Abstract

We present theoretical predictions and experimental measurements for the achievable phase noise, timing jitter, and frequency stability in the coherent transport of an optical frequency over a fiber-optic link. Both technical and fundamental limitations to the coherent transfer are discussed. Measurements of the coherent transfer of an optical carrier over links ranging from 38to251km demonstrate good agreement with theory. With appropriate experimental design and bidirectional transfer on a single optical fiber, the frequency instability at short times can reach the fundamental limit imposed by delay-unsuppressed phase noise from the fiber link, yielding a frequency instability that scales as link length to the 32 power. For two-way transfer on separate outgoing and return fibers, the instability is severely limited by differential fiber noise.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  3. A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, 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,” Metrologia 43, 109-120 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  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,” (2007), http://arxiv.org/abs/0711.0933v3.
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    [CrossRef] [PubMed]
  25. S.-T. Lee and C.-J. Chae, “Low-cost bidirectional optical amplifier using a unidirectional Er-doped fiber amplifier and a fiber Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett. 13, 76-78 (2001).
    [CrossRef]
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2007 (6)

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, 021101 (2007).
[CrossRef] [PubMed]

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).
[CrossRef]

S. M. Foreman, A. D. Ludlow, M. H. D. Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1-s instability at 10−17,” Phys. Rev. Lett. 99, 153601 (2007).
[CrossRef] [PubMed]

S. T. Dawkins, J. J. McFerran, and A. N. Luiten, “Considerations on the measurement of the stability of oscillators with frequency counters,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918-925 (2007).
[CrossRef] [PubMed]

J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kartner, F. Loehl, and H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett. 32, 1044-1046 (2007).
[CrossRef] [PubMed]

N. R. Newbury, P. A. Williams, and W. C. Swann, “Coherent transfer of an optical carrier over 251 km,” Opt. Lett. 32, 3056-3058 (2007).
[CrossRef] [PubMed]

2006 (4)

B. S. Sheard, M. B. Gray, and D. E. McClelland, “High-bandwidth laser frequency stabilization to a fiber-optic delay line,” Appl. Phys. Lett. 45, 8491-8499 (2006).

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

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, 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,” Metrologia 43, 109-120 (2006).
[CrossRef]

2005 (2)

E. Rubiola, “On the measurement of frequency and of its sample variance with high-resolution counters,” Rev. Sci. Instrum. 76, 054703 (2005).
[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, 203904 (2005).
[CrossRef] [PubMed]

2003 (1)

2001 (1)

S.-T. Lee and C.-J. Chae, “Low-cost bidirectional optical amplifier using a unidirectional Er-doped fiber amplifier and a fiber Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett. 13, 76-78 (2001).
[CrossRef]

1999 (1)

P. A. Williams, “Modulation phase-shift measurement of PMD using only four launched polarisation states: A new algorithm,” Electron. Lett. 35, 1578-1579 (1999).
[CrossRef]

1994 (1)

1983 (1)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Achkar, J.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, 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,” Metrologia 43, 109-120 (2006).
[CrossRef]

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic Press, 2001).

Allan, D. W.

D. B. Sullivan, D. W. Allan, D. A. Howe, and F. L. Walls, “Characterization of clocks and oscillators,” in NIST Technical Note 1337 (National Institute of Standards and Technology, 1990).

Amy-Klein, A.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 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, 203904 (2005).
[CrossRef] [PubMed]

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

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,” (2007), http://arxiv.org/abs/0711.0933v3.

O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “Fiber frequency dissemination with resolution in the 10−18 range,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2006), pp. 80-82.

Bauch, A.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, 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,” Metrologia 43, 109-120 (2006).
[CrossRef]

Bergquist, J.

W. C. Swann, L. Lorini, J. Bergquist, and N. R. Newbury, “Narrow linewidth 1.5 μm sources and the thermal limit,” in Digest of IEEE LEOS Summer Topical Meetings (IEEE, 2007), pp. 165-166.

Bergquist, J. C.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).
[CrossRef]

J. Ye, J.-L. 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.-S. Ma, “Delivery of high-stability optical and microwave frequency standards over an optical fiber network,” J. Opt. Soc. Am. B 20, 1459-1467 (2003).
[CrossRef]

J. C. Bergquist, W. M. Itano, and D. J. Wineland, in International School of Physics “Enrico Fermi,” W.Hansch and M.Inguscio, eds. (North-Holland, 1992), p. 359.

