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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 16 — Aug. 12, 2013
  • pp: 18754–18764
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Stable radio-frequency transfer over optical fiber by phase-conjugate frequency mixing

Yabai He, Brian J. Orr, Kenneth G. H. Baldwin, Michael J. Wouters, Andre N. Luiten, Guido Aben, and R. Bruce Warrington  »View Author Affiliations


Optics Express, Vol. 21, Issue 16, pp. 18754-18764 (2013)
http://dx.doi.org/10.1364/OE.21.018754


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Abstract

We demonstrate long-distance (≥100-km) synchronization of the phase of a radio-frequency reference over an optical-fiber network without needing to actively stabilize the optical path length. Frequency mixing is used to achieve passive phase-conjugate cancellation of fiber-length fluctuations, ensuring that the phase difference between the reference and synchronized oscillators is independent of the link length. The fractional radio-frequency-transfer stability through a 100-km “real-world” urban optical-fiber network is 6 × 10−17 with an averaging time of 104 s. Our compensation technique is robust, providing long-term stability superior to that of a hydrogen maser. By combining our technique with the short-term stability provided by a remote, high-quality quartz oscillator, this system is potentially applicable to transcontinental optical-fiber time and frequency dissemination where the optical round-trip propagation time is significant.

© 2013 OSA

1. Introduction

In this paper, we are concerned with highly stable transfer of a radio-frequency (RF) reference over long distances via optical fiber. Many scientific applications can benefit from low-noise transfer of RF reference signals. These include geodesy, gravitational-wave detectors, high-energy accelerators, and radio astronomy using very long baseline interferometry. For instance, in the recently-announced Square Kilometre Array (SKA) project, fiber-optic RF transfer would avoid installing a local synchronization reference (e.g., a relatively costly hydrogen maser) at each SKA radio-telescope receiver cluster. Our research points the way to cost-effective technological solutions of this type.

Many groups [1

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

,8

8. C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10-17.,” Phys. Rev. Lett. 94(20), 203904 (2005). [CrossRef] [PubMed]

17

17. M. T. L. 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]

], have achieved RF-frequency transfer over fiber-optic distances of at least 50 km, using amplitude modulation to encode a RF signal onto the optical carrier; the transfer stability and precision attained are better than those of the best conventional methods based on the GPS satellite system (i.e., a fractional frequency stability of ~10−15 with an averaging time of 104 s [18

18. A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavać, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 1015 uncertainty level,” Metrologia 43(1), 109–120 (2006). [CrossRef]

]) or on dedicated satellite transfer.

In order to attain the highest-possible stability, there is a need to address the effect of fluctuations in the optical-fiber path length (e.g., due to temperature changes or mechanical vibrations). The most commonly used remedy is to measure the round-trip phase and then to suppress the effect of phase fluctuations by either actively altering the fiber length [1

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

,8

8. C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10-17.,” Phys. Rev. Lett. 94(20), 203904 (2005). [CrossRef] [PubMed]

10

10. M. Musha, F.-L. Hong, K. Nakagawa, and K. Ueda, “Coherent optical frequency transfer over 50-km physical distance using a 120-km-long installed telecom fiber network,” Opt. Express 16(21), 16459–16466 (2008). [CrossRef] [PubMed]

,13

13. O. Lopez, A. Amy-Klein, M. Lours, C. Chardonnet, and G. Santarelli, “High-resolution microwave frequency dissemination on an 86-km urban optical link,” Appl. Phys. B 98(4), 723–727 (2010). [CrossRef]

15

15. 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(4), 511–513 (2011). [CrossRef] [PubMed]

] or indirectly by electronically pre-compensating the outgoing signal phase/frequency [1

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

,8

8. C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10-17.,” Phys. Rev. Lett. 94(20), 203904 (2005). [CrossRef] [PubMed]

,9

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

,11

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

12. M. Fujieda, M. Kumagai, and S. Nagano, “Coherent microwave transfer over a 204-km telecom fiber link by a cascaded system,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 168–174 (2010). [CrossRef] [PubMed]

,16

16. 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]

,17

17. M. T. L. 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]

,19

19. B. Ning, P. Du, D. Hou, and J. Zhao, “Phase fluctuation compensation for long-term transfer of stable radio frequency over fiber link,” Opt. Express 20(27), 28447–28454 (2012). [CrossRef] [PubMed]

,20

20. 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]

