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

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References

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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).
[Crossref]

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.

Holzwarth, R.

Hosokawa, M.

Hou, D.

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]

Lin, J.

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).
[Crossref]

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).
[Crossref] [PubMed]

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)

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]

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]

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]

Other (3)

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

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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