Bize, S.

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

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, 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,” Metrologia 43, 109-120 (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, 203904 (2005).
[CrossRef] [PubMed]

J. Ye, J.-L. 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.-S. Ma, “Delivery of high-stability optical and microwave frequency standards over an optical fiber network,” J. Opt. Soc. Am. B 20, 1459-1467 (2003).
[CrossRef]

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Calonico, D.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, 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,” Metrologia 43, 109-120 (2006).
[CrossRef]

Chae, C.-J.

S.-T. Lee and C.-J. Chae, “Low-cost bidirectional optical amplifier using a unidirectional Er-doped fiber amplifier and a fiber Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett. 13, 76-78 (2001).
[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, 203904 (2005).
[CrossRef] [PubMed]

Chardonnet, C.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 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, 203904 (2005).
[CrossRef] [PubMed]

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “Fiber frequency dissemination with resolution in the 10−18 range,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2006), pp. 80-82.

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,” (2007), http://arxiv.org/abs/0711.0933v3.

Chen, J.

Clairon, 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, 203904 (2005).
[CrossRef] [PubMed]

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Clarion, A.

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

Coddington, I.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).
[CrossRef]

Collett, E.

E. Collett, Polarized Light: Fundamentals and Applications (Marcel Dekker, 1992).

Coq, Y. L.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).
[CrossRef]

Dach, R.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, 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,” Metrologia 43, 109-120 (2006).
[CrossRef]

Daussy, C.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 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, 203904 (2005).
[CrossRef] [PubMed]

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,” (2007), http://arxiv.org/abs/0711.0933v3.

O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “Fiber frequency dissemination with resolution in the 10−18 range,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2006), pp. 80-82.

Dawkins, S. T.

S. T. Dawkins, J. J. McFerran, and A. N. Luiten, “Considerations on the measurement of the stability of oscillators with frequency counters,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918-925 (2007).
[CrossRef] [PubMed]

Diddams, S. A.

S. M. Foreman, A. D. Ludlow, M. H. D. Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1-s instability at 10−17,” Phys. Rev. Lett. 99, 153601 (2007).
[CrossRef] [PubMed]

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).
[CrossRef]

J. Ye, J.-L. 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.-S. Ma, “Delivery of high-stability optical and microwave frequency standards over an optical fiber network,” J. Opt. Soc. Am. B 20, 1459-1467 (2003).
[CrossRef]

Drever, R. W. P.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Feder, K. S.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).
[CrossRef]

Ford, G. M.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Foreman, S. M.

S. M. Foreman, A. D. Ludlow, M. H. D. Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1-s instability at 10−17,” Phys. Rev. Lett. 99, 153601 (2007).
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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, 021101 (2007).
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Gardner, F. M.

F. M. Gardner, Phaselock Techniques (Wiley, 1979).

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, 203904 (2005).
[CrossRef] [PubMed]

Gray, M. B.

B. S. Sheard, M. B. Gray, and D. E. McClelland, “High-bandwidth laser frequency stabilization to a fiber-optic delay line,” Appl. Phys. Lett. 45, 8491-8499 (2006).

Grosche, G.

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

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, 203904 (2005).
[CrossRef] [PubMed]

Hall, J. L.

Hlavac, R.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, 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,” Metrologia 43, 109-120 (2006).
[CrossRef]

Hollberg, L. W.

Holman, K. W.

Hough, J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Howe, D. A.

D. B. Sullivan, D. W. Allan, D. A. Howe, and F. L. Walls, “Characterization of clocks and oscillators,” in NIST Technical Note 1337 (National Institute of Standards and Technology, 1990).

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, 021101 (2007).
[CrossRef] [PubMed]

Ishiguro, M.

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

Itano, W. M.

J. C. Bergquist, W. M. Itano, and D. J. Wineland, in International School of Physics “Enrico Fermi,” W.Hansch and M.Inguscio, eds. (North-Holland, 1992), p. 359.

Jones, D. J.

Jones, R. J.

Jungner, P.

Kartner, F. X.

Kikuchi, K.

T. Okoshi and K. Kikuchi, Coherent Optical Fiber Communications (KTK Scientific Publishers, 1988).

Kim, J.

Kitching, J.