]. In the latter case, the principle of phase conjugation is sometimes used to adjust the outgoing signal phase [1

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

,8

8. C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10-17.,” Phys. Rev. Lett. 94(20), 203904 (2005). [CrossRef] [PubMed]

,11

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]

,17

17. M. T. L. 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]

,21

21. L. E. Primas, G. F. Lutes, and R. L. Sydnor, “Stabilized fiber-optic frequency distribution system,” The Telecommunications and Data Acquisition Progress Report TDA PR 42–97, 88–97 (1989). http://ipnpr.jpl.nasa.gov/progress_report/42-97/97H.pdf

,22

22. M. Calhoun, R. Sydnor, and W. Diener, “A stabilized 100-Megahertz and 1-Gigahertz reference frequency distribution for Cassini radio science,” The Interplanetary Network Progress Report IPN PR 42–148, 1–11 (2002). http://ipnpr.jpl.nasa.gov/progress_report/42-148/148L.pdf

]. In this paper, we introduce a particularly simple frequency-mixing process to achieve phase conjugation in order to passively compensate the effect of optical-fiber fluctuations in RF-over-fiber frequency transfer.

Here we combine a high-quality quartz oscillator, for short-term stability during the RTT (<1 s), with the phase-conjugate frequency-mixing technique to compensate longer-term (>1 s) phase fluctuations. A key outcome of our work is to demonstrate phase synchronization (or RF-frequency syntonization) with better stability than that of a hydrogen maser.

2. Our technique

Our passive noise-cancellation scheme can be understood simply as follows. Commencing at the local site, as in Fig. 1, the Master oscillator output with frequency RFM is frequency doubled and mixed down with the photodetector signal of frequency (RFS + Fiber) which contains both the Slave oscillator frequency RFS and the above-mentioned fiber noise contribution denoted by Fiber. The resulting Mixer 1 output signal (frequency 2 RFM – RFSFiber) is then used to modulate the drive current of Laser 1, from which the output light is sent through the optical fiber and detected at the remote site. Subsequently, the frequency of the detected signal at the remote site is thus (2 RFM – RFS), since the returning noise term Fiber algebraically cancels the phase-conjugate fiber-optic noise term. This noise-free signal is then mixed with the Slave oscillator output RFS via Mixer 2 to yield a phase-error signal to lock the Slave oscillator, with the proportional-integral (P.I.) control minimizing the difference between oscillator frequencies 2 (RFM – RFS).

The corresponding algebraic formulation is presented in detail in the Appendix, which addresses the possibility that the above Fiber noise contribution might not actually be independent of the direction of propagation and so might not be exactly cancelled out. By considering the phase contributions at each step of the RF signal propagation process, the mechanistic analysis shows that the RF-over-fiber transfer is affected by two sources of residual phase noise: (a) the phase difference between the Master RFM and Slave RFS waves accumulated during the last round trip – this corresponds to their short-term passive stability; (b) the phase difference associated with the possibly different transit times for propagation in opposite directions (e.g., as may result from birefrigence in an optical fiber). In general, minimization of these two sources of residual phase noise is required to enable stable phase transfer from Master RFM to Slave RFS.

Our RF-dissemination method relies on accurate generation of the desired phase-conjugate signal via Mixer 1, as shown in Fig. 1; the isolation between the ports of this analog double-balanced mixer is typically ~40 dB or less. RF leakage is expected to degrade the performance if the desired product frequency of the mixer is similar to that of the inputs.

We have therefore introduced two additional common-frequency shifters (by an amount of 1.5 × RFM in this case), as shown within the dotted box with three mixers in Fig. 2. The output component of Mixer 1 can then be isolated from its input frequency components. Various RF bandpass filters are used to select relevant RF components. Two sets of optical bandpass filters (each with passwidth ~1.3 nm FWHM and suppression ratio >60 dB) allow the detectors to receive light only from opposite lasers operating at different wavelengths.

3. Experimental tests of our technique

To demonstrate that the phase-error signal detected is immune to fiber-length fluctuations, a free-space delay line was inserted temporarily into the fiber-optic link. The length of the delay line could be adjusted over 40 cm to generate a significant (~1/5 of a period after a round trip) phase change to the 80-MHz RF signal. In this measurement, a signal taken from the Master RF oscillator was used as the Slave RFS signal, with the quartz oscillator itself deactivated. As expected, the phase-error signal of Mixer 2 remained unchanged while the delay line was scanned, whereas the delay-line contribution (as measured by the out-of-loop phase check 2 mixer) varied correspondingly.

