Abstract

In this paper, we propose a phase-conjugation-based fast radio frequency (RF) phase auto stabilization technique for long-distance fiber delivery. By phase conjugation at the center site, the proposed scheme pre-phase-promotes the RF signal with the shift which is acquired by round-trip transferring another RF whose frequency is half of the one to be sent. Such phase pre-promotion is then used to counteract exactly the following retard induced by one-way delivery. Different from the previous phase-locking-loop-based schemes, the proposed open-loop design avoids the use of any tunable parts and dynamic phase tracking, enabling a fast phase stabilization at the remote site. An end-less compensation capacity can also be achieved. Our design is analyzed by theory. Experimentally, the new scheme is verified by transferring a frequency of 2.42 GHz through a 30-km optical fiber link. Significant phase drift compression is observed. The rapid phase stabilization is verified by introducing sudden time delay change into the link. The recovery time equals to the round-trip time of the link plus the transitional duration of the delay change, which is much shorter than the traditional trial-and-error phase locking loop. Important issues of the system design are discussed.

© 2014 Optical Society of America

1. Introduction

It has been attractive to connect many and long-distance-distributed radio telescopes together to create a much larger virtual telescope, since the interferometer technology provides a very high angular resolution if the antennas are placed far away to measure the RF phase co-sourced from one target [1]. In order to obtain the theoretically predicted precision, the antennas have to be connected coherently, which is usually achieved by highly stable delivery of a RF reference frequency to each antenna from a center station [2]. Due to its low loss, optical fiber has been used widely to transfer such RF references, based on the radio over fiber (RoF) technology [35]. However, optical fiber still suffers from the environment perturbations such as physical vibration and temperature fluctuations, which degrade the RF phase and frequency stability [68]. Many RF phase stabilization schemes have been demonstrated experimentally until now [915], and the remote frequency stability can be as high as 7x10−15 /s [16] and the phase variation can be suppressed to below 0.01 rad during several days [17].

Note that besides the phase or frequency stability, the duration to achieve the stabilized phase at the remote site after sudden and large delivery link perturbations is also one of the important figures of merit. Many applications or particular circumstances require a rapid recovery time. For example, the railway induces a severely vibration on the nearby fibers, and the feasible delivery technique must be fast enough to track the resulted RF phase variations. In a multistatic radar system, the center station should switch agilely among the antenna ends in order to follow one rapid target, and the corresponding fiber links and the stabilized phase transfers inside are required to be activated promptly. Such short-duration phase recovery at the remote site is a challenge for current demonstrated schemes. Nowadays the remote phase stabilization technologies are all based on the feedback loop control [315]. The reference RF signal is transferred round-trip, based on which a phase discriminator measures the delay variation of the fiber dynamically. A tunable phase shifter or delay line is then employed to compensate any change correspondingly. Such controlling is based on traditional trial-and-error procedures such as the proportional-integral-derivative (PID) algorithm [17]. The tunable part is usually a limit for the phase recovery time. For example, optical delay lines with tunable range larger than hundreds of pico-seconds are mostly motor-driven or based on thermally-controlled fiber spool [3, 4, 8]. The piezoelectric fiber stretcher is fast with however very limited tunable range (a few pico-seconds) [8]. In [16, 17], phase conjugation technique was proposed to measure the phase difference introduced by the fluctuation of the link delay. These schemes could offer a large compensation range. However, they were still closed-loop feedback control systems. The feedback control is another physical limit for the phase recovery time. The algorithm requires trying a few rounds to minimize any phase fluctuation, so that the realization of claimed phase stability has to cost duration much longer than the round-trip time after an impulsive link delay variation.

In [18], we have proposed a phase stabilization scheme for transfer and downconvert RF signal from remote antenna to center station via a RoF link. Benefit from phase conjugation technique and the open-loop scheme, rapid and endless post error cancellation was realized. In this paper we propose and demonstrate a novel stable RF delivery scheme for transfer RF standard from center station to remote site, which is capable of fast remote phase stabilization. Rather than the use of widely-reported phase-locking-loop-based phase tracking, we acquire the phase retard precisely by sending a round-trip probe tone, according to which the reference RF frequency is pre-phase-promoted by phase conjugation at the center station. Such phase-shift-free delivery link is then immune to any delay fluctuation. Neither phase discrimination nor tunable parts are required, and the open-loop design without dynamic phase tracking enables a fast and endless phase error cancellation at the remote site. Our scheme is analyzed theoretically to show the rapid stabilization, which is also verified by a 30-km fiber link under impulsive delay change experimentally.

2. Principle

The proposed remote RF phase stabilization scheme involving phase conjugation is illustrated in Fig. 1(a). In order to transfer the RF reference with frequency of ω0 to the remote site, two assistant signals with frequency of ω0/2, 3ω0/2 are employed at the center station. Firstly, the RF1 with frequency of ω0/2, as a probe, is transferred to the remote site via the optical fiber link. At the remote site, the RF1 is transferred back to the center station directly through the same optical fiber link. Then the round-trip RF1 is mixed by the RF2 with frequency of 3ω0/2 at the center site (where the phase conjugation occurs) and the generated RF tone, RF0 with frequency of ω0, is delivered to the remote site again. The remote site finally uses the RF0 as the phase-stabilized reference. Figure 1(b) shows the principle of the automatic phase fluctuation suppression. Note that the propagation-induced RF phase retard is in direct proportion to the carrier frequency multiplied by the fiber delay. So the round-trip phase shift of ω0/2 is exactly the same as the one-way shift that ω0 will suffer. By phase conjugation at the center, the proposed scheme pre-phase-promotes ω0 with the shift acquired by the round-trip ω0/2, which is then used to counteract exactly the following retard induced by delivery. As a result, the fiber link is actually phase-shift-free, and the delivered ω0 is then free from any time delay fluctuation.

 figure: Fig. 1

Fig. 1 (a) The proposed remote RF phase stabilization scheme involving phase conjugation. (b) The principle of the automatic phase fluctuation suppression.

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Mathematically, we can assume that RF1 and RF2 at the center station have the initial phase of φ1 and φ2, respectively. The time delay accumulated from center station to remote site is assumed to τf and that of the return flight is τb. Under slowly-changed circumstances, the time delay variation of the fiber link is much slower than the round-trip transmission time, so τf = τb = τp. Without considering its intensity, the round-trip RF1 can then be expressed as

V1,R=cos[ω02(t2τp)+φ1]

Since RF2 has the following expression as V2 = cos(3ω0t/s + φ2), after phase conjugation we can get the RF0 at the center station as

V0=cos(ω0t+ω0τp+φ2φ1)

After the fiber delivery with time delay of the same τp and phase retarded of ω0τp as a result, we then get

V0=cos(ω0t+φ2φ1)
at the remote site. Equation (3) shows clearly that the proposed phase conjugation eliminates all phase shifts induced by fiber propagation. So V0 is immune of the delay of the fiber link, as well as the delay variation. The only contribution to the possible phase variation is the instability of the two RF sources at the center. Note that both RF1 and RF2 are easily to be phase locked to a standard frequency source, e.g. an atomic clock, so that φ1 and φ2 are constant. As a result, one can obtain a stabilized phase under carrier frequency of ω0 remotely.

Note that the traditional method employs certain tunable part to dynamically compensate any variable time delay or phase shift of the delivery link. However, in our scheme, the phase conjugation compensates the whole phase shift, rather than the fluctuations only. As a result, such compensation is actually endless. Independent from the fiber length, we can always get a fixed phase as Eq. (3) at the remote, without a π uncertainty like before. The phase conjugation also avoids the use of tunable delay/phase discrimination, and dynamic tracking algorithm, enabling a fast stabilization under sudden delay change. Figure 2 shows the principle. Assume that there is an impulsive time delay change at point A when t = 0, the remote site will begin to get wrong phase after t = τp2. Note that only if the signal travels the same fiber link three times (i.e. a round trip in ω0/2 and a single one in ω0), the remote phase can be stabilized. So after the signal distributed along the fiber at t = 0 as shown by the red dash line in Fig. 2, is received by the remote, the remote can then receive the correct phase again described by Eq. (3). The transitional duration is the round-trip time, i.e. 2τp. Such duration is much less than that of the traditional phase-locking-loop-based schemes, where trial-and-error procedure costs a few round-trips.

 figure: Fig. 2

Fig. 2 The principle of the fast phase stabilization by phase conjugation.