Kowalski, F. V.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

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S.-T. Lee and C.-J. Chae, “Low-cost bidirectional optical amplifier using a unidirectional Er-doped fiber amplifier and a fiber Mach-Zehnder interferometer,” IEEE Photon. Technol. Lett. 13, 76-78 (2001).
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Lemonde, P.

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Lipphardt, B.

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Loehl, F.

Lopez, O.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 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, 203904 (2005).
[CrossRef] [PubMed]

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

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,” (2007), http://arxiv.org/abs/0711.0933v3.

O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “Fiber frequency dissemination with resolution in the 10−18 range,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2006), pp. 80-82.

Lorini, L.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).
[CrossRef]

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, 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,” Metrologia 43, 109-120 (2006).
[CrossRef]

W. C. Swann, L. Lorini, J. Bergquist, and N. R. Newbury, “Narrow linewidth 1.5 μm sources and the thermal limit,” in Digest of IEEE LEOS Summer Topical Meetings (IEEE, 2007), pp. 165-166.

Lours, M.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 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, 203904 (2005).
[CrossRef] [PubMed]

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,” (2007), http://arxiv.org/abs/0711.0933v3.

O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “Fiber frequency dissemination with resolution in the 10−18 range,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2006), pp. 80-82.

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Ludlow, A. D.

S. M. Foreman, A. D. Ludlow, M. H. D. Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1-s instability at 10−17,” Phys. Rev. Lett. 99, 153601 (2007).
[CrossRef] [PubMed]

Luiten, A. N.

S. T. Dawkins, J. J. McFerran, and A. N. Luiten, “Considerations on the measurement of the stability of oscillators with frequency counters,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918-925 (2007).
[CrossRef] [PubMed]

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, 203904 (2005).
[CrossRef] [PubMed]

Ma, L. S.

Ma, L.-S.

McClelland, D. E.

B. S. Sheard, M. B. Gray, and D. E. McClelland, “High-bandwidth laser frequency stabilization to a fiber-optic delay line,” Appl. Phys. Lett. 45, 8491-8499 (2006).

McFerran, J. J.

S. T. Dawkins, J. J. McFerran, and A. N. Luiten, “Considerations on the measurement of the stability of oscillators with frequency counters,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 918-925 (2007).
[CrossRef] [PubMed]

Miranda, M. H. D.

S. M. Foreman, A. D. Ludlow, M. H. D. Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1-s instability at 10−17,” Phys. Rev. Lett. 99, 153601 (2007).
[CrossRef] [PubMed]

Munley, A. J.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Musha, M.

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

Nakagawa, K.

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

Narbonneau, F.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 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, 203904 (2005).
[CrossRef] [PubMed]

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,” (2007), http://arxiv.org/abs/0711.0933v3.

O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “Fiber frequency dissemination with resolution in the 10−18 range,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2006), pp. 80-82.

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Newbury, N. R.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).
[CrossRef]

N. R. Newbury, P. A. Williams, and W. C. Swann, “Coherent transfer of an optical carrier over 251 km,” Opt. Lett. 32, 3056-3058 (2007).
[CrossRef] [PubMed]

W. C. Swann, L. Lorini, J. Bergquist, and N. R. Newbury, “Narrow linewidth 1.5 μm sources and the thermal limit,” in Digest of IEEE LEOS Summer Topical Meetings (IEEE, 2007), pp. 165-166.

Nicholson, J. W.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).
[CrossRef]

Oates, C. W.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).
[CrossRef]

Okoshi, T.

T. Okoshi and K. Kikuchi, Coherent Optical Fiber Communications (KTK Scientific Publishers, 1988).

Parker, T.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, 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,” Metrologia 43, 109-120 (2006).
[CrossRef]

Peng, J.-L.

Petit, G.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, 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,” Metrologia 43, 109-120 (2006).
[CrossRef]

Piester, D.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, 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,” Metrologia 43, 109-120 (2006).
[CrossRef]

Quraishi, Q.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).
[CrossRef]

Robertsson, L.

Rubiola, E.

E. Rubiola, “On the measurement of frequency and of its sample variance with high-resolution counters,” Rev. Sci. Instrum. 76, 054703 (2005).
[CrossRef]

Santarelli, G.

F. Narbonneau, M. Lours, S. Bize, A. Clarion, G. Santarelli, O. Lopez, C. Daussy, A. Amy-Klein, and C. Chardonnet, “High resolution frequency standard dissemination via optical fiber metropolitan network,” Rev. Sci. Instrum. 77, 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, 203904 (2005).
[CrossRef] [PubMed]

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

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,” (2007), http://arxiv.org/abs/0711.0933v3.