In Experiment I, our phase-conjugate RF-dissemination system was tested by transmitting the RF-modulated light over 20 km of single-mode optical fiber on a spool in our laboratory. In Experiment II, the system was tested using a long-distance “real-world” urban optical-fiber network. This was carried out on the Intra-governmental Communications Network (ICON) in Canberra, Australia’s capital city; it provides 100 km of dark single-mode fiber around the city in a loop accessible from the Australian National University (ANU) campus. Both of these experiments employed modern single-mode fiber with attenuation less than 0.3 dB/km.

3.1 Experiment I: frequency stability results for RF transmission over a 20-km fiber spool

Figure 3
Fig. 3 Fractional frequency stability results, expressed as the Allan deviation σ(τ) for averaging time τ, comparing RF-transfer stability on a 20-km fiber spool with the stability of other system components.
presents Allan deviation plots for a number of baseline measurements in our laboratory. Trace (i) shows the phase-detection noise floor of the RF phasemeter [23

23. M. T. L. Hsu, I. C. M. Littler, D. A. Shaddock, J. Herrmann, R. B. Warrington, and M. B. Gray, “Subpicometer length measurement using heterodyne laser interferometry and all-digital rf phase meters,” Opt. Lett. 35(24), 4202–4204 (2010). [CrossRef] [PubMed]

] used to measure the RF transfer stability “out-of-loop” as indicated in Figs. 1 and 2. Traces (ii) and (iii) show the specified stability of the remote quartz oscillator and our measurement of two independent hydrogen masers (constructed at NMI), respectively. Trace (ii) indicates that the free-running quartz oscillator frequency RFS has good short-term stability (τ < 1 s) but that additional stabilization is required on longer time scales.

The result for our passive phase-conjugate RF-stabilization technique using a 20-km single-mode optical fiber spool in the laboratory is shown in trace (iv). It indicates a frequency-transfer stability of 6 × 10−17 at an averaging time τ = 104 s; this matches or is better than that of the hydrogen maser for integration times greater than 10 s.

3.2 Experiment II: results for RF transmission over the 100-km ICON urban fiber network

Allan deviation plots for our frequency-stabilization experiments on the 100-km ICON fiber network, are presented in Fig. 4
Fig. 4 Fractional frequency stability results, measured on the ICON urban network.
, with various system configurations. Trace (i) again shows the noise floor of the RF phasemeter, while trace (ii) shows ICON’s intrinsic fiber noise (measured by a digital technique [17

17. M. T. L. 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]

,23

23. M. T. L. Hsu, I. C. M. Littler, D. A. Shaddock, J. Herrmann, R. B. Warrington, and M. B. Gray, “Subpicometer length measurement using heterodyne laser interferometry and all-digital rf phase meters,” Opt. Lett. 35(24), 4202–4204 (2010). [CrossRef] [PubMed]

,26

26. A. J. Mullavey, B. J. J. Slagmolen, D. A. Shaddock, and D. E. McClelland, “Stable transfer of an optical frequency standard via a 4.6 km optical fiber,” Opt. Express 18(5), 5213–5220 (2010). [CrossRef] [PubMed]

]). Traces (iii) and (iv) were recorded using the phase-conjugate RF-transfer system, not only with the original 100-km length of the ICON network (trace (iii)) but also augmented by an additional 50-km fiber spool (trace (iv)). The fractional frequency stability for the 100-km ICON network is 6 × 10−17 (with an averaging time τ = 104 s), the same as in the laboratory experiments on the 20-km fiber spool shown in Fig. 3(iv). This confirms that in-fiber path-length fluctuations have effectively been cancelled by using our passive phase-conjugate compensation scheme based on frequency mixing, as already suggested by the earlier free-space delay-line test. Finally, trace (v) of Fig. 4 shows the corresponding fractional frequency-transfer stability recorded with a relatively short (10-m) fiber cable; at an averaging time τ = 104 s, it is ~2.5 × 10−17 – approximately half that recorded with the 100-km fiber link.

The results indicate that, for RF transfer on the real-world ICON fiber-optic network over distances up to ~150 km and with an averaging time τ of more than ~200 s, our phase-conjugate, frequency-mixing system can yield fractional stabilities that are better than those typically obtained with a hydrogen maser as in Fig. 3(iii). Likewise, fractional instabilities below 10−15 are maintained with averaging times τ above ~2 × 103 s (i.e., ~0.5 h).

