

Phys. Rev. Lett. (1)

R. M. Godun, P. B. R. Nisbet-Jones, J. M. Jones, S. A. King, L. A. M. Johnson, H. S. Margolis, K. Szymaniec, S. N. Lea, K. Bongs, and P. Gill, “Frequency ratio of two optical clock transitions in 171Yb+ and constraints on the time variation of fundamental constants,” Phys. Rev. Lett. 113(21), 210801 (2014).
[Crossref]

Phys. Rev. X (1)

J. D. Deschenes, L. C. Sinclair, F. R. Giorgetta, W. C. Swann, E. Baumann, H. Bergeron, M. Cermak, I. Coddington, and N. R. Newbury, “Synchronization of distant optical clocks at the femtosecond level,” Phys. Rev. X 6(2), 021016 (2016).
[Crossref]

Rev. Mod. Phys. (1)

A. D. Ludlow, M. M. Boyd, J. Ye, E. Peik, and P. O. Schmidt, “Optical atomic clocks,” Rev. Mod. Phys. 87(2), 637–701 (2015).
[Crossref]

Rev. Sci. Instrum. (2)

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum. 78(2), 021101 (2007).
[Crossref]

C. Gao, B. Wang, X. Zhu, Y. B. Yuan, and L. J. Wang, “Dissemination stability and phase noise characteristics in a cascaded, fiber-based long-haul radio frequency dissemination network,” Rev. Sci. Instrum. 86(9), 093111 (2015).
[Crossref]

Sci. Rep. (2)

Z. Feng, F. Yang, X. Zhang, D. Chen, F. Wei, N. Cheng, Y. Sun, Y. Gui, and H. Cai, “Ultra-low noise optical injection locking amplifier with AOM-based coherent detection scheme,” Sci. Rep. 8(1), 13135 (2018).
[Crossref]

H. Yang, B. Han, J. Shin, D. Hou, H. Chung, I. H. Baek, Y. U. Jeong, and J. Kim, “10-fs-level synchronization of photocathode laser with RF-oscillator for ultrafast electron and X-ray sources,” Sci. Rep. 7(1), 39966 (2017).
[Crossref]

Science (1)

K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, T. Legero, T. W. Haensch, T. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science 336(6080), 441–444 (2012).
[Crossref]

Other (1)

M. J. Underhill, “Time jitter and phase noise-now and in the future?” in 2012 IEEE International Frequency Control Symposium (IFCS) (2012), pp. 1–8.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (10)

Fig. 1.
Fig. 1. Principle of the proposed absolute phase marking technology. C, control signal; F, frequency signal; M, mark signal; Tc, repetition period of C; Wc, pulse width of C; Tf, period of F; Tm, repetition period of M; Wm, pulse width of M; τcf, transmission delay from C to F; τfm, transmission delay from F to M.
Fig. 2.
Fig. 2. Measurement setup of the absolute phase marking technology.
Fig. 3.
Fig. 3. Waveform traces when Tc = 1 µs, Wc = 1.75 ns, and τcf = 0.39 ns. X position from (a) −1.5 µs to 2.5 µs, (b) −4 ns to 5 ns, and (c) 1996 ns to 2005 ns.
Fig. 4.
Fig. 4. (a) Period of the control signal and mark signal and (b) pulse width of the mark signal.
Fig. 5.
Fig. 5. Waveform traces when (a) Tc = 1 s, Wc = 4.52 ns, τcf = 0.39 ns, and (b) Tc = 1 s, Wc = 5.22 ns, τcf = 0.85 ns.
Fig. 6.
Fig. 6. Schematic diagram of the proposed coherent phase transmission system. E/O, electro-optical conversion; O/E, opto-electrical conversion; HSLM, high-speed logic module; CL, control signal of local site; FL, frequency signal of local site; CR, control signal of remote site; Crt, round-trip control signal; Frt, round-trip frequency signal; CLd, delayed control signal of local site; FLd, delayed frequency signal of local site; ML, mark signal of local site; MR, mark signal of remote site; Δφfr, round-trip phase difference; Δtfr, round-trip link delay.
Fig. 7.
Fig. 7. Timing relationships between these signals in coherent transmission process when (a) only the transmission delay is stabilized, (b) the control signals are synchronized, and (c) both the control signals and frequency signals are synchronized.
Fig. 8.
Fig. 8. Experimental setup. REF, reference frequency; PLM, phase-locked multiplier; DPG, digital pulse generator; LD, laser diode; PD, photodetector; DWDM, dense wavelength division multiplex; OC, optical coupler; PS, polarization scrambler; CIR, circulator; ODL, optical delay line; Bi-EDFA, bidirectional erbium-doped fiber amplifier; PFD, phase frequency detector; TIC, time interval counter; PID, proportion integration differentiation controller; EDL, electrical delay line; HSLM, high-speed logic module; ÷10, 10 frequency divider; ×10, 10 frequency multiplier; OCXO, oven controlled crystal oscillator.
Fig. 9.
Fig. 9. (a) Relative stabilities of the marking time difference under different fiber lengths (the inset shows the result of a 150 km fiber link and 10 km ODL) and (b) absolute phase noise of frequency signals under a 100 km fiber link and 10 km ODL (the inset shows relative stability of frequency signal after cleaner).
Fig. 10.
Fig. 10. (a) Measured mean values of the control time difference and marking time difference under different delay settings in local DPG and (b) time fluctuation of the control time difference.

Tables (3)

Tables Icon

Table 1. Average delay values under system multiple shutdowns and restarts a

Tables Icon

Table 2. Average delay values before and after the control signal calibration a

Tables Icon

Table 3. Average delay values before and after the frequency signal calibration a

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

{ τ f = Δ t c N T f Δ t c = Δ t c r / 2 N = Δ t c / T f .
2 π v 0 τ f = ( Δ φ f r /2) or ( π + Δ φ f r /2),
Δ t c = Δ t c r / 2 + Δ t λ + Δ t 0 ,
Δ t c = Δ t c r / 2 + 104768 ,
τ = Δ φ 2 π v 0 ,
Δ N = [ Δ t c r Δ t r e f T f ] ,

Metrics