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

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2013

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]

2012

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]

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]

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]

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]

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]

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]

2011

2010

2009

2008

2007

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

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]

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]

2005

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]

Achkar, J.

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]

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]

Alnis, J.

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]

Amy-Klein, A.

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]

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]

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]

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]

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]

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]

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 Rep2, 556 (2012).
[CrossRef] [PubMed]

Bauch, A.

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]

Bize, S.

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]

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]

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]

Buczek, L.

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.

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]

Chambon, D.

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]

Chang, L.

Chanteau, B.

Chardonnet, C.

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]

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]

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]

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]

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]

Chardonnet, Ch.

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]

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 Rep2, 556 (2012).
[CrossRef] [PubMed]

Clairon, A.

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]

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]

Dach, R.

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]

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. D48(1), 35–41 (2008).
[CrossRef]

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]

Daussy, Ch.

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]

Dong, Y.

Droste, S.

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]

Du, P.

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 Rep2, 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.

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]

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]

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 Rep2, 556 (2012).
[CrossRef] [PubMed]

Gill, P.

Goncharov, A.

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]

Gray, M. B.

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]

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]

Grosche, G.

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]

Guinet, M.

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]

Haboucha, A.

Hänsch, T. W.

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]

He, H.

He, Y.

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]

Herrmann, J.

Hlavac, R.

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]

Holman, K. W.

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]

Holzwarth, R.

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]

Hong, F.-L.

Hosokawa, M.

Hou, D.

Hsu, M. T. L.

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]

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]

Hu, W.

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]

Jones, D. J.

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]

Kanj, A.

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]

Krehlik, P.

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]

Kumagai, M.

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]

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]

Lea, S. N.

Legero, Th.

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]

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 Rep2, 556 (2012).
[CrossRef] [PubMed]

Lipinski, M.

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]

Littler, I. C. M.

Lopez, O.

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]

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]

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]

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]

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]

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]

Lorini, L.

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]

Lours, M.

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]

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]

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]

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]

Luiten, A. N.

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]

Margolis, H. S.

Marra, G.

McClelland, D. E.

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 Rep2, 556 (2012).
[CrossRef] [PubMed]

Mullavey, A. J.

Musha, M.

Nagano, S.

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]

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]

Nakagawa, K.

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. D48(1), 35–41 (2008).
[CrossRef]

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]

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]

Newbury, N. R.

Ning, B.

Parker, T.

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]

Petit, G.

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]

Petropoulos, P.

Piester, D.

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]

Pottie, P.-E.

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]

Predehl, K.

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]

Raupach, S. M. F.

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]

Richardson, D. J.

Rovera, D.

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]

Santarelli, G.

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]

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]

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]

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]

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]

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]

Schnatz, H.

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]

Shaddock, D. A.

Slagmolen, B. J. J.

Slavík, R.

Sliwczynski, L.

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]

Swann, W. C.

Szymaniec, K.

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]

Terra, O.

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]

Tobar, M. E.

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]

Udem, Th.

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]

Ueda, K.

Uhrich, P.

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]

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 Rep2, 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 Rep2, 556 (2012).
[CrossRef] [PubMed]

Warrington, R. B.

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]

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]

Williams, P. A.

Xie, W.

Ye, J.

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]

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 Rep2, 556 (2012).
[CrossRef] [PubMed]

Zhang, L.

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 Rep2, 556 (2012).
[CrossRef] [PubMed]

Appl. Phys. B

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]

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]

Eur. Phys. J. D

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]

IEEE Photon. Technol. Lett.

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]

IEEE Trans. Instrum. Meas.

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. Ferroelectr. Freq. Control

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]

J. Opt. Soc. Am. B

Metrologia

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]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

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]

Rev. Sci. Instrum.

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]

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

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]

Science

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]

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

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
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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]

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Figures (4)

Fig. 1
Fig. 1

Schematic for RF transfer over an optical-fiber link using passive phase conjugation based on frequency mixing. Relevant frequencies are labeled. AM: amplitude modulator; OC: optical circulator; × 2: frequency doubler; P.I. control: proportional-integral servo. Other symbols are conventional.

Fig. 2
Fig. 2

More detailed schematic of an improved phase-conjugate RF transfer system that eliminates mixer crosstalk. Two common-frequency shifters of 1.5 × RFM (indicated within the dotted box containing three mixers) help to isolate the resulting signal of Mixer 1 at ~RFM from interferences with shifted input frequency components at ~3.5 × RFM and ~2.5 × RFM.

Fig. 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.

Fig. 4
Fig. 4

Fractional frequency stability results, measured on the ICON urban network.

Equations (8)

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ϕ M ( t )= ϕ M ( t 0 )+δ ϕ M ( t;  t 0 )= ϕ M ( t 0 )+ 2π t 0 t f M ( t' )dt' ,
ϕ S ( t )= ϕ S ( t 0 )+δ ϕ S ( t;  t 0 )= ϕ S ( t 0 )+ 2π t 0 t f S ( t' )dt' ,
δ ϕ Λ ( t;  t 0 )=2π t 0 t f Λ ( t' )dt' .
ϕ MIXER1 ( tΔ t MS )=2  ϕ M ( tΔ t MS )  ϕ S ( tΔ t SM Δ t MS ).
ϕ MIXER2 ( t )= ϕ MIXER1 ( tΔ t MS ) ϕ S ( t ).
ϕ MIXER2 ( t ) = 2 [ ϕ M ( t ) ϕ S ( t )]    [δ ϕ M ( t; tΔ t SM Δ t MS ) δ ϕ S ( t; tΔ t SM Δ t MS )]    [δ ϕ M ( t; tΔ t MS )δ ϕ M ( tΔ t MS ; tΔ t SM Δ t MS )].
ϕ MIXER2 ( t )2 [ ϕ M ( t ) ϕ S ( t )].
2 [ ϕ M ( t ) ϕ S ( t )]=[δ ϕ M ( t; tΔ t SM Δ t MS )δ ϕ S ( t; tΔ t SM Δ t MS )]+ [δ ϕ M ( t; tΔ t MS )δ ϕ M ( tΔ t MS ; tΔ t SM Δ t MS )] .

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