Abstract

We describe the use of fiber Brillouin amplification (FBA) for the coherent transmission of optical frequencies over a 480 km long optical fiber link. FBA uses the transmission fiber itself for efficient, bi-directional coherent amplification of weak signals with pump powers around 30 mW. In a test setup we measured the gain and the achievable signal-to-noise ratio (SNR) of FBA and compared it to that of the widely used uni-directional Erbium doped fiber amplifiers (EDFA) and to our recently built bi-directional EDFA. We measured also the phase noise introduced by the FBA and used a new and simple technique to stabilize the frequency of the FBA pump laser. We then transferred a stabilized laser frequency over a wide area network with a total fiber length of 480 km using only one intermediate FBA station. After compensating the noise induced by the fiber, the frequency is delivered to the user end with an uncertainty below 2 × 10−18 and an instability σy(τ) = 2 × 10−14 /(τ/s).

© 2010 OSA

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    [CrossRef]
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    [CrossRef]
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2010 (2)

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

W. Lee, D. Yu, C. Park, and J. Mun, “The uncertainty associated with the weigted mean frequency of a phase-stabilized signal with white phase noise,” Metrologia 47(1), 24–32 (2010).
[CrossRef]

2009 (2)

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[CrossRef]

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

2008 (3)

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

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

G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fiber-based femtosecond lasers,” Eur. Phys. J. D 48(1), 27–33 (2008).
[CrossRef]

2007 (1)

2005 (1)

E. Rubiola, “On the measurement of frequency and of its sample variance with high-resolution counters,” Rev. Sci. Instrum. 76(5), 054703 (2005).
[CrossRef]

2004 (1)

S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306(5700), 1318–1324 (2004).
[CrossRef] [PubMed]

1994 (2)

1989 (1)

R. Tkach and A. Chraplyvy, “Fibre Brillouin amplifiers,” Opt. Quantum Electron. 21(1), S105–S112 (1989).
[CrossRef]

1986 (1)

N. Olsson and J. van der Ziel, “Cancellation of fiber loss by semi-conductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48(20), 1329 (1986).
[CrossRef]

1972 (2)

Amy-Klein, A.

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

Bergquist, J. C.

S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306(5700), 1318–1324 (2004).
[CrossRef] [PubMed]

Blake, M.

Chardonnet, Ch.

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

Chraplyvy, A.

R. Tkach and A. Chraplyvy, “Fibre Brillouin amplifiers,” Opt. Quantum Electron. 21(1), S105–S112 (1989).
[CrossRef]

Daussy, C.

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

Diddams, S. A.

S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306(5700), 1318–1324 (2004).
[CrossRef] [PubMed]

Ertmer, W.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

Feldmann, T.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

Ferreira, M.

M. Ferreira, J. Rocha, and J. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26(1), 35–44 (1994).
[CrossRef]

Friebe, J.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

Geng, J.

Grosche, G.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[CrossRef]

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

G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fiber-based femtosecond lasers,” Eur. Phys. J. D 48(1), 27–33 (2008).
[CrossRef]

Hall, J. L.

Hansch, T.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

Holzwarth, R.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[CrossRef]

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

Ippen, E.

E. Ippen and R. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21(11), 539 (1972).
[CrossRef]

Jefferts, S. R.

S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306(5700), 1318–1324 (2004).
[CrossRef] [PubMed]

Jiang, S.

Jungner, P.

Lee, W.

W. Lee, D. Yu, C. Park, and J. Mun, “The uncertainty associated with the weigted mean frequency of a phase-stabilized signal with white phase noise,” Metrologia 47(1), 24–32 (2010).
[CrossRef]

Legero, T.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[CrossRef]

Lipphardt, B.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[CrossRef]

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

G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fiber-based femtosecond lasers,” Eur. Phys. J. D 48(1), 27–33 (2008).
[CrossRef]

Lopez, O.

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

Lours, M.

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

Lu, Z.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

Ma, L. S.

Mun, J.

W. Lee, D. Yu, C. Park, and J. Mun, “The uncertainty associated with the weigted mean frequency of a phase-stabilized signal with white phase noise,” Metrologia 47(1), 24–32 (2010).
[CrossRef]

Narbonneau, F.

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

Newbury, N. R.

Oates, C. W.

S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306(5700), 1318–1324 (2004).
[CrossRef] [PubMed]

Olsson, N.

N. Olsson and J. van der Ziel, “Cancellation of fiber loss by semi-conductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48(20), 1329 (1986).
[CrossRef]

Pape, A.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

Park, C.

W. Lee, D. Yu, C. Park, and J. Mun, “The uncertainty associated with the weigted mean frequency of a phase-stabilized signal with white phase noise,” Metrologia 47(1), 24–32 (2010).
[CrossRef]

Pinto, J.

M. Ferreira, J. Rocha, and J. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26(1), 35–44 (1994).
[CrossRef]

Predehl, K.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[CrossRef]

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

Rasel, E.-M.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

Riedmann, M.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

Rocha, J.

M. Ferreira, J. Rocha, and J. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26(1), 35–44 (1994).
[CrossRef]

Rubiola, E.