4. Conclusion

In summary, we have shown that RF-phase synchronization and RF-frequency syntonization can be achieved with high stability over fiber networks up to 150 km in length, and without optical amplification. This is achieved by means of a simple, relatively inexpensive system that combines the short-term stability of a remotely located high-quality quartz oscillator, with stabilization on longer time scales provided by a distinctive passive phase-conjugate approach based on frequency mixing.

Our 100-km performance trial of this RF transfer system over a real-world urban fiber-optic network yields a fractional frequency-transfer stability σ(τ) = 6 × 10−17 for an averaging time τ = 104 s. The long-term stability (above τ ≈102 s) of our frequency-mixing phase-conjugate RF-transfer system is superior to that of an independent hydrogen maser, obviating the need for such an expensive and maintenance-intensive reference source at each remote location.

In addition, the short-term stability of this system is potentially applicable to very long (>1000 km) fiber-optic networks where the round-trip time would otherwise limit the frequency stability over such time scales. This work is a first step towards developing techniques for time and frequency dissemination via optical fiber across the Australian continent (>3000 km). This includes applications such as the SKA project, for which our technique could be used to greatly reduce the number of relatively expensive hydrogen masers that would otherwise need to be located at SKA radio-telescope receivers.

Appendix

In this Appendix, we present the algebraic framework for our approach to RF-over-fiber transfer, based on passive phase conjugation using frequency-mixing. The algebra and associated mechanistic details follow the system layout depicted in Fig. 1.

It should be noted that the RF signals appear in different manifestations during the various stages of the RF-over-fiber transfer process. For instance, electronic voltages at various radio frequencies are converted into amplitude modulation of optical carrier waves (from both Laser 1 and Laser 2) and then converted back (by photodetectors PD2 and PD1, respectively) into electronic signals. Although these RF and optical signals carry phase information, they are generated and observed as amplitudes, rather than via direct phase measurements.

δϕΛ(t; t0)=2πt0tfΛ(t')dt'.
(3)

ϕMIXER1(tΔtMS)=2 ϕM(tΔtMS) ϕS(tΔtSMΔtMS).
(4)

The light carrying this phase-difference information propagates back after an interval ΔtMS to the Remote site at time t, to be mixed at Mixer 2 with the instantaneous phase information from Slave RFS. This generates the phase-difference output at Mixer 2 at time t, as follows:

ϕMIXER2(t)=ϕMIXER1(tΔtMS)ϕS(t).
(5)

By substituting Eq. (4) into Eq. (5), then manipulating and re-arranging the integrals that correspond to Eq. (5) via Eqs. (1)-(3), it can be shown that:

ϕMIXER2(t) = 2 [ϕM(t)ϕS(t)]   [δϕM(t; tΔtSMΔtMS) δϕS(t; tΔtSMΔtMS)]   [δϕM(t; tΔtMS)δϕM(tΔtMS; tΔtSMΔtMS)].
(6)

It should be noted that the three square-bracketed terms on the right-hand-side of Eq. (6), which result from re-arrangement of Eq. (5), do not represent three separate physical processes. They merely assist our understanding of the source of various noise contributions.

In Eq. (6), the first square-bracketed term [ϕM(t)ϕS(t)] corresponds to the phase difference between the Master RFM and Slave RFS oscillators. This term dominates the other two square-bracketed terms (as will be further explained below). This leads to:

ϕMIXER2(t)2 [ϕM(t)ϕS(t)].
(7)

This is consistent with our description in Section 2, where the Mixer 2 output represents the phase difference between the Master RFM and Slave RFS oscillators; it can thus serve as an error signal for phase locking of the Slave RFS oscillator to the Master RFM oscillator.

Let us check now the residual contributions of the other two terms in Eq. (6). Under phase-locked conditions, ϕMIXER2(t) in Eq. (6) is reduced to zero by feedback control of the Slave RFS oscillator. It follows that Eq. (6) can be re-arranged, which leads to:

2 [ϕM(t)ϕS(t)]=[δϕM(t; tΔtSMΔtMS)δϕS(t; tΔtSMΔtMS)]+[δϕM(t; tΔtMS)δϕM(tΔtMS; tΔtSMΔtMS)].
(8)

Therefore, the final quality of phase locking (in which the error signal ϕMIXER2(t) needs to be set to zero) is limited by the two residual terms on the right-hand-side of Eq. (8).