O. Lopez, C. Daussy, A. Amy-Klein, C. Chardonnet, F. Narbonneau, M. Lours, and G. Santarelli, “Fiber frequency dissemination with resolution in the 10−18 range,” in Proceedings of IEEE International Frequency Control Symposium and Exposition (IEEE, 2006), pp. 80-82.

Sato, Y.

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

Schlarb, H.

Schnatz, H.

G. Grosche, B. Lipphardt, H. Schnatz, G. Santarelli, P. Lemonde, S. Bize, M. Lours, F. Narbonneau, A. Clairon, O. Lopez, A. Amy-Klein, and C. Chardonnet, “Transmission of an optical carrier frequency over a telecommunication fiber link,” in Digest of Conference on Lasers and Electro-Optics/Quantum Electronics (CLEO) (Optical Society of America, 2007), paper CMKK1.

Sheard, B. S.

B. S. Sheard, M. B. Gray, and D. E. McClelland, “High-bandwidth laser frequency stabilization to a fiber-optic delay line,” Appl. Phys. Lett. 45, 8491-8499 (2006).

Stalnaker, J. E.

S. M. Foreman, A. D. Ludlow, M. H. D. Miranda, J. E. Stalnaker, S. A. Diddams, and J. Ye, “Coherent optical phase transfer over a 32-km fiber with 1-s instability at 10−17,” Phys. Rev. Lett. 99, 153601 (2007).
[CrossRef] [PubMed]

Sullivan, D. B.

D. B. Sullivan, D. W. Allan, D. A. Howe, and F. L. Walls, “Characterization of clocks and oscillators,” in NIST Technical Note 1337 (National Institute of Standards and Technology, 1990).

Swann, W. C.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).
[CrossRef]

N. R. Newbury, P. A. Williams, and W. C. Swann, “Coherent transfer of an optical carrier over 251 km,” Opt. Lett. 32, 3056-3058 (2007).
[CrossRef] [PubMed]

W. C. Swann, L. Lorini, J. Bergquist, and N. R. Newbury, “Narrow linewidth 1.5 μm sources and the thermal limit,” in Digest of IEEE LEOS Summer Topical Meetings (IEEE, 2007), pp. 165-166.

Szymaniec, K.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, 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,” Metrologia 43, 109-120 (2006).
[CrossRef]

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, 203904 (2005).
[CrossRef] [PubMed]

Ueda, A.

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

Ueda, K.

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

Uhrich, P.

A. Bauch, J. Achkar, S. Bize, D. Calonico, R. Dach, R. Hlavac, 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,” Metrologia 43, 109-120 (2006).
[CrossRef]

Walls, F. L.

D. B. Sullivan, D. W. Allan, D. A. Howe, and F. L. Walls, “Characterization of clocks and oscillators,” in NIST Technical Note 1337 (National Institute of Standards and Technology, 1990).

Wanser, K. H.

K. H. Wanser, “Theory of thermal phase noise in michelson and Sagnac fiber interferometers,” in Proceedings of the Tenth International Conference on Optical Fiber Sensors (OFS 10), Proc. SPIE 2360, 584-587 (1994).

Ward, H.

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

Westbrook, P. S.

I. Coddington, W. C. Swann, L. Lorini, J. C. Bergquist, Y. L. Coq, C. W. Oates, Q. Quraishi, K. S. Feder, J. W. Nicholson, P. S. Westbrook, S. A. Diddams, and N. R. Newbury, “Coherent optical link over hundreds of metres and hundreds of terahertz with subfemtosecond timing jitter,” Nat. Photonics 1, 283-287 (2007).
[CrossRef]

Williams, P. A.

N. R. Newbury, P. A. Williams, and W. C. Swann, “Coherent transfer of an optical carrier over 251 km,” Opt. Lett. 32, 3056-3058 (2007).
[CrossRef] [PubMed]

P. A. Williams, “Modulation phase-shift measurement of PMD using only four launched polarisation states: A new algorithm,” Electron. Lett. 35, 1578-1579 (1999).
[CrossRef]

Wineland, D. J.

J. C. Bergquist, W. M. Itano, and D. J. Wineland, in International School of Physics “Enrico Fermi,” W.Hansch and M.Inguscio, eds. (North-Holland, 1992), p. 359.

