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Abstract
A stable frequency downlink transmission scheme, which delivers the frequency signal back to the central station from an arbitrary injection point along a radio-over-fiber (RoF) loop link, is proposed and demonstrated. The frequency signal at the arbitrary remote point is injected into the RoF loop link in both clockwise and counter-clockwise directions, simultaneously. The phase variation induced by the fiber loop link is obtained in real time with the help of a round-trip assistant frequency signal. The phase error can be exactly cancelled by a series of frequency mixing (i.e., up-conversion and down-conversion) among the signals. In the experiment, a 1.21-GHz frequency signal at an arbitrary remote point is downlink transferred to the central station in a 45-km fiber loop link. The result shows the overlapping Allan deviation (ADEV) of 1.04×10−12 at 0.1 s, 1.3×10−13 at 1 s and 1.1×10−15 at 104 s, respectively. The phase error correction operates entirely at the central station, leaving a simple and robust configuration of the remote site. No active adjusting part is integrated, and the all-passive compensation achieves an endless phase error correction range, as well as quick response to fiber delay changes.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Long-distance radio-over-fiber (RoF) frequency transmission has found its vast applications in decades. In cutting edge researches in metrological science, up to hundreds of distributed clocks are linked, and stable frequency transfer from different remote sites to one local laboratory allows phase comparison between all the distributed clocks [1–5]. Similarly, in radio astronomical engineering, the downlink array system needs to accurately record the signal phase on each distributed antenna, in order to correlated the signals and achieve higher angular resolution [6,7]. In both applications, the signals at multiple remote ends usually require to be transferred back to the central station without additional phase error induced by the transmission link (e.g. optical fiber), and that is the concept of frequency downlink transmission [8–10]. Note that the direct downlink transmission is in different concept with the local-to-remote uplink frequency transfer [11–15], since the downlink transmission aims to minimize the complexity at each remote end, and all the subsequent signal processing (e.g. digitization, frequency conversion, etc.) are expected to be performed at the central station. Previously, different end-to-end downlink frequency transmission schemes have been proposed, where the frequency signal from one certain remote end can be directly transferred back to the central station with the phase error cause by fiber link compensated [16,17]. However, the point-to-point frequency downlink scheme still lacks flexibility in applications such as remote frequency comparison, where numbers of distributed clocks need to be accessed in the central station at the same time. That is to say, a downlink frequency transfer scheme from arbitrary remote point is still expected.
In this paper, we propose and demonstrate for the first time a stable downlink frequency transmission scheme from an arbitrary injection point along the fiber loop link. The remote frequency signal at the arbitrary point is first directly injected into the RoF loop link and transferred bi-directionally (i.e. both clockwise and counter-clockwise) to the central station. A round-trip assistant frequency signal is emitted from the central station at the same time, in order to obtain the real-time phase error along the loop link. Then after a frequency up-conversion followed by a frequency down-conversion process, the phase error induced by the fiber delay variation is exactly corrected. The arbitrary point downlink scheme employs passive phase correction [18], which is different from the widely presented active phase compensation method, where a tunable optical delay line (ODL) is usually integrated to dynamically compensate the fiber delay variations [19–21]. Since neither trial-and-error feedback process nor active tuning part is involved, the passive phase correction achieves a quick response to fiber delay changes. The all-passive approach also brings an endless phase error correction range, breaking the range limitation of the actively tuned ODLs.
2. Principle and experiment
The proposed arbitrary point downlink frequency transmission scheme, as well as the experimental set up, is shown in Fig. 1. The central station, along with an arbitrary frequency injection point, is constructed in a radio-over-fiber loop link. The remote frequency signal at the arbitrary point, which is denoted by $\boldsymbol { V}_{\boldsymbol {in}}$, is injected into the fiber loop link, and downlink transferred to the central station in both clockwise and counter-clockwise directions. The finally recovered signal at the central station is denoted by $\boldsymbol { {V}}_{\boldsymbol { {out}}}$. The downlink system aims to transfer the frequency signal at the arbitrary point (${V_{in}}$) back to the central station (${V_{out}}$) with the phase error induced by the fiber link automatically corrected.
Fig. 1. Schematic and experimental principle of stable downlink frequency transmission from arbitrary injection point. MZM, Mach-Zehnder modulator. PD, photodetector. OC, optical coupler. DWDM, dense wavelength division multiplexer. ISO: optical isolator. PODL, programmable optical delay line. OBPF, optical bandpass filter. EBPF, electric bandpass filter.