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3. Experiments and results

A proof-of-concept experiment is carried out and the setup is illustrated in Fig. 3, which follows exactly the scheme of Fig. 1(a). In order to measure the phase stabilization at the remote site, the local RF1 and RF2 are mixed at the center, which is then used to compare with the remote phase of ω0. The comparison is performed both by a sampling oscilloscope (HP Digital communications analyzer which is triggered by the above ω0) and by a phase discriminator. The discriminator has the advantage of high-speed comparison between the two input phases with up to 10 MHz.

 figure: Fig. 3

Fig. 3 Experiment setup of the phase-conjugation-based remote RF phase stabilization. LD: laser diode; PD: photo detector; WDM: wavelength division multiplexer; DCM: dispersion compensation module; ODL: optical delay line. The 10 MHz reference is from one of the Agilent Vector Signal Generator.

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Four issues are concerned in our design. Firstly, ω0 = 2.42 GHz in our experiment, and RF10/2) and RF2 (3ω0/2) are generated from two Agilent signal generators (Agilent Vector Signal Generator, E8267D). The two generators are synchronized by the same 10 MHz reference to maintain a constant phase difference φ2-φ1. Secondly, each of the three RoF transmissions in Fig. 1(b) is implemented by a pair of a directly-modulated LD and a PD. The three LDs have different wavelengths, and the three links are wavelength-division-multiplexed into the same fiber, with the help of two WDMs at both sites. The Rayleigh backscattering noise can then be reduced easily, promising a high signal to noise ratio (SNR).

Thirdly, the optical fiber link consists of a 30-km standard G.652 single-mode optical fiber on a spool in the laboratory environment. Note that it is required by Eq. (3) that the time delays of the three fiber links in Fig. 1(b) are the same. Though the link dispersion will result in slightly different time delays when the three LDs have different wavelengths, such delay difference is fixed so that it is reasonable to neglect it. The possible phase fluctuation may result from the laser wavelength drift under large fiber dispersion. To prevent this, we introduce a dispersion compensation module (DCM) to compensate the fiber dispersion precisely, which is located between the fiber link and the WDM at the center site. As a result, the fiber delay is independent of the wavelength difference or drift. Note that most long-haul underground fiber links are already dispersion-compensated, so dispersion compensation of the fiber link is realistic.

Fourthly, the proposed phase stabilization relies on the accurate pre-phase-promoting the signal to be sent. Such phase shift is achieved by mixing the round-trip ω0/2 and 3ω0/2. Note that after a direct mixing between ω0/2 and its tripling, the generated ω0 contains not only the desired 3ω0/2-ω0/2, but also other crosstalk from harmonics as well as mixing products among the harmonics. For commercial mixer, the power ratio between the desired product and the unwanted ones are only around 30 dB. Such heavy crosstalk is expected to degrade the performance greatly. In order to suppress the crosstalk, we introduce an additional common frequency, as shown in Fig. 3, which is used to down-convert both the round-trip ω0/2 and 3ω0/2, so that the two output low IFs are no longer harmonics, whose further mixing is therefore clear from any crosstalk. Any phase noise from the common frequency is also eliminated by the last mixing. Note that proper RF filters are used after each mixing.

In our setup, a variable optical delay line with around 700-ps range, corresponding to 10.6 rad at 2.42 GHz, is inserted to simulate the environment-induced fiber length fluctuation. The phase-conjugation-based phase delivery is demonstrated by observing the stable RF phase at the remote site by the sampling oscilloscope. As a comparison, a direct delivery of 2.42 GHz RF frequency is measured under the same fiber link and measurement equipment. As shown in Fig. 4, while the optical delay line is continuously tuned from 0 to 700 ps (10.6 rad), the peak-to-peak phase difference of the received RF signal is 0.042 rad with pre-phase-promotion, which shows a significant phase drift compression ratio.

 figure: Fig. 4

Fig. 4 Phase difference of the received RF signal with (red) and without pre-phase-promotion (black) while the optical delay line (ODL) is tuned from 0 to 700 ps; the insertion shows the detail.

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To verify the long time compensation performance of our scheme, the eye diagram of the received RF signal is measured while the fiber link’s delay is drifting as the environment (e.g., physical vibration, temperature) changes in the lab. Figure 5 shows the eye diagrams without and with compensation for half an hour recorded by the sampling oscilloscope. Without the pre-compensation, the received RF signal has obvious phase drift, which is about 3.8 rad. On the contrary, with the pre-compensation, the root-mean-square (RMS) time jitter after half an hour is 1.70 ps corresponding to a phase drift of 0.026 rad. The phase drift is significantly reduced and the compression is demonstrated quantitatively. The system electronic sensitivity to thermal and mechanical stress (especially of the synchronized RF sources and the mixers) is believed to account for the residual phase drift after compensation.

 figure: Fig. 5

Fig. 5 Eye diagrams (a) without and (b) with compensation after half an hour.

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To verify the dynamic characteristic of our phase-conjugation-based phase stabilization, the step response of the system is measured by applying a 1 × 2 MEMS optical switch combined with a 3-dB fiber coupler, as shown in Fig. 3. The sudden change of the link delay is simulated by such optical switch module. The length difference between the two arms is 2 m, corresponding to 5-ns delay difference or 76-rad phase difference at 2.42 GHz. The switching time of the MEMS optical switch is 70 us. The step response of the phase error is measured by the phase discriminator, which is then recorded by a digital sampling oscilloscope (Agilent DSO-3034A). Figure 6 shows the system step response during the sudden 5-ns link delay change. It is obvious that in both situations (the delay change occurs before or after the fiber link) the recovery time of the phase-delivery system is only 400 us. Note that the round-trip time delay of the fiber link (including the dispersion compensation module) is 340 us and the switching time is 70 us, the recovery time equals only the round-trip time of the fiber link. Such results agree well with our theory in Fig. 2. From Fig. 6 one can also see a very different step response from a phase-look-loop-based system which generally has overshot and oscillations, as well as a phase recovery time much longer than the time delay of one round trip.

 figure: Fig. 6

Fig. 6 Phase-error measured by the phase discriminator as the link delay is changed suddenly by 76 rad. (a): The optical switch is placed before the fiber link. (b): The optical switch is placed after the fiber link. A-B: the link delay is decreased by 76 rad; B-A: the link delay is increased by 76 rad.

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4. Conclusion

In summary, we proposed and demonstrated a stabilized RF phase delivery scheme. By phase conjugation at the center station, our scheme builds a phase-shift-free RF-over-fiber link, which is then free from any link delay fluctuation. Different from traditional phase-locking-loop design, the phase conjugation avoids the use of phase discrimination, tunable delay/phase, as well as dynamic phase tracking, enabling a rapid and endless compensation of the link phase variation. Experimentally, a RF frequency of 2.42 GHz was transferred through a 30-km optical fiber link, which showed a significant phase drift compression from 10.6 rad to 0.042 ps. The long-term RMS phase drift of the received RF signal was 0.026 rad. The rapid phase recovery under impulsive link delay change was investigated. The recovery time is about 400 us which equals to the round-trip time of the fiber link plus the switching time of the optical switch. All these characteristics make the phase-conjugation-based error auto-correction a promising method for stable RF delivery via long distance optical fiber link when a short remote phase recovery time is required.

Acknowledgments

This work was supported in part by National 973 Program (2012CB315705), NSFC Program (61271042, 61302016, and 61335002), NCET-13-0682, and China Postdoctoral Science Foundation (2013M540891).

References and links

1. J. Cliché and B. Shillue, “Precision timing control for radio astronomy: maintaining femtosecond synchronization in the Atacama Large Millimeter Array,” IEEE Contr. Syst. Mag. 26(1), 19–26 (2006). [CrossRef]  

2. S. Huang and R. L. Tjoelker, “Stabilized photonic links for deep space tracking, navigation, and radio science applications,” 43rd Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting, (2012).