Wong, F. N. C.

Ye, J.

Zhang, Z.

Appl. Phys. B (2)

R. W. P. Drever, J. L. Hall, F. V. Kowalski, J. Hough, G. M. Ford, A. J. Munley, and H. Ward, “Laser phase and frequency stabilization using an optical-resonator,” Appl. Phys. B 31, 97-105 (1983).
[CrossRef]

M. Musha, Y. Sato, K. Nakagawa, K. Ueda, A. Ueda, and M. Ishiguro, “Robust and precise length stabilization of a 25-km long optical fiber using an optical interferometric method with a digital phase-frequency discriminator,” Appl. Phys. B 82, 555-559 (2006).
[CrossRef]

Appl. Phys. Lett. (1)

B. S. Sheard, M. B. Gray, and D. E. McClelland, “High-bandwidth laser frequency stabilization to a fiber-optic delay line,” Appl. Phys. Lett. 45, 8491-8499 (2006).

Electron. Lett. (1)

P. A. Williams, “Modulation phase-shift measurement of PMD using only four launched polarisation states: A new algorithm,” Electron. Lett. 35, 1578-1579 (1999).
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IEEE Photon. Technol. Lett. (1)

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Figures (10)

Fig. 1
Fig. 1

Schematic of (a) phase noise and (b) frequency instability behavior for optimized optical frequency transfer over optical fiber. Dashed line indicates unlocked fiber phase noise; solid curves indicate phase noise and modified Allan deviation when the system is phase-locked.

Fig. 2
Fig. 2

Experimental setup for frequency transfer and fiber stabilization. AOM, acousto-optic modulator; CSFL, cavity-stabilized fiber laser; Det, detector; FM, Faraday mirror; OBPF, optical bandpass filter; PLL, phase-locked loop; Pol Ctrl, fiber-optic polarization controller; VCO, voltage-controlled oscillator. Thick curves are optical fiber, thin lines are free-space propagation; and dashed lines are electrical paths. Laser light is split by a wedge and cube beam splitters to act as the LO on the remote and local detectors. The remaining light is frequency shifted by AOM1 and traverses the amplified link and receives a second frequency shift from AOM2. The FM transmits 50% of the light to mix with the LO at the remote detector. The remaining light is reflected by the FM back through the link and mixes with the LO at the local detector.

Fig. 3
Fig. 3

(a) Photograph of colocated free-space transmit and receive interferometers. Dimensions 25 cm × 25 cm . (b) Frequency error ( 1 s gate time) versus time for one-way transmission of optical frequency. The interferometer is exposed to room air currents until time = 83   s , when it is covered with a box for isolation, yielding a 9 dB improvement in frequency noise. For comparison, we assembled an all-fiber interferometer and found a considerably larger standard deviation of 20 mHz under the same isolated conditions.

Fig. 4
Fig. 4

Optical time-domain reflectometer (OTDR) trace for the 38 km BRAN fiber link traversing Boulder. Each spike represents a point where the fiber emerges from the ground to a patch panel. The light traveled from NIST to NCAR Mesa lab, returned on a different fiber passed by NIST again, through University of Colorado campus (CU), to NCAR foothills lab, returned on a different fiber, took the southern route around CU, and finally returned to NIST, for a total of 38 km. The same loop could be traversed again on different fiber for a total of 76 km.

Fig. 5
Fig. 5

Phase-noise power spectral density for the full 251 km link (consisting of 76 km of installed fiber and 175 km of spooled fiber) for just the 76 km of installed fiber and for 50 km of spooled fiber.

Fig. 6
Fig. 6

Phase-noise spectra for 251 km link of the unlocked, one-way fiber noise, S fiber , (solid, gray curve); the one-way locked signal, S remote , (solid, black curve); the predicted S remote from Eq. (3.1) (dashed, brown curve), which is in good agreement; and the residual phase noise on the round-trip locked signal (solid, red curve).