E. Rubiola, “On the measurement of frequency and of its sample variance with high-resolution counters,” Rev. Sci. Instrum. 76(5), 054703 (2005).
[CrossRef]

Santarelli, G.

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

Schnatz, H.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[CrossRef]

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

G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fiber-based femtosecond lasers,” Eur. Phys. J. D 48(1), 27–33 (2008).
[CrossRef]

Smith, R. G.

Staines, S.

Sterr, U.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[CrossRef]

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

Stolen, R.

E. Ippen and R. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21(11), 539 (1972).
[CrossRef]

Swann, W. C.

Terra, O.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[CrossRef]

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

Tkach, R.

R. Tkach and A. Chraplyvy, “Fibre Brillouin amplifiers,” Opt. Quantum Electron. 21(1), S105–S112 (1989).
[CrossRef]

Udem, T.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

van der Ziel, J.

N. Olsson and J. van der Ziel, “Cancellation of fiber loss by semi-conductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48(20), 1329 (1986).
[CrossRef]

Vogt, F.

Wang, L.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

Williams, W.

Wub, T.

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

Ye, J.

Yu, D.

W. Lee, D. Yu, C. Park, and J. Mun, “The uncertainty associated with the weigted mean frequency of a phase-stabilized signal with white phase noise,” Metrologia 47(1), 24–32 (2010).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. B (1)

O. Terra, G. Grosche, K. Predehl, R. Holzwarth, T. Legero, U. Sterr, B. Lipphardt, and H. Schnatz, “Phase-coherent comparison of two optical frequency standards over 146 km using a telecommunication fiber link,” Appl. Phys. B 97(3), 541–551 (2009).
[CrossRef]

Appl. Phys. Lett. (2)

N. Olsson and J. van der Ziel, “Cancellation of fiber loss by semi-conductor laser pumped Brillouin amplification at 1.5 μm,” Appl. Phys. Lett. 48(20), 1329 (1986).
[CrossRef]

E. Ippen and R. Stolen, “Stimulated Brillouin scattering in optical fibers,” Appl. Phys. Lett. 21(11), 539 (1972).
[CrossRef]

Eur. Phys. J. D (2)

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

G. Grosche, B. Lipphardt, and H. Schnatz, “Optical frequency synthesis and measurement using fiber-based femtosecond lasers,” Eur. Phys. J. D 48(1), 27–33 (2008).
[CrossRef]

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

H. Schnatz, O. Terra, K. Predehl, T. Feldmann, T. Legero, B. Lipphardt, U. Sterr, G. Grosche, R. Holzwarth, T. Hansch, T. Udem, Z. Lu, L. Wang, W. Ertmer, J. Friebe, A. Pape, E.-M. Rasel, M. Riedmann, and T. Wub, “Phase-coherent frequency comparison of optical clocks using a telecommunication fiber link,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 57(1), 175–181 (2010).
[CrossRef]

J. Opt. Soc. Am. B (1)

Metrologia (1)

W. Lee, D. Yu, C. Park, and J. Mun, “The uncertainty associated with the weigted mean frequency of a phase-stabilized signal with white phase noise,” Metrologia 47(1), 24–32 (2010).
[CrossRef]

Opt. Lett. (2)

Opt. Quantum Electron. (2)

R. Tkach and A. Chraplyvy, “Fibre Brillouin amplifiers,” Opt. Quantum Electron. 21(1), S105–S112 (1989).
[CrossRef]

M. Ferreira, J. Rocha, and J. Pinto, “Analysis of the gain and noise characteristics of fibre Brillouin amplifiers,” Opt. Quantum Electron. 26(1), 35–44 (1994).
[CrossRef]

Rev. Sci. Instrum. (1)

E. Rubiola, “On the measurement of frequency and of its sample variance with high-resolution counters,” Rev. Sci. Instrum. 76(5), 054703 (2005).
[CrossRef]

Science (1)

S. A. Diddams, J. C. Bergquist, S. R. Jefferts, and C. W. Oates, “Standards of time and frequency at the outset of the 21st century,” Science 306(5700), 1318–1324 (2004).
[CrossRef] [PubMed]

Other (4)

E. Desurvire, Erbium-doped fiber amplifiers: principle and applications, (Wiley-Interscience publication, 1994).

K. Predehl, R. Holzwarth, T. Udem, T. W. Hänsch, O. Terra, G. Grosche, B. Lipphardt, and H. Schnatz, “Ultra Precise Frequency Dissemination across Germany - Towards a 900 km Optical Fiber Link from PTB to MPQ,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CTuS2.

F. Walls, A. Clements, C. Felton, M. Lombardi, and M. Vanek, “Extending the Range and Accuracy of Phase Noise Measurements,” National Institute of Standards and Technology (NIST) Technical Note 1337, TN129 (1990).

G. Agrawal, Applications of Nonlinear Fiber Optics, (Academic Press, 2001).

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Figures (8)

Fig. 1
Fig. 1

Set-up to measure the gain of FBA or EDFA: VA: variable attenuator, PD: photