Abstract

We propose and experimentally demonstrate a stable radio frequency (RF) phase dissemination scheme for a long-haul optical fiber loop link based on frequency mixing. Using a single optical source in both directions of the loop link, additional timing jitter caused by group velocity dispersion (GVD) can be eliminated. Impressive scalability provided by the optical link ensures that arbitrary-access node can obtain an RF signal with a stabilized phase to meet the requirements of multiple users. In our experiment, a 2.4 GHz RF signal is distributed to arbitrary points along a 100 km fiber-optic loop link steadily. Stabilities of the recovered signals from two accessing nodes are recorded. The root-mean-square (RMS) phase jitter of the received signal at either accessing node is reduced from 1.87 rad to no more than 0.027 rad during 1800-second measuring time.

© 2016 Optical Society of America

1. Introduction

A large number of applications require high stable frequency dissemination, which include deep space network, particle accelerators and long-distance-distributed radio telescopes [1–3]. Optical fiber is considered to be an ideal media for frequency transmission due to advantages such as low cost, low attenuation and immunity to electromagnetic interference. Resulting from the variations of temperature and vibrations of environment, the stability of phase dissemination will be destroyed. Various schemes have been proposed and demonstrated to improve the stability of the signals transmitted in the optical fiber [4–15]. Actively compensating schemes usually include a piezoelectrical transducer, voltage-controlled oscillator (VCO), or proportional-integral-derivative algorithm. These schemes can achieve high compensation precision, but they are limited by the response speed and the compensation range of compensation devices. Passive phase correction is another method to disseminate radio-frequency (RF) signals based on frequency mixing [16–20]. Compared with actively compensating schemes, the passive phase correction method has attracted a lot of attentions because of the fast compensation speed and infinite compensation range.

In passive phase correction method, the optical fiber links are usually designed to be shared by multi-user. In applications such as distributed synthetic aperture radar systems and radio astronomy, RF signals are required to be transferred to multiple stations with stabilized phase. Consequently, multiple wavelengths are employed to distribute the RF signal to multi-user [21, 22]. The cardinal disadvantage of these schemes, however, is that it is sensitive to group velocity dispersion (GVD), especially for longer-distance transfer and relatively larger wavelength gap. In reality, group dispersion parameter D(λ) changes with temperature and therefore will give rise to additional timing jitter among different wavelengths. Owing to the variation characteristic, this kind of timing jitter can not be alleviated by dispersion compensation technology which generally compensates a fixed dispersion value. Yu et al. have proved that temperature-induced variation of group velocity dispersion (TIVGVD) is a systematic performance restriction in multi-wavelength dissemination systems [21]. Gao et al. proposed a phase recovery technique in an arbitrary access node which served multiple users [23]. They mixed phase information from two directions. But the phase correction method used in their paper was based on the measurement of round-trip phase fluctuation and active compensation of the outgoing signal phase.

In this paper, a novel passive arbitrary-access stable phase delivery scheme based on single optical source is proposed and demonstrated. Compared with the previous scheme [23], precise phase correction is obtained by imbedding the phase information into a second harmonic signal to avoid having to actively stabilize the RF signal. The optical link provides impressive scalability so that any remote point can obtain stable RF signal by inserting in the nearby link. Figure. 1 illustrates a topological diagram of our circle network. In addition, only one laser diode (LD) is applied in the central station, therefore, single wavelength brings better symmetry to the bidirectional link and eliminates the group delay caused by GVD. The root-mean-square (RMS) phase jitter is 1.87 rad without compensation, while it is reduced to no more than 0.027 rad after compensation.

 figure: Fig. 1

Fig. 1 Diagram of the circle topology including basic optical loop link(Black line) and the expanding link(red dashed line).

Download Full Size | PPT Slide | PDF

2. Principle

Figure. 2 illustrates the schematic diagram of the proposed delivery scheme. Our goal is to transmit a RF signal to an arbitrary remote station via single-mode fiber (SMF) with stabilized phase. At the central station, the standard RF signal can be expressed as a cosine function:

Vs=cos(ωst+φs),
where ωs and φs are its angular frequency and initial phase, respectively. The amplitude is normalized for conciseness. Vs modulates an optical carrier and then the modulated signal is transmitted back to the central station along the entire fiber-optic loop link as a probe signal. At the central station, the probe signal is detected by a photo-detector (PD) and goes through an electrical bandpass filter (BPF) with the center frequency of ωs to get a cleared round-trip probe signal which can be denoted as
V1=cos(ωst+φs+φp),
where φp is the phase fluctuation corresponding to the entire fiber-optic loop link and ωs. The phase fluctuation varies with thermal and mechanical fluctuations. Another branch of the standard RF signal is frequency tripled and mixed with the cleared round-trip probe signal V1. The output of mixer1 is filtered by BPF2 with the center frequency of 2ωs to generate a beat signal, which can be written as
V2=cos(2ωst+2φsφp).

The phase pre-compensated RF signal is then modulated on the same laser device with the probe signal and sent to both the clockwise and anticlockwise directions via SMF. At the remote node, a 2 × 2 fiber coupler is used to couple out the clockwise and the anticlockwise transferred optical signals in the fiber link. One pair of PD and BPF are applied to recover signals with the angular frequency of 2ωs. The signal after BPF3 and BPF4 can be expressed as

V3=cos(2ωst+2φsφp+2φa),
V4=cos(2ωst+2φsφp+2φb),
respectively, where φa and φb are the phase fluctuations of the clockwise and anticlockwise transferred signals corresponding to the angular frequency ωs respectively. φp= φa + φb. Then the two signals are mixed and the term of sum frequency is filtered and frequency divided by 4. The output signal of the divide-by-4 device can be written as
V5=cos(ωst+φs).

 figure: Fig. 2

Fig. 2 Schematic diagram of the arbitrary-access stable phase dissemination scheme. LD: laser diode. MZM: Mach-Zehnder modulator. RF: radio frequency. PD: photo-detector. EC: electrical coupler. OC: optical coupler. EBPF: electrical bandpass filter. SMF: single-mode fiber. FM: frequency multiplier. FD: frequency divider.

Download Full Size | PPT Slide | PDF

It’s clear that the RF signal V5 received at an arbitrary remote station has the same frequency and phase with the standard RF signal generated at the central station. Therefore, the vibration of the RF phase is effectively reduced by using only one LD and two-stage frequency mixing. Neither active phase tracking nor phase discrimination is required in our loop link design which simplifies the system structure and reduces the cost.

3. Experiment setup and results

A proof-of-concept experiment is carried out based on Fig. 2 to verify the proposed scheme. Figure. 3 illustrates the experimental setup of our system. In the experiment, ωs is set to be 2.4 GHz (generated by Agilent E8257D), ISM (Industrial Scientific Medical) Band, which is free and universal around the world. It should be noted that because of relatively large power attenuation of the frequency multiplier, we employ a second signal generator (Agilent E8257D) to provide a stable 7.2 GHz RF signal, 3ωs, 15 dBm. In commercialisation, the third harmonic could be generated by frequency tripler and an electrical amplifier could be added on the frequency tripled branch to amplify the power of the third harmonic. While the power of 2.4 GHz RF signal is set to be −3 dBm to decrease the influence of second harmonic to the phase pre-compensated RF signal V2. Clocks of the two microwave signal generators are synchronized to eliminate phase fluctuations between the two signals. The standard RF signal Vs and the phase pre-compensated RF signal V2 jointly modulate one LD through a Mach-Zehnder modulator (MZM) biased at Vπ/2. The output optical power of LD whose center wavelength is 1550.00 nm is 5.6 dBm after MZM. The modulated optical carrier is sent both clockwise and anticlockwise to the remote node after passing through an optical coupler. The optical signal is then amplified at the remote end by an unidirectional erbium-doped fiber amplifier (EDFA). It should be noted here that only the anti-clockwise light needs to go through the loop and return to central station. Clockwise light does not return to the central station, so an unidirectional EDFA is good enough to only amplify anti-clockwise light. Although only anti-clockwise light is amplified, the imbalanced optical power received by two PDs in the access node will not affect the phase performance. Since clockwise light cannot be amplified unless using a bidirectional EDFA, the fiber loss above an access node will be the limiting factor of the distribution loop length. The gain of EDFA is controlled to be no more than 20 dB to prevent stimulated Brillouin scattering. A 90-km and a 10-km standard single-mode fiber spools are located in our laboratory and the connection of the two fiber spools is taken as an example of an arbitrary accessing node. At the remote node, frequency down-conversion is performed by a low noise, divide-by-4 digital frequency divider block, ADF5001 prescaler. To test the performance of the proposed system, we compare Vs with V5 to measure the stability of frequency delivery with compensation. As a comparison, the uncompensated stability is measured by comparing Vs with V6 in Fig. 3, which is filtered out at point A by BPF6 with the center frequency of 2.4 GHz. During 1800-second time, the optical link runs freely in the laboratory environment. Figure. 4 shows the phase differences between the local reference signal and the recovered signal at the node with and without compensation measured by the oscilloscope (ROHDE&SCHWARZ, RTO1024). It should be noted that our oscilloscope can only measure delay between the edges of two waveforms for one period of the RF signal. As can be seen from Fig. 4(a), the waveform of the uncompensated signal drifts periodically during 1800-second recording time which could be attributed to the fact that the temperature increases monotonically in the morning of July in our laboratory. The root-mean-square (RMS) timing jitter of the uncompensated signal is 124.0 ps, corresponding to about 1.87 rad, while the RMS timing jitter of the compensated signal is reduced to 1.57 ps, corresponding to about 0.024 rad.

 figure: Fig. 3

Fig. 3 Experimental setup of the proposed phase fluctuation cancellation scheme for arbitrary-access loop link. The node between a 90/50km and a 10/50km standard single-mode fiber spools. OSC: oscilloscope. EDFA: erbium-doped fiber amplifier. EA: electrical amplifier.

Download Full Size | PPT Slide | PDF

 figure: Fig. 4

Fig. 4 Measured phase differences between the recovered signal and the standard RF signal at the connection of a 90-km and a 10-km standard single-mode fiber spools (a), connection of a 50-km and a 50-km standard single-mode fiber spools (b) (red, green: compensated, blue: uncompensated;).

Download Full Size | PPT Slide | PDF

Figure. 5 shows the persistence of the recovered 2.4 GHz RF signal at the connection of a 90-km and a 10-km standard single-mode fiber spools with and without compensation for 300, 600, and 900 s. Obviously, the uncompensated signal V6 has a large phase jitter, whereas the phase vibration of the compensated signal V5 is effectively decreased.

 figure: Fig. 5

Fig. 5 Measured waveforms of the recovered 2.4GHz RF signal at the connection of a 90-km and a 10-km standard single-mode fiber spools without (A)–(C), and with (D)–(F) phase-drift cancellation.

Download Full Size | PPT Slide | PDF

In order to verify that our experimental scheme is applicable to any node of the optical loop link and the dissemination performance will not be deteriorated when arbitrarily adding a new node, we set another accessing node between a 50-km and a 50-km standard SMF spools. The same photoelectric devices are needed when testing every node. As shown in Fig. 3, EDFA is reasonably placed in the middle of the two standard SMF spools, gain of which is set to be no more than 10 dB. Apart from the different position of EDFA and accessing node, other experiment configuration is identical to the first test. As shown in Fig. 4(b), the second experiment result is ideal as before with RMS timing jitter of the compensated signal reduced to 1.76 ps, corresponding to about 0.027 rad. Our dissemination loop can support multiple users simultaneously. Though there is 3dB insertion loss at every intermediate point, proper EDFAs and electrical amplifiers can be used to amplify the desired optical signals and detected RF signals. Thus, it ensures that multiple intermediate points can be inserted in the optical loop link. It should be noted that several intermediate points along the fiber loop were tested besides 90/10km and 50/50km. Because of the similarity among the test results of different intermediate points, we just show the test results of the two typical inserting points selected in the fiber link, the most symmetric one (50/50km) and a relative most asymmetric one (90/10km).

4. Conclusion

In summary, we demonstrate an arbitrary-access stable phase dissemination scheme insensitive to GVD. Only one optical source is involved. At the same time, the proposed scheme provides a flexible and robust online insertion of additional remote nodes. Stable RF phase dissemination over a 100 km fiber-optic loop link is experimentally demonstrated and the RMS phase jitter of 2.4 GHz compensated signal is measured no more than 0.027 rad, while the RMS phase jitter of uncompensated signal is 1.87 rad during 1800-second measuring time. The results show that the proposed scheme is not only effective but also practical. Transmission distance can be further improved by adding bidirectional EDFAs.

Funding

National Basic Research Program of China (2012CB315605, 2014CB340102); National Natural Science Foundation (61531003, 61427813, 61271193); China Postdoctoral Science Foundation (2015M570056); Fund of State Key Laboratory of Information Photonics and Optical Communications.

References and links

1. 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. 1–8 (2012).

2. T. Akiyama, H. Matsuzawa, E. Haraguchi, T. Ando, and Y. Hirano, “Phase stabilized RF reference signal dissemination over optical fiber employing instantaneous frequency control by vco,” IEEE MTT-S International Microwave Symposium Digest. 217–219 (2012).

3. W. Wang, “GPS-Based Time & Phase Synchronization Processing for Distributed SAR,” IEEE Trans. Aerosp. Electron. Syst. 45(3), 1040–1051 (2009). [CrossRef]  

4. K. W. Holman, D. D. Hudson, and J. Ye, “Remote transfer of a high-stability and ultralow-jitter timing signal,” Opt. Lett. 30(10), 1225–1227 (2005). [CrossRef]  

5. 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]  

6. G. Marra, R. Slavík, H. S. Margolis, S. N. Lea, P. Petropoulos, D. J. Richardson, and P. Gill, “High-resolution microwave frequency transfer over an 86-km-long optical fiber network using a mode-locked laser,” Opt. Lett. 36(7), 511–513 (2011). [CrossRef]  

7. 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]  

8. 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]  

9. A. Zhang, Y. Dai, F. Yin, T. Ren, K. Xu, J. Li, and G. Tang, “Phase stabilized downlink transmission for wideband radio frequency signal via optical fiber link,” Opt. Express 22(18), 21560–21566 (2014). [CrossRef]  

10. 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]  

11. 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, 35–41 (2008). [CrossRef]  

12. Ł. Śliwczyński, P. Krehlik, Ł. Buczek, and M. Lipiński, “Active propagation delay stabilization for fiber-optic frequency distribution using controlled electronic delay lines,” IEEE Trans. Instrum. Meas. 60(4), 1480–1488 (2011). [CrossRef]  

13. P. Krehlik, Ł. Śliwczyński, Ł. Buczek, and M. lipiński, “Multipoint Dissemination of RF Frequency in Fiber Optic Link With Stabilized Propagation Delay,” IEEE Trans. Ultrason. Ferroeletr. Freq. Control 60(9), 1804–1810 (2013). [CrossRef]  

14. G. Grosche, O. Terra, K. Predehl, R. Holzwarth, B. Lipphardt, F. Vogt, U. Sterr, and H. Schnatz, “Optical frequency transfer via 146 km fiber link with 10−19 relative accuracy,” Opt. Lett. 34(15), 2270–2272 (2009). [CrossRef]  

15. D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014). [CrossRef]  

16. L. Yu, R. Wang, L. Lu, Y. Zhu, C. Wu, B. Zhang, and P. Wang, “Stable radio frequency dissemination by simple hybrid frequency modulation scheme,” Opt. Lett. 39(18), 5255–5258 (2014). [CrossRef]  

17. J. Wei, F. Zhang, Y. Zhou, D. Ben, and S. Pan, “Stable fiber delivery of radio-frequency signal based on passive phase correction,” Opt. Lett. 39(11), 3360–3362 (2014). [CrossRef]  

18. F. Yin, A. Zhang, Y. Dai, T. Ren, K. Xu, J. Li, J. Lin, and G. Tang, “Phase-conjugation-based fast RF phase stabilization for fiber delivery,” Opt. Express 22(1), 878–884 (2014). [CrossRef]  

19. 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]  

20. W. Li, W. Wang, W. Sun, W. Wang, and N. Zhu, “Stable radio-frequency phase distribution over optical fiber by phase-drift auto-cancellation,” Opt. Lett. 39(15), 4294–4296 (2014). [CrossRef]  

21. L. Yu, R. Wang, L. Lu, Y. Zhu, J. Zheng, C. Wu, B. Zhang, and P. Wang, “WDM-based radio frequency dissemination in a tree-topology fiber optic network,” Opt. Express 23(15), 19783–19792 (2015). [CrossRef]  

22. Y. Bai, B. Wang, C. Gao, J. Miao, X. Zhu, and L. Wang, “Fiber-based radio frequency dissemination for branching networks with passive phase-noise cancelation,” Chin. Opt. Lett. 13(6), 061201 (2015). [CrossRef]  

23. C. Gao, B. Wang, W. Chen, Y. Bai, J. Miao, X. Zhu, T. Li, and L. Wang, “Fiber-based multiple-access ultrastable frequency dissemination,” Opt. Lett. 37(22), 4690–4692 (2012). [CrossRef]  

References

  • View by:

  1. 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. 1–8 (2012).
  2. T. Akiyama, H. Matsuzawa, E. Haraguchi, T. Ando, and Y. Hirano, “Phase stabilized RF reference signal dissemination over optical fiber employing instantaneous frequency control by vco,” IEEE MTT-S International Microwave Symposium Digest. 217–219 (2012).
  3. W. Wang, “GPS-Based Time & Phase Synchronization Processing for Distributed SAR,” IEEE Trans. Aerosp. Electron. Syst. 45(3), 1040–1051 (2009).
    [Crossref]
  4. K. W. Holman, D. D. Hudson, and J. Ye, “Remote transfer of a high-stability and ultralow-jitter timing signal,” Opt. Lett. 30(10), 1225–1227 (2005).
    [Crossref]
  5. 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]
  6. G. Marra, R. Slavík, H. S. Margolis, S. N. Lea, P. Petropoulos, D. J. Richardson, and P. Gill, “High-resolution microwave frequency transfer over an 86-km-long optical fiber network using a mode-locked laser,” Opt. Lett. 36(7), 511–513 (2011).
    [Crossref]
  7. 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]
  8. 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]
  9. A. Zhang, Y. Dai, F. Yin, T. Ren, K. Xu, J. Li, and G. Tang, “Phase stabilized downlink transmission for wideband radio frequency signal via optical fiber link,” Opt. Express 22(18), 21560–21566 (2014).
    [Crossref]
  10. 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]
  11. 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, 35–41 (2008).
    [Crossref]
  12. Ł. Śliwczyński, P. Krehlik, Ł. Buczek, and M. Lipiński, “Active propagation delay stabilization for fiber-optic frequency distribution using controlled electronic delay lines,” IEEE Trans. Instrum. Meas. 60(4), 1480–1488 (2011).
    [Crossref]
  13. P. Krehlik, Ł. Śliwczyński, Ł. Buczek, and M. lipiński, “Multipoint Dissemination of RF Frequency in Fiber Optic Link With Stabilized Propagation Delay,” IEEE Trans. Ultrason. Ferroeletr. Freq. Control 60(9), 1804–1810 (2013).
    [Crossref]
  14. G. Grosche, O. Terra, K. Predehl, R. Holzwarth, B. Lipphardt, F. Vogt, U. Sterr, and H. Schnatz, “Optical frequency transfer via 146 km fiber link with 10−19 relative accuracy,” Opt. Lett. 34(15), 2270–2272 (2009).
    [Crossref]
  15. D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
    [Crossref]
  16. L. Yu, R. Wang, L. Lu, Y. Zhu, C. Wu, B. Zhang, and P. Wang, “Stable radio frequency dissemination by simple hybrid frequency modulation scheme,” Opt. Lett. 39(18), 5255–5258 (2014).
    [Crossref]
  17. J. Wei, F. Zhang, Y. Zhou, D. Ben, and S. Pan, “Stable fiber delivery of radio-frequency signal based on passive phase correction,” Opt. Lett. 39(11), 3360–3362 (2014).
    [Crossref]
  18. F. Yin, A. Zhang, Y. Dai, T. Ren, K. Xu, J. Li, J. Lin, and G. Tang, “Phase-conjugation-based fast RF phase stabilization for fiber delivery,” Opt. Express 22(1), 878–884 (2014).
    [Crossref]
  19. 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]
  20. W. Li, W. Wang, W. Sun, W. Wang, and N. Zhu, “Stable radio-frequency phase distribution over optical fiber by phase-drift auto-cancellation,” Opt. Lett. 39(15), 4294–4296 (2014).
    [Crossref]
  21. L. Yu, R. Wang, L. Lu, Y. Zhu, J. Zheng, C. Wu, B. Zhang, and P. Wang, “WDM-based radio frequency dissemination in a tree-topology fiber optic network,” Opt. Express 23(15), 19783–19792 (2015).
    [Crossref]
  22. Y. Bai, B. Wang, C. Gao, J. Miao, X. Zhu, and L. Wang, “Fiber-based radio frequency dissemination for branching networks with passive phase-noise cancelation,” Chin. Opt. Lett. 13(6), 061201 (2015).
    [Crossref]
  23. C. Gao, B. Wang, W. Chen, Y. Bai, J. Miao, X. Zhu, T. Li, and L. Wang, “Fiber-based multiple-access ultrastable frequency dissemination,” Opt. Lett. 37(22), 4690–4692 (2012).
    [Crossref]

2015 (2)

2014 (6)

2013 (3)

2012 (1)

2011 (4)

2010 (1)

2009 (2)

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, 35–41 (2008).
[Crossref]

2005 (1)

Akiyama, T.

T. Akiyama, H. Matsuzawa, E. Haraguchi, T. Ando, and Y. Hirano, “Phase stabilized RF reference signal dissemination over optical fiber employing instantaneous frequency control by vco,” IEEE MTT-S International Microwave Symposium Digest. 217–219 (2012).

Amy-Klein, A.

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, 35–41 (2008).
[Crossref]

Ando, T.

T. Akiyama, H. Matsuzawa, E. Haraguchi, T. Ando, and Y. Hirano, “Phase stabilized RF reference signal dissemination over optical fiber employing instantaneous frequency control by vco,” IEEE MTT-S International Microwave Symposium Digest. 217–219 (2012).

Bai, Y.

Ben, D.

Bertacco, E. K.

D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
[Crossref]

Buczek, L.

P. Krehlik, Ł. Śliwczyński, Ł. Buczek, and M. lipiński, “Multipoint Dissemination of RF Frequency in Fiber Optic Link With Stabilized Propagation Delay,” IEEE Trans. Ultrason. Ferroeletr. Freq. Control 60(9), 1804–1810 (2013).
[Crossref]

Ł. Śliwczyński, P. Krehlik, Ł. Buczek, and M. Lipiński, “Active propagation delay stabilization for fiber-optic frequency distribution using controlled electronic delay lines,” IEEE Trans. Instrum. Meas. 60(4), 1480–1488 (2011).
[Crossref]

Calonico, D.

D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
[Crossref]

Calosso, C. E.

D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
[Crossref]

Chang, L.

Chardonnet, 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, 35–41 (2008).
[Crossref]

Chen, W.

Clivati, C.

D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
[Crossref]

Costanzo, G. A.

D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
[Crossref]

Dai, Y.

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, 35–41 (2008).
[Crossref]

Dong, Y.

Frittelli, M.

D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
[Crossref]

Gao, C.

Gill, P.

Godone, A.

D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
[Crossref]

Grosche, G.

Haraguchi, E.

T. Akiyama, H. Matsuzawa, E. Haraguchi, T. Ando, and Y. Hirano, “Phase stabilized RF reference signal dissemination over optical fiber employing instantaneous frequency control by vco,” IEEE MTT-S International Microwave Symposium Digest. 217–219 (2012).

He, H.

Hirano, Y.

T. Akiyama, H. Matsuzawa, E. Haraguchi, T. Ando, and Y. Hirano, “Phase stabilized RF reference signal dissemination over optical fiber employing instantaneous frequency control by vco,” IEEE MTT-S International Microwave Symposium Digest. 217–219 (2012).

Holman, K. W.

Holzwarth, R.

Hou, D.

Hu, W.

Huang, S.

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. 1–8 (2012).

Hudson, D. D.

Ji, Y.

Krehlik, P.

P. Krehlik, Ł. Śliwczyński, Ł. Buczek, and M. lipiński, “Multipoint Dissemination of RF Frequency in Fiber Optic Link With Stabilized Propagation Delay,” IEEE Trans. Ultrason. Ferroeletr. Freq. Control 60(9), 1804–1810 (2013).
[Crossref]

Ł. Śliwczyński, P. Krehlik, Ł. Buczek, and M. Lipiński, “Active propagation delay stabilization for fiber-optic frequency distribution using controlled electronic delay lines,” IEEE Trans. Instrum. Meas. 60(4), 1480–1488 (2011).
[Crossref]

Lea, S. N.

Levi, F.

D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
[Crossref]

Li, J.

Li, P.

Li, T.

Li, W.

Lin, J.

lipinski, M.

P. Krehlik, Ł. Śliwczyński, Ł. Buczek, and M. lipiński, “Multipoint Dissemination of RF Frequency in Fiber Optic Link With Stabilized Propagation Delay,” IEEE Trans. Ultrason. Ferroeletr. Freq. Control 60(9), 1804–1810 (2013).
[Crossref]

Ł. Śliwczyński, P. Krehlik, Ł. Buczek, and M. Lipiński, “Active propagation delay stabilization for fiber-optic frequency distribution using controlled electronic delay lines,” IEEE Trans. Instrum. Meas. 60(4), 1480–1488 (2011).
[Crossref]

Lipphardt, B.

Liu, C.

Lopez, O.

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, 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, 35–41 (2008).
[Crossref]

Lu, L.

Margolis, H. S.

Marra, G.

Matsuzawa, H.

T. Akiyama, H. Matsuzawa, E. Haraguchi, T. Ando, and Y. Hirano, “Phase stabilized RF reference signal dissemination over optical fiber employing instantaneous frequency control by vco,” IEEE MTT-S International Microwave Symposium Digest. 217–219 (2012).

Miao, J.

Mura, A.

D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
[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, 35–41 (2008).
[Crossref]

Pan, S.

Petropoulos, P.

Poli, N.

D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
[Crossref]

Predehl, K.

Ren, T.

Richardson, D. J.

Santarelli, G.

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, 35–41 (2008).
[Crossref]

Schnatz, H.

Slavík, R.

Sliwczynski, L.

P. Krehlik, Ł. Śliwczyński, Ł. Buczek, and M. lipiński, “Multipoint Dissemination of RF Frequency in Fiber Optic Link With Stabilized Propagation Delay,” IEEE Trans. Ultrason. Ferroeletr. Freq. Control 60(9), 1804–1810 (2013).
[Crossref]

Ł. Śliwczyński, P. Krehlik, Ł. Buczek, and M. Lipiński, “Active propagation delay stabilization for fiber-optic frequency distribution using controlled electronic delay lines,” IEEE Trans. Instrum. Meas. 60(4), 1480–1488 (2011).
[Crossref]

Sterr, U.

Sun, W.

Sutyrin, D. V.

D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
[Crossref]

Tang, G.

Terra, O.

Tino, G.

D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
[Crossref]

Tjoelker, R. L.

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. 1–8 (2012).

Vogt, F.

Wang, B.

Wang, L.

Wang, P.

Wang, R.

Wang, W.

Wei, J.

Wu, C.

Wu, Z.

Xie, W.

Xu, K.

Ye, J.

Yin, F.

Yu, L.

Zhang, A.

Zhang, B.

Zhang, F.

Zhang, L.

Zhang, Z.

Zhao, J.

Zheng, J.

Zhou, Y.

Zhu, N.

Zhu, X.

Zhu, Y.

Zucco, M. E.

D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
[Crossref]

Appl. Phys. B (1)

D. Calonico, E. K. Bertacco, C. E. Calosso, C. Clivati, G. A. Costanzo, M. Frittelli, A. Godone, A. Mura, N. Poli, D. V. Sutyrin, G. Tino, M. E. Zucco, and F. Levi, ”High-accuracy coherent optical frequency transfer over a doubled 642-km fiber link,” Appl. Phys. B 117(3), 979–986 (2014).
[Crossref]

Chin. Opt. Lett. (1)

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, 35–41 (2008).
[Crossref]

IEEE Trans. Aerosp. Electron. Syst. (1)

W. Wang, “GPS-Based Time & Phase Synchronization Processing for Distributed SAR,” IEEE Trans. Aerosp. Electron. Syst. 45(3), 1040–1051 (2009).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

Ł. Śliwczyński, P. Krehlik, Ł. Buczek, and M. Lipiński, “Active propagation delay stabilization for fiber-optic frequency distribution using controlled electronic delay lines,” IEEE Trans. Instrum. Meas. 60(4), 1480–1488 (2011).
[Crossref]

IEEE Trans. Ultrason. Ferroeletr. Freq. Control (1)