Fig. 7
Fig. 7

(a) Phase-noise spectra, S remote , of the locked remote signal for various fiber links (the 251 and 38 km installed links yield significantly more residual phase noise due to greater intrinsic fiber noise). Note servo bumps at multiples of ( 1 4 τ ) in frequency. (b) Locked one-way RF power spectra at 38 km with a resolution bandwidth (RBW) of 300 Hz . The servo bumps cause strong sidebands at multiples of 1 4 τ ( 1.3 kHz ) in frequency, but there remains a central coherent peak. (Inset: Expanded view of this central coherent peak with a RBW-limited 1 Hz peak). The RF power spectra at 175 and 251 km ( RBW = 1 kHz ) show the collapse of the coherent peak at higher phase-noise levels. (c) The timing and phase jitter versus fiber link length as in [7]; jitter integrated from 0.06 Hz to 1 MHz (solid squares); jitter excluding servo bumps (open circles). The solid line is the theoretical prediction based on integrating Eq. (3.1).

Fig. 8
Fig. 8

(a) Residual fractional frequency uncertainty (modified Allan deviation) versus gate time for various fiber link lengths. Shorted indicates a link length of less than 2 m . Note: as gate time t g approaches 100 s , the interferometric noise S Int begins to dominate. The thick solid lines illustrate the power law scaling with a t g 1.6 dependence. (b) Residual fractional frequency uncertainty at a fixed 1 s gate time versus fiber link length (square points) and the prediction from Eq. (4.1). Noise differences between spooled and installed fiber contribute to the deviations from theory. All points above the curve are from links that include installed fiber; points below the curve include only spooled fiber.

Fig. 9
Fig. 9

(a) Experimental setup to replace bidirectional fiber link (single fiber) with a duplexed link and a pair of circulators. (b) Counted frequency error (difference from transmitted frequency) for a 1   h running average on the one-way locked signal after the 38 km link for the duplexed configuration (solid) compared to the bidirectional configuration (dashed). (c) Relative frequency instability (modified Allan deviation) for the duplexed configuration of the 38 km BRAN link and a 400 m spooled fiber compared to the instability for a bidirectional configuration for the 38 km BRAN link and a 400 m spool.

Fig. 10
Fig. 10

Simplified schematic of the phase-locked loop for the Doppler cancellation, which defines the various contributions to the open-loop gain (A6).

Equations (20)

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S remote ( f ) = S Int ( f ) + S D ( f ) + other terms ,
σ ν , remote 2 = κ Int 2 t g + κ D 2 L 3 t g 3 + other terms ,
S D ( f ) a ( 2 π f τ ) 2 S fiber ( f ) ,
S Int ( f ) < a ( 2 π f τ ) 2 S fiber ( f ) .
S Laser ( f ) < a S fiber ( f ) .
S RF ( f ) < a ( 2 π f τ ) 2 S fiber ( f ) ,
S fiber , PMD ( τ DGD 2 τ ) 2 S fiber ,
σ D 2 ( t g , L ) = χ a h L ν 2 c n 2 ( L 3 t g 3 ) = κ D 2 L 3 t g 3 .
φ fiber ( t ) = 0 L δ φ ( z , t ( τ z c n ) ) d z ,
φ fiber , RT ( t ) = 0 L [ δ φ ( z , t z c n ) + δ φ ( z , t ( 2 τ z c n ) ) ] d z .
φ ̃ fiber ( ω ) = 0 L e i ω z c n 1 e i ω τ δ φ ̃ ( z , ω ) d z ,
φ ̃ fiber , RT ( ω ) = 2 0 L cos ( ω ( τ z c n ) ) e i ω τ δ φ ̃ ( z , ω ) d z .
S fiber ( ω ) = φ ̃ fiber ( ω ) 2 = 0 L δ φ ̃ ( z , ω ) 2 d z ,
S fiber , RT ( ω ) = φ ̃ fiber , RT ( ω ) 2 = 2 S fiber ( ω ) ( 1 + sinc ( 2 L ω c n ) ) ,
G ( s ) = G 0 F ( s ) s 1 K ( 1 + e 2 s τ ) ,
S local ( ω ) = 1 1 + G ( ω ) 2 S fiber , RT ( ω ) ,
φ ̃ remote ( s ) = φ ̃ fiber ( s ) ( G 1 + G ) φ ̃ fiber , RT ( s ) 2 cosh ( s τ ) .
S remote ( ω ) = 0 L { i tan ( ω τ ) } sin ( ω z c n 1 ) δ φ ̃ ( z , ω ) d z 2 .
S remote ( ω ) a ( ω τ ) 2 S fiber ( ω ) ,
a L 2 S fiber 1 0 L z 2 δ φ ̃ ( z , ω ) 2 d z ,

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