The second term, [δϕM(t; tΔtMS)δϕM(tΔtMS; tΔtSMΔtMS)], corresponds to the phase difference acting on the Master RFM signal that arises from the different propagation times for light travelling in opposite directions. The two terms δϕM(t; tΔtMS) and δϕM(tΔtMS; tΔtSMΔtMS) correspond here to the fiber noise that was simply labeled as “Fiber” for either direction in the terse description of Section 2 and that therefore resulted in their cancellation. However, in this more general treatment, ΔtSM and ΔtSM now also include additional propagation times inside the Local and Remote electro-optical transfer units, which could create a phase offset between the Remote RFS and Local RFM waves. Furthermore, an imbalance in this term could be generated, for example, by rapid fluctuations or vibrations of optical-fiber length, by changes of stress-induced birefringence and polarization of the optical-carrier wave in the fiber-optical link, or by a wavelength change of the optical carrier in a dispersive fiber. Use of fast optical polarization scramblers could randomize and help average out the polarization effect. Likewise, a local flywheel (e.g., a high-quality quartz oscillator, as employed in our experiments) can be used at the remote location to provide good short-term stability and overcome rapid fluctuations.

The two sources of residual phase noise identified on the right-hand side of Eq. (8) are common to many forms of fiber-optic frequency transfer. For RF-over-fiber transfer systems such as that presented in this paper, any minimization of fluctuations in these residual phase-shift contributions will enable satisfactory phase transfer of ϕM to ϕS, from Master RFM to Slave RFS.

Acknowledgments

This work has received support from the Australian Research Council through its Linkage Project funding scheme (project number LP110100270) and a Future Fellowship (project number FT0991631) awarded to one of us (A. L.). We acknowledge helpful discussions with, and advice from, J. Chow, P. Fisk, A. Gajaweera, M. Gray, M. Hsu, S. Quigg, G. Santarelli, S. Schediwy, and D. Shaddock.

References and links

1.

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

2.

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O. Lopez, A. Kanj, P.-E. Pottie, D. Rovera, J. Achkar, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network,” Appl. Phys. B 110(1), 3–6 (2013). [CrossRef]

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C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10-17.,” Phys. Rev. Lett. 94(20), 203904 (2005). [CrossRef] [PubMed]

9.

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

10.

M. Musha, F.-L. Hong, K. Nakagawa, and K. Ueda, “Coherent optical frequency transfer over 50-km physical distance using a 120-km-long installed telecom fiber network,” Opt. Express 16(21), 16459–16466 (2008). [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.

M. Fujieda, M. Kumagai, and S. Nagano, “Coherent microwave transfer over a 204-km telecom fiber link by a cascaded system,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 168–174 (2010). [CrossRef] [PubMed]

13.

O. Lopez, A. Amy-Klein, M. Lours, C. Chardonnet, and G. Santarelli, “High-resolution microwave frequency dissemination on an 86-km urban optical link,” Appl. Phys. B 98(4), 723–727 (2010). [CrossRef]

14.

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]

15.

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(4), 511–513 (2011). [CrossRef] [PubMed]

16.

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]

17.

M. T. L. 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]

18.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavać, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 1015 uncertainty level,” Metrologia 43(1), 109–120 (2006). [CrossRef]

19.

B. Ning, P. Du, D. Hou, and J. Zhao, “Phase fluctuation compensation for long-term transfer of stable radio frequency over fiber link,” Opt. Express 20(27), 28447–28454 (2012). [CrossRef] [PubMed]

20.

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]

21.

L. E. Primas, G. F. Lutes, and R. L. Sydnor, “Stabilized fiber-optic frequency distribution system,” The Telecommunications and Data Acquisition Progress Report TDA PR 42–97, 88–97 (1989). http://ipnpr.jpl.nasa.gov/progress_report/42-97/97H.pdf

22.

M. Calhoun, R. Sydnor, and W. Diener, “A stabilized 100-Megahertz and 1-Gigahertz reference frequency distribution for Cassini radio science,” The Interplanetary Network Progress Report IPN PR 42–148, 1–11 (2002). http://ipnpr.jpl.nasa.gov/progress_report/42-148/148L.pdf

23.

M. T. L. Hsu, I. C. M. Littler, D. A. Shaddock, J. Herrmann, R. B. Warrington, and M. B. Gray, “Subpicometer length measurement using heterodyne laser interferometry and all-digital rf phase meters,” Opt. Lett. 35(24), 4202–4204 (2010). [CrossRef] [PubMed]

24.

Y. He, M. T. L. Hsu, M. J. Wouters, M. B. Gray, R. B. Warrington, B. J. Orr, D. A. Shaddock, K. G. H. Baldwin, and G. Aben, “An optical fiber-based system for high-stability distribution of reference radio-frequencies,” in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim 2011, (Optical Society of America, 2011), paper C1126. http://www.opticsinfobase.org/abstract.cfm?URI=CLEOPR-2011-C1126 [CrossRef]

25.

K. G. H. Baldwin, Y. He, M. T. L. Hsu, M. J. Wouters, M. B. Gray, B. J. Orr, A. N. Luiten, S. W. Schediwy, J. H. Chow, D. A. Shaddock, G. Aben, P. T. H. Fisk, and R. B. Warrington, “Analog and all-digital frequency distribution via optical fiber links,” in Conference on Lasers and Electro-Optics 2012, OSA Technical Digest (online) (Optical Society of America, 2012), paper CTh4A.2. http://www.opticsinfobase.org/abstract.cfm?URI=CLEO_SI-2012-CTh4A.2&origin=search [CrossRef]

26.

A. J. Mullavey, B. J. J. Slagmolen, D. A. Shaddock, and D. E. McClelland, “Stable transfer of an optical frequency standard via a 4.6 km optical fiber,” Opt. Express 18(5), 5213–5220 (2010). [CrossRef] [PubMed]

27.

P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B 25(8), 1284–1293 (2008). [CrossRef]

OCIS Codes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(120.5050) Instrumentation, measurement, and metrology : Phase measurement
(060.5625) Fiber optics and optical communications : Radio frequency photonics

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: May 2, 2013
Revised Manuscript: July 17, 2013
Manuscript Accepted: July 21, 2013
Published: July 30, 2013

Citation
Yabai He, Brian J. Orr, Kenneth G. H. Baldwin, Michael J. Wouters, Andre N. Luiten, Guido Aben, and R. Bruce Warrington, "Stable radio-frequency transfer over optical fiber by phase-conjugate frequency mixing," Opt. Express 21, 18754-18764 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-16-18754


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References

  1. F. Narbonneau, M. Lours, S. Bize, A. Clairon, G. Santarelli, O. Lopez, Ch. Daussy, A. Amy-Klein, and Ch. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum.77(6), 064701 (2006). [CrossRef]
  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]
  3. G. Marra, H. S. Margolis, and D. J. Richardson, “Dissemination of an optical frequency comb over fiber with 3 × 10-18 fractional accuracy,” Opt. Express20(2), 1775–1782 (2012). [CrossRef] [PubMed]
  4. K. Predehl, G. Grosche, S. M. F. Raupach, S. Droste, O. Terra, J. Alnis, Th. Legero, T. W. Hänsch, Th. Udem, R. Holzwarth, and H. Schnatz, “A 920-kilometer optical fiber link for frequency metrology at the 19th decimal place,” Science336(6080), 441–444 (2012). [CrossRef] [PubMed]
  5. O. Lopez, A. Haboucha, B. Chanteau, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Ultra-stable long distance optical frequency distribution using the Internet fiber network,” Opt. Express20(21), 23518–23526 (2012). [CrossRef] [PubMed]
  6. O. Lopez, A. Kanj, P.-E. Pottie, D. Rovera, J. Achkar, C. Chardonnet, A. Amy-Klein, and G. Santarelli, “Simultaneous remote transfer of accurate timing and optical frequency over a public fiber network,” Appl. Phys. B110(1), 3–6 (2013). [CrossRef]
  7. 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 Rep2, 556 (2012). [CrossRef] [PubMed]
  8. C. Daussy, O. Lopez, A. Amy-Klein, A. Goncharov, M. Guinet, C. Chardonnet, F. Narbonneau, M. Lours, D. Chambon, S. Bize, A. Clairon, G. Santarelli, M. E. Tobar, and A. N. Luiten, “Long-distance frequency dissemination with a resolution of 10-17.,” Phys. Rev. Lett.94(20), 203904 (2005). [CrossRef] [PubMed]
  9. O. Lopez, A. Amy-Klein, C. Daussy, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “86-km optical link with a resolution of 2 × 10−18 for RF frequency transfer,” Eur. Phys. J. D48(1), 35–41 (2008). [CrossRef]
  10. M. Musha, F.-L. Hong, K. Nakagawa, and K. Ueda, “Coherent optical frequency transfer over 50-km physical distance using a 120-km-long installed telecom fiber network,” Opt. Express16(21), 16459–16466 (2008). [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. M. Fujieda, M. Kumagai, and S. Nagano, “Coherent microwave transfer over a 204-km telecom fiber link by a cascaded system,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control57(1), 168–174 (2010). [CrossRef] [PubMed]
  13. O. Lopez, A. Amy-Klein, M. Lours, C. Chardonnet, and G. Santarelli, “High-resolution microwave frequency dissemination on an 86-km urban optical link,” Appl. Phys. B98(4), 723–727 (2010). [CrossRef]
  14. 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]
  15. 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(4), 511–513 (2011). [CrossRef] [PubMed]
  16. 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]
  17. M. T. L. 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]
  18. A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavać, L. Lorini, T. Parker, G. Petit, D. Piester, K. Szymaniec, and P. Uhrich, “Comparison between frequency standards in Europe and the USA at the 10−15 uncertainty level,” Metrologia43(1), 109–120 (2006). [CrossRef]
  19. B. Ning, P. Du, D. Hou, and J. Zhao, “Phase fluctuation compensation for long-term transfer of stable radio frequency over fiber link,” Opt. Express20(27), 28447–28454 (2012). [CrossRef] [PubMed]
  20. 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]
  21. L. E. Primas, G. F. Lutes, and R. L. Sydnor, “Stabilized fiber-optic frequency distribution system,” The Telecommunications and Data Acquisition Progress Report TDA PR 42–97, 88–97 (1989). http://ipnpr.jpl.nasa.gov/progress_report/42-97/97H.pdf
  22. M. Calhoun, R. Sydnor, and W. Diener, “A stabilized 100-Megahertz and 1-Gigahertz reference frequency distribution for Cassini radio science,” The Interplanetary Network Progress Report IPN PR 42–148, 1–11 (2002). http://ipnpr.jpl.nasa.gov/progress_report/42-148/148L.pdf
  23. M. T. L. Hsu, I. C. M. Littler, D. A. Shaddock, J. Herrmann, R. B. Warrington, and M. B. Gray, “Subpicometer length measurement using heterodyne laser interferometry and all-digital rf phase meters,” Opt. Lett.35(24), 4202–4204 (2010). [CrossRef] [PubMed]
  24. Y. He, M. T. L. Hsu, M. J. Wouters, M. B. Gray, R. B. Warrington, B. J. Orr, D. A. Shaddock, K. G. H. Baldwin, and G. Aben, “An optical fiber-based system for high-stability distribution of reference radio-frequencies,” in Proceedings of the International Quantum Electronics Conference and Conference on Lasers and Electro-Optics Pacific Rim 2011, (Optical Society of America, 2011), paper C1126. http://www.opticsinfobase.org/abstract.cfm?URI=CLEOPR-2011-C1126 [CrossRef]
  25. K. G. H. Baldwin, Y. He, M. T. L. Hsu, M. J. Wouters, M. B. Gray, B. J. Orr, A. N. Luiten, S. W. Schediwy, J. H. Chow, D. A. Shaddock, G. Aben, P. T. H. Fisk, and R. B. Warrington, “Analog and all-digital frequency distribution via optical fiber links,” in Conference on Lasers and Electro-Optics 2012, OSA Technical Digest (online) (Optical Society of America, 2012), paper CTh4A.2. http://www.opticsinfobase.org/abstract.cfm?URI=CLEO_SI-2012-CTh4A.2&origin=search [CrossRef]
  26. A. J. Mullavey, B. J. J. Slagmolen, D. A. Shaddock, and D. E. McClelland, “Stable transfer of an optical frequency standard via a 4.6 km optical fiber,” Opt. Express18(5), 5213–5220 (2010). [CrossRef] [PubMed]
  27. P. A. Williams, W. C. Swann, and N. R. Newbury, “High-stability transfer of an optical frequency over long fiber-optic links,” J. Opt. Soc. Am. B25(8), 1284–1293 (2008). [CrossRef]

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