P. Krehlik, Ł. Śliwczyński, Ł. Buczek, and M. lipiński, “Multipoint Dissemination of RF Frequency in Fiber Optic Link With Stabilized Propagation Delay,” IEEE Trans. Ultrason. Ferroeletr. Freq. Control 60(9), 1804–1810 (2013).
[Crossref]

Opt. Express (4)

Opt. Lett. (11)

C. Gao, B. Wang, W. Chen, Y. Bai, J. Miao, X. Zhu, T. Li, and L. Wang, “Fiber-based multiple-access ultrastable frequency dissemination,” Opt. Lett. 37(22), 4690–4692 (2012).
[Crossref]

K. W. Holman, D. D. Hudson, and J. Ye, “Remote transfer of a high-stability and ultralow-jitter timing signal,” Opt. Lett. 30(10), 1225–1227 (2005).
[Crossref]

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]

G. Marra, R. Slavík, H. S. Margolis, S. N. Lea, P. Petropoulos, D. J. Richardson, and P. Gill, “High-resolution microwave frequency transfer over an 86-km-long optical fiber network using a mode-locked laser,” Opt. Lett. 36(7), 511–513 (2011).
[Crossref]

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]

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]

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]

W. Li, W. Wang, W. Sun, W. Wang, and N. Zhu, “Stable radio-frequency phase distribution over optical fiber by phase-drift auto-cancellation,” Opt. Lett. 39(15), 4294–4296 (2014).
[Crossref]

L. Yu, R. Wang, L. Lu, Y. Zhu, C. Wu, B. Zhang, and P. Wang, “Stable radio frequency dissemination by simple hybrid frequency modulation scheme,” Opt. Lett. 39(18), 5255–5258 (2014).
[Crossref]

J. Wei, F. Zhang, Y. Zhou, D. Ben, and S. Pan, “Stable fiber delivery of radio-frequency signal based on passive phase correction,” Opt. Lett. 39(11), 3360–3362 (2014).
[Crossref]

G. Grosche, O. Terra, K. Predehl, R. Holzwarth, B. Lipphardt, F. Vogt, U. Sterr, and H. Schnatz, “Optical frequency transfer via 146 km fiber link with 10−19 relative accuracy,” Opt. Lett. 34(15), 2270–2272 (2009).
[Crossref]

Other (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. 1–8 (2012).

T. Akiyama, H. Matsuzawa, E. Haraguchi, T. Ando, and Y. Hirano, “Phase stabilized RF reference signal dissemination over optical fiber employing instantaneous frequency control by vco,” IEEE MTT-S International Microwave Symposium Digest. 217–219 (2012).

Cited By

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

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1 Diagram of the circle topology including basic optical loop link(Black line) and the expanding link(red dashed line).
Fig. 2
Fig. 2 Schematic diagram of the arbitrary-access stable phase dissemination scheme. LD: laser diode. MZM: Mach-Zehnder modulator. RF: radio frequency. PD: photo-detector. EC: electrical coupler. OC: optical coupler. EBPF: electrical bandpass filter. SMF: single-mode fiber. FM: frequency multiplier. FD: frequency divider.
Fig. 3
Fig. 3 Experimental setup of the proposed phase fluctuation cancellation scheme for arbitrary-access loop link. The node between a 90/50km and a 10/50km standard single-mode fiber spools. OSC: oscilloscope. EDFA: erbium-doped fiber amplifier. EA: electrical amplifier.
Fig. 4
Fig. 4 Measured phase differences between the recovered signal and the standard RF signal at the connection of a 90-km and a 10-km standard single-mode fiber spools (a), connection of a 50-km and a 50-km standard single-mode fiber spools (b) (red, green: compensated, blue: uncompensated;).
Fig. 5
Fig. 5 Measured waveforms of the recovered 2.4GHz RF signal at the connection of a 90-km and a 10-km standard single-mode fiber spools without (A)–(C), and with (D)–(F) phase-drift cancellation.

Equations (6)

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

V s = cos ( ω s t + φ s ) ,
V 1 = cos ( ω s t + φ s + φ p ) ,
V 2 = cos ( 2 ω s t + 2 φ s φ p ) .
V 3 = cos ( 2 ω s t + 2 φ s φ p + 2 φ a ) ,
V 4 = cos ( 2 ω s t + 2 φ s φ p + 2 φ b ) ,
V 5 = cos ( ω s t + φ s ) .

Metrics