3. 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]   [PubMed]  

4. J. Ye, J. Peng, R. J. Jones, K. W. Holman, J. L. Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize, J. C. Bergquist, L. W. Hollberg, L. Robertsson, and L. Ma, “Delivery of high-stability optical and microwave frequency standards over an optical fiber network,” J. Opt. Soc. Am. B 20(7), 1459–1467 (2003). [CrossRef]  

5. A. Zhang, Y. Dai, F. Yin, T. Ren, K. Xu, J. Li, Y. Ji, J. Lin, and G. Tang, “Stable radio-frequency delivery by λ dispersion-induced optical tunable delay,” Opt. Lett. 38(14), 2419–2421 (2013). [CrossRef]   [PubMed]  

6. M. Calhoun, R. Sydnor, and W. Diener, “A stabilized 100-megahertz and 1-gigahertz reference frequency distribution for Cassini Radio Science,” Interplanetary Network Progress Rep: 42–148 (2001).

7. B. Bernhardt, T. W. Hänsch, and R. Holzwarth, “Implementation and characterization of a stable optical frequency distribution system,” Opt. Express 17(19), 16849–16860 (2009). [CrossRef]   [PubMed]  

8. F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006). [CrossRef]  

9. H. Jiang, F. Kéfélian, S. Crane, O. Lopez, M. Lours, J. Millo, D. Holleville, P. Lemonde, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Long-distance frequency transfer over an urban fiber link using optical phase stabilization,” J. Opt. Soc. Am. B 25(12), 2029–2035 (2008). [CrossRef]  

10. R. Wilcox, J. M. Byrd, L. Doolittle, G. Huang, and J. W. Staples, “Stable transmission of radio frequency signals on fiber links using interferometric delay sensing,” Opt. Lett. 34(20), 3050–3052 (2009). [CrossRef]   [PubMed]  

11. M. Kumagai, M. Fujieda, S. Nagano, and M. Hosokawa, “Stable radio frequency transfer in 114 km urban optical fiber link,” Opt. Lett. 34(19), 2949–2951 (2009). [CrossRef]   [PubMed]  

12. L. Zhang, L. Chang, Y. Dong, W. Xie, H. He, and W. Hu, “Phase drift cancellation of remote radio frequency transfer using an optoelectronic delay-locked loop,” Opt. Lett. 36(6), 873–875 (2011). [CrossRef]   [PubMed]  

13. G. Marra, H. S. Margolis, S. N. Lea, and P. Gill, “High-stability microwave frequency transfer by propagation of an optical frequency comb over 50 km of optical fiber,” Opt. Lett. 35(7), 1025–1027 (2010). [CrossRef]   [PubMed]  

14. M. T. Hsu, Y. He, D. A. Shaddock, R. B. Warrington, and M. B. Gray, “All-digital radio-frequency signal distribution via optical fibers,” IEEE Photon. Technol. Lett. 24(12), 1015–1017 (2012). [CrossRef]  

15. D. Hou, P. Li, C. Liu, J. Zhao, and Z. Zhang, “Long-term stable frequency transfer over an urban fiber link using microwave phase stabilization,” Opt. Express 19(2), 506–511 (2011). [CrossRef]   [PubMed]  

16. L. Primas, G. Lutes, and R. Sydnor, “Fiber optic frequency transfer link, Frequency Control Symposium,” IEEE Proceedings of the 42nd Annual, 478–484 (1988).

17. B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10⁻19 accuracy level,” Sci. Rep. 2, 556 (2012). [CrossRef]   [PubMed]  

18. Z. Wu, Y. Dai, F. Yin, K. Xu, J. Li, and J. Lin, “Stable radio frequency phase delivery by rapid and endless post error cancellation,” Opt. Lett. 38(7), 1098–1100 (2013). [CrossRef]   [PubMed]  

References

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  1. J. Cliché and B. Shillue, “Precision timing control for radio astronomy: maintaining femtosecond synchronization in the Atacama Large Millimeter Array,” IEEE Contr. Syst. Mag. 26(1), 19–26 (2006).
    [Crossref]
  2. S. Huang and R. L. Tjoelker, “Stabilized photonic links for deep space tracking, navigation, and radio science applications,” 43rd Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting, (2012).
  3. 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] [PubMed]
  4. J. Ye, J. Peng, R. J. Jones, K. W. Holman, J. L. Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize, J. C. Bergquist, L. W. Hollberg, L. Robertsson, and L. Ma, “Delivery of high-stability optical and microwave frequency standards over an optical fiber network,” J. Opt. Soc. Am. B 20(7), 1459–1467 (2003).
    [Crossref]
  5. A. Zhang, Y. Dai, F. Yin, T. Ren, K. Xu, J. Li, Y. Ji, J. Lin, and G. Tang, “Stable radio-frequency delivery by λ dispersion-induced optical tunable delay,” Opt. Lett. 38(14), 2419–2421 (2013).
    [Crossref] [PubMed]
  6. M. Calhoun, R. Sydnor, and W. Diener, “A stabilized 100-megahertz and 1-gigahertz reference frequency distribution for Cassini Radio Science,” Interplanetary Network Progress Rep: 42–148 (2001).
  7. B. Bernhardt, T. W. Hänsch, and R. Holzwarth, “Implementation and characterization of a stable optical frequency distribution system,” Opt. Express 17(19), 16849–16860 (2009).
    [Crossref] [PubMed]
  8. F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
    [Crossref]
  9. H. Jiang, F. Kéfélian, S. Crane, O. Lopez, M. Lours, J. Millo, D. Holleville, P. Lemonde, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Long-distance frequency transfer over an urban fiber link using optical phase stabilization,” J. Opt. Soc. Am. B 25(12), 2029–2035 (2008).
    [Crossref]
  10. R. Wilcox, J. M. Byrd, L. Doolittle, G. Huang, and J. W. Staples, “Stable transmission of radio frequency signals on fiber links using interferometric delay sensing,” Opt. Lett. 34(20), 3050–3052 (2009).
    [Crossref] [PubMed]
  11. M. Kumagai, M. Fujieda, S. Nagano, and M. Hosokawa, “Stable radio frequency transfer in 114 km urban optical fiber link,” Opt. Lett. 34(19), 2949–2951 (2009).
    [Crossref] [PubMed]
  12. L. Zhang, L. Chang, Y. Dong, W. Xie, H. He, and W. Hu, “Phase drift cancellation of remote radio frequency transfer using an optoelectronic delay-locked loop,” Opt. Lett. 36(6), 873–875 (2011).
    [Crossref] [PubMed]
  13. G. Marra, H. S. Margolis, S. N. Lea, and P. Gill, “High-stability microwave frequency transfer by propagation of an optical frequency comb over 50 km of optical fiber,” Opt. Lett. 35(7), 1025–1027 (2010).
    [Crossref] [PubMed]
  14. M. T. Hsu, Y. He, D. A. Shaddock, R. B. Warrington, and M. B. Gray, “All-digital radio-frequency signal distribution via optical fibers,” IEEE Photon. Technol. Lett. 24(12), 1015–1017 (2012).
    [Crossref]
  15. D. Hou, P. Li, C. Liu, J. Zhao, and Z. Zhang, “Long-term stable frequency transfer over an urban fiber link using microwave phase stabilization,” Opt. Express 19(2), 506–511 (2011).
    [Crossref] [PubMed]
  16. L. Primas, G. Lutes, and R. Sydnor, “Fiber optic frequency transfer link, Frequency Control Symposium,” IEEE Proceedings of the 42nd Annual, 478–484 (1988).
  17. B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10⁻19 accuracy level,” Sci. Rep. 2, 556 (2012).
    [Crossref] [PubMed]
  18. Z. Wu, Y. Dai, F. Yin, K. Xu, J. Li, and J. Lin, “Stable radio frequency phase delivery by rapid and endless post error cancellation,” Opt. Lett. 38(7), 1098–1100 (2013).
    [Crossref] [PubMed]

2013 (2)

2012 (2)

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10⁻19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

M. T. Hsu, Y. He, D. A. Shaddock, R. B. Warrington, and M. B. Gray, “All-digital radio-frequency signal distribution via optical fibers,” IEEE Photon. Technol. Lett. 24(12), 1015–1017 (2012).
[Crossref]

2011 (2)

2010 (1)

2009 (3)

2008 (1)

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] [PubMed]

2006 (2)

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

J. Cliché and B. Shillue, “Precision timing control for radio astronomy: maintaining femtosecond synchronization in the Atacama Large Millimeter Array,” IEEE Contr. Syst. Mag. 26(1), 19–26 (2006).
[Crossref]

2003 (1)

Amy-Klein, A.

Bai, Y.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10⁻19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Bergquist, J. C.

Bernhardt, B.

Bize, S.

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

J. Ye, J. Peng, R. J. Jones, K. W. Holman, J. L. Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize, J. C. Bergquist, L. W. Hollberg, L. Robertsson, and L. Ma, “Delivery of high-stability optical and microwave frequency standards over an optical fiber network,” J. Opt. Soc. Am. B 20(7), 1459–1467 (2003).
[Crossref]

Byrd, J. M.

Chang, L.

Chardonnet, C.

H. Jiang, F. Kéfélian, S. Crane, O. Lopez, M. Lours, J. Millo, D. Holleville, P. Lemonde, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Long-distance frequency transfer over an urban fiber link using optical phase stabilization,” J. Opt. Soc. Am. B 25(12), 2029–2035 (2008).
[Crossref]

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

Chen, W. L.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10⁻19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Clairon, A.

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

Cliché, J.

J. Cliché and B. Shillue, “Precision timing control for radio astronomy: maintaining femtosecond synchronization in the Atacama Large Millimeter Array,” IEEE Contr. Syst. Mag. 26(1), 19–26 (2006).
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Crane, S.

Dai, Y.

Diddams, S. A.

Dong, Y.

Doolittle, L.

Feng, Y. Y.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10⁻19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

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] [PubMed]

Fujieda, M.

Gao, C.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10⁻19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Gill, P.

Gray, M. B.

M. T. Hsu, Y. He, D. A. Shaddock, R. B. Warrington, and M. B. Gray, “All-digital radio-frequency signal distribution via optical fibers,” IEEE Photon. Technol. Lett. 24(12), 1015–1017 (2012).
[Crossref]

Hall, J. L.

Hänsch, T. W.

He, H.

He, Y.

M. T. Hsu, Y. He, D. A. Shaddock, R. B. Warrington, and M. B. Gray, “All-digital radio-frequency signal distribution via optical fibers,” IEEE Photon. Technol. Lett. 24(12), 1015–1017 (2012).
[Crossref]

Hollberg, L. W.

Holleville, D.

Holman, K. W.

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Hsu, M. T.

M. T. Hsu, Y. He, D. A. Shaddock, R. B. Warrington, and M. B. Gray, “All-digital radio-frequency signal distribution via optical fibers,” IEEE Photon. Technol. Lett. 24(12), 1015–1017 (2012).
[Crossref]

Hu, W.

Huang, G.

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] [PubMed]

Ji, Y.

Jiang, H.

Jones, D. J.

Jones, R. J.

Kéfélian, F.

Kitching, J.

Kumagai, M.

Lea, S. N.

Lemonde, P.

Li, J.

Li, P.

Li, T. C.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10⁻19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

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Liu, C.

Lopez, O.

H. Jiang, F. Kéfélian, S. Crane, O. Lopez, M. Lours, J. Millo, D. Holleville, P. Lemonde, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Long-distance frequency transfer over an urban fiber link using optical phase stabilization,” J. Opt. Soc. Am. B 25(12), 2029–2035 (2008).
[Crossref]

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

Lours, M.

H. Jiang, F. Kéfélian, S. Crane, O. Lopez, M. Lours, J. Millo, D. Holleville, P. Lemonde, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Long-distance frequency transfer over an urban fiber link using optical phase stabilization,” J. Opt. Soc. Am. B 25(12), 2029–2035 (2008).
[Crossref]

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
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Ma, L.

Margolis, H. S.

Marra, G.

Miao, J.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10⁻19 accuracy level,” Sci. Rep. 2, 556 (2012).
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Millo, J.

Nagano, S.

Narbonneau, F.

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

Peng, J.

Ren, T.

Robertsson, L.

Santarelli, G.

H. Jiang, F. Kéfélian, S. Crane, O. Lopez, M. Lours, J. Millo, D. Holleville, P. Lemonde, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Long-distance frequency transfer over an urban fiber link using optical phase stabilization,” J. Opt. Soc. Am. B 25(12), 2029–2035 (2008).
[Crossref]

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

Shaddock, D. A.