At the arbitrary injection point, the input frequency signal ${V_{in}}$, with the angular frequency ${\omega _r}$ and its phase ${\varphi _r}(t )$:
is electro-optically converted by a Mach-Zehnder modulator (MZM), with the optical carrier wavelength ${\lambda _1}$. The modulated optical signal at the arbitrary point is then injected into the RoF loop link bi-directionally (i.e. both clockwise and counter-clockwise), with the assistance of a 2×2 optical coupler (OC). Note that two optical isolators (ISOs) must be installed before injection into the 2×2 coupler, so as to prevent the injected signal from re-entering the arbitrary point. Meanwhile at the central station, a highly precise frequency standard, also with the angular frequency ${\omega _r}$, is electro-optically converted by another MZM, with the optical carrier wavelength ${\lambda _2}$. The modulated optical signal carrying the local frequency standard is unidirectionally transferred along the fiber loop link until back to the central station. Both the two MZMs work at the quadrature bias point. Note that although the local and remote oscillators have the same angular frequency ${\omega _r}$, they oscillate independently. In practical applications, the two oscillators may have slight frequency difference (e.g. the atomic clock on the satellite and the standard clock in the local laboratory), which can be included in the phase jitter ${\varphi _r}(t )$ in the remote oscillator.Assume that the real time delay clockwise from the injection point to the central station is ${\tau _1}$, and the delay counter-clockwise from the injection point to the central station is ${\tau _2}$. Then the loop link delay $\tau $ equals $\; {\tau _1} + {\tau _2}$ in real time. At the central station, the clockwise optical signal from the injection point is retrieved first by a dense wavelength division multiplexer (DWDM). After the photodetector (PD) and electric bandpass filter (EBPF), the recovered clockwise injected signal, which is denoted by ${V_{cl}}$, carries the angular frequency of ${\omega _r}$ and the phase of $- {\omega _r}{\tau _1} + {\varphi _r}({t - {\tau_1}} )$:
where $- {\omega _r}{\tau _1}$ is the phase error induce by the fiber delay fluctuation.Likewise, an optical bandpass filter (OBPF) with the central wavelength ${\lambda _1}$ extracts the counter-clockwise optical signal after an optical circulator (CIR). The recovered counter-clockwise injected signal after the PD and EBPF, which is denoted by ${V_{cc}}$, holds the angular frequency of ${\omega _r}$ and the phase of $- {\omega _r}{\tau _2} + {\varphi _r}({t - {\tau_2}} )$:
where $- {\omega _r}{\tau _2}$ is also the phase error induce by the fiber link.Then the two recovered electric signals, ${V_{cl}}$ and ${V_{cc}}$, are frequency up-converted by the three-stage frequency up-converter, the detail of which is shown in Fig. 2. The output of the frequency up-converter, ${V_{up}}$, then has the angular frequency of $2{\omega _r}$ and the phase of $- {\omega _r}\tau + {\varphi _r}({t - {\tau_1}} )+ {\varphi _r}({t - {\tau_2}} )$ (where $\tau $ is the whole loop link delay):
At the same time, the round-trip transferred optical signal from the central station that carries the precise frequency standard, is also retrieved by the DWDM, and opto-electrically converted by another PD and EBPF. The recovered electric round-trip signal, ${V_{rt}}$, has the angular frequency of ${\omega _r}$ and the phase of $- {\omega _r}\tau $:
Then the output of the frequency up-converter, ${V_{up}}$, is frequency down-converted by ${V_{rt}}$, resulting in the output of the frequency down-converter, ${V_{down}}$, which is also the finally recovered frequency signal, ${V_{out}}$:Fig. 2. Three-stage mixing configuration of the frequency up-converter and frequency down-converter.
In the experiment, both the frequency up-converter and frequency down-converter employ a three-stage frequency mixing scheme, in order to suppress the nonlinear effects of the frequency mixers, especially when the inputs are in the same or harmonic frequencies. The three-stage frequency mixing works as follows. As is shown in Fig. 2, the clockwise recovered signal, ${V_{cl}}$, and the counter-clockwise recovered signal, ${V_{cc}}$, are first fed into the frequency up-converter. Both the two signals have the frequency of ${\omega _r}$. A common frequency ${\omega _c}$ up-converts one input to ${\omega _r} + {\omega _c}$ (sum frequency), and down-converts the other input to ${\omega _r} - {\omega _c}$ (difference frequency). Then after a third frequency mixer, the $2{\omega _r}$ frequency is obtained (sum frequency), which is the output of the three-stage frequency up-converter, ${V_{up}}$. No harmonics of the input will interfere with the desired output throughout the three-stage mixing. The frequency down-converter operates in a similar manner.
Note that the traditional active compensation method employs trial-and-error feedback and integrates certain tunable parts (e.g. motor-driven ODLs or thermally controlled ones) to dynamically compensate any phase shift induced by the fiber link. However, in our scheme, a passive phase correction is established where the frequency up-conversion and down-conversion procedures automatically correct the phase error. No active tuning part or trial-and-error process is involved, and the feedback bandwidth of the whole PLL (including the fiber link) is mostly dominated by the fiber delay time $\tau $ [22], not limited anymore by the device tuning speed in the active compensation methods [16]. As a result, the all-passive phase compensation gives a quick response to the time delay changes along the link. As is already demonstrated in our previous work concerning a passive end-to-end frequency transmission, the passive phase correction gives quick response to a sudden fiber delay change [18].
3. Experimental results
A proof-of-concept experiment is conducted. The RoF loop link consists of two fiber spools (20-km and 25-km, respectively) in the laboratory. The arbitrary injection point is chosen to be located at the intersection point of the two fiber spools. Both the remote and local frequency signals are preset to be 1.21 GHz, generated by two microwave signal sources (Agilent E8257D). The two optical carrier wavelengths, ${\lambda _1}$ and ${\lambda _2}$, are 1551.72 nm (C32) and 1549.32 nm (C35), respectively. A programmable optical delay line (PODL) with a 560-ps maximum tunable range is inserted into the 20-km fiber branch, to help verify the phase correction effect.
Figure 3 illustrates the eye diagrams of the recovered frequency signal at the central station with and without phase error correction, sampled by a high-speed digital oscilloscope (Agilent DSO80604). The directly recovered frequency signal along the counter-clockwise fiber direction, ${V_{cl}}$, is measured to evaluate the phase error without compensation (the same in the following measurements). In Fig. 3(a) and Fig. 3(b), the PODL is tuned to sweep its optical delay between 0 ps and 560 ps (maximum range) periodically in a 4 ps/s speed. In Fig. 3(c) and Fig. 3(d), the system is set to run at natural temperature change environment for 2 hours. Without phase error correction, the recovered signal experiences drastic delay fluctuations both under PODL sweeping and natural temperature changing situations. The eye diagrams with the proposed phase error correction scheme are recorded under the same conditions. As a contrast, the delay drifts of the recovered signals are significantly suppressed, as is shown in Fig. 3(a) and Fig. 3(c).
Fig. 3. Eye diagrams of recovered frequency signal with and without arbitrary downlink phase error correction. (a), with phase error correction under PODL sweeping; (b), without phase error correction under PODL sweeping; (c), with phase error correction after 2 hours under natural temperature changing; (d), without phase error correction after 2 hours under natural temperature changing.
The phase variation is also calculated and compared quantitatively. When the PODL is programmed to tune its optical delay from 0 ps to 560 ps, the phase jitter with and without compensation is measured and calculated by a phase and frequency comparator (Agilent 53230a) and the result is shown in Fig. 4. In the compensated link, the phase jitter is suppressed to only around 0.04 rad. Without compensation, however, the phase variation goes up to as large as 4.3 rad, and the variation range is expected to become larger if the PODL had a wider tunable range. A phase jitter suppression ratio of larger than 100 is thus achieved. The system’s electronic sensitivity to thermal changes as well as mechanical stress (especially in the central station) is believed to account for the residual phase fluctuations after compensation.
Fig. 4. (a), Relative phase jitter with and without passive compensation when PODL delay tuning from 0 ps to 560 ps; (b), Phase jitter with passive phase compensation alone.