M. T. Hsu, Y. He, D. A. Shaddock, R. B. Warrington, and M. B. Gray, “All-digital radio-frequency signal distribution via optical fibers,” IEEE Photon. Technol. Lett. 24(12), 1015–1017 (2012).
[Crossref]

Shillue, B.

J. Cliché and B. Shillue, “Precision timing control for radio astronomy: maintaining femtosecond synchronization in the Atacama Large Millimeter Array,” IEEE Contr. Syst. Mag. 26(1), 19–26 (2006).
[Crossref]

Staples, J. W.

Tang, G.

Wang, B.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10⁻19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Wang, L. J.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10⁻19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Warrington, R. B.

M. T. Hsu, Y. He, D. A. Shaddock, R. B. Warrington, and M. B. Gray, “All-digital radio-frequency signal distribution via optical fibers,” IEEE Photon. Technol. Lett. 24(12), 1015–1017 (2012).
[Crossref]

Wilcox, R.

Wu, Z.

Xie, W.

Xu, K.

Ye, J.

Yin, F.

Zhang, A.

Zhang, J. W.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10⁻19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

Zhang, L.

Zhang, Z.

Zhao, J.

Zhu, X.

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10⁻19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

IEEE Contr. Syst. Mag. (1)

J. Cliché and B. Shillue, “Precision timing control for radio astronomy: maintaining femtosecond synchronization in the Atacama Large Millimeter Array,” IEEE Contr. Syst. Mag. 26(1), 19–26 (2006).
[Crossref]

IEEE Photon. Technol. Lett. (1)

M. T. Hsu, Y. He, D. A. Shaddock, R. B. Warrington, and M. B. Gray, “All-digital radio-frequency signal distribution via optical fibers,” IEEE Photon. Technol. Lett. 24(12), 1015–1017 (2012).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Express (2)

Opt. Lett. (6)

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] [PubMed]

F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77(6), 064701 (2006).
[Crossref]

Sci. Rep. (1)

B. Wang, C. Gao, W. L. Chen, J. Miao, X. Zhu, Y. Bai, J. W. Zhang, Y. Y. Feng, T. C. Li, and L. J. Wang, “Precise and continuous time and frequency synchronisation at the 5×10⁻19 accuracy level,” Sci. Rep. 2, 556 (2012).
[Crossref] [PubMed]

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M. Calhoun, R. Sydnor, and W. Diener, “A stabilized 100-megahertz and 1-gigahertz reference frequency distribution for Cassini Radio Science,” Interplanetary Network Progress Rep: 42–148 (2001).

S. Huang and R. L. Tjoelker, “Stabilized photonic links for deep space tracking, navigation, and radio science applications,” 43rd Annual Precise Time and Time Interval (PTTI) Systems and Applications Meeting, (2012).

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Figures (6)

Fig. 1
Fig. 1 (a) The proposed remote RF phase stabilization scheme involving phase conjugation. (b) The principle of the automatic phase fluctuation suppression.
Fig. 2
Fig. 2 The principle of the fast phase stabilization by phase conjugation.
Fig. 3
Fig. 3 Experiment setup of the phase-conjugation-based remote RF phase stabilization. LD: laser diode; PD: photo detector; WDM: wavelength division multiplexer; DCM: dispersion compensation module; ODL: optical delay line. The 10 MHz reference is from one of the Agilent Vector Signal Generator.
Fig. 4
Fig. 4 Phase difference of the received RF signal with (red) and without pre-phase-promotion (black) while the optical delay line (ODL) is tuned from 0 to 700 ps; the insertion shows the detail.
Fig. 5
Fig. 5 Eye diagrams (a) without and (b) with compensation after half an hour.
Fig. 6
Fig. 6 Phase-error measured by the phase discriminator as the link delay is changed suddenly by 76 rad. (a): The optical switch is placed before the fiber link. (b): The optical switch is placed after the fiber link. A-B: the link delay is decreased by 76 rad; B-A: the link delay is increased by 76 rad.

Equations (3)

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

V 1,R =cos[ ω 0 2 ( t2 τ p )+ φ 1 ]
V 0 =cos( ω 0 t+ ω 0 τ p + φ 2 φ 1 )
V 0 =cos( ω 0 t+ φ 2 φ 1 )

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