To verify the frequency stability (both short-term under PODL sweeping and long-term under natural temperature changing) of the downlink recovered signal, a dual-frequency-mixing measurement method is employed, as is illustrated in the experimental setup in Fig. 1. The frequency signal at the remote injection point and the recovered signal at the central station are both frequency down-converted to 10 MHz by a common frequency of 1.2 GHz, and the two 10-MHz signals are phase-compared by a phase and frequency comparator (Agilent 53230a). Figure 5 shows the system’s short-term stability under PODL sweeping at 8 ps/s speed 0∼400 ps range (which means theoretically the frequency stability will be most deteriorated at around 50-s averaging time without phase error correction). As is illustrated in Fig. 5, the overlapping Allan deviation (ADEV) without compensation starts worsening after 0.3-s averaging time under the 8 ps/s fast delay changing speed, and become the most deteriorated at 50 s, which is exactly consistent with the theoretical prediction. Quantitatively, the ADEV without phase error correction is measured to be 2.0×10−12 at 0.1-s averaging, 1.14×10−12 at 1-s averaging and 7.43×10−12 at 50-s averaging, respectively. As a comparison, the frequency stability when applying the proposed transmission scheme is optimized to be 1.04×10−12 at 0.1 s, 2.5×10−13 at 1 s and 3.48×10−14 at 50 s, respectively. More often in practical applications, the fiber link is under natural temperature changing environment. Considering the temperature-delay coefficient of ∼35/ps/km/${\circ{C}}$ of standard fiber, the 8 ps/s PODL sweeping speed is usually faster than that under natural temperature changing situation (as is also verified by comparing Fig. 3(b) and Fig. 3(d)).
Fig. 5. Frequency stabilities under fiber delay changes simulated by the PODL sweeping at the speed of 8 ps/s in 0∼400 ps range.
The frequency stability under natural temperature changing environment is also recorded by the frequency comparator for a long time, as is shown in Fig. 6. For the short-term stability, the ADEV is measured to be 1.3×10−13 at 1 s with compensation and 2.0×10−13 at 1 s without compensation. Note that the 1-s frequency stability here under natural temperature changing situation (1.3×10−13) is in consistency with the 1-s stability in the previous PODL sweeping situation (2.5×10−13), which indicates that the proposed passive compensation method is capable of suppressing most of the phase fluctuations induced by the above PODL sweeping situations. For the long-term stability comparison, the overlapping Allan Deviation severely degraded when the averaging time comes to hundreds of seconds or more, without phase error correction. On the contrary, the long-term stability with phase correction is optimized to 1.1×10−15 at 104-s averaging time. The system’s electric noise floor is also measured and plotted in Fig. 6. We directly measured the stability of the injected frequency signal ${V_{in}}$ without fiber transmission to evaluate the system’s electric noise performance (including the measurement devices). The frequency stability measurement under PODL sweeping situation, together with the measurement under natural temperature changing environment, demonstrates the system’s phase correction capability in both short-term fluctuations and long-term drifts. Note that in Fig. 5 and Fig. 6, both the short-term and long-term stability perform better than free running situation. Whereas in our previous end-to-end downlink transmission scheme employing a wavelength tunable laser (WTL) [16], the 1-s stability with active compensation is three times larger than that of free running, which is caused by the limited PLL bandwidth of the active compensation.
Fig. 6. Frequency stability with and without downlink phase error correction under natural temperature changing environment.
4. Conclusion
In summary, we have proposed and demonstrated an arbitrary-point stable frequency downlink transmission scheme. By a series of frequency mixing at the central station, our scheme builds a phase-shift-free radio-over-fiber downlink, which automatically corrects the phase error along the RoF loop link from an arbitrary remote point. Different from the widely employed active compensation scheme using optical delay lines, the phase correction operates totally in a passive manner, achieving an endless phase error correction range, as well as quick response to fiber delay changes. Experimentally, a 1.21-GHz frequency signal at an arbitrary remote point was downlink transferred along a 45-km fiber loop link. The frequency stability in terms of overlapping Allan Deviation was 1.04×10−12 at 0.1 s, 1.3×10−13 at 1 s and 1.1×10−15 at 104 s, respectively. The direct radio-over-fiber frequency injection without additional remote down-conversion or digitization also brings a simple, robust, and cost-effective configuration in any remote end. The scheme shows the potential of constructing a simultaneous multi-point stable downlink frequency transmission network for remote frequency comparison in metrological sciences and distributed array systems in radio astronomical applications.
Funding
National Key Research and Development Program of China (2018YFA0701902); National Natural Science Foundation of China (61671071, 61675031, 62001043).
Disclosures
The authors declare no conflicts of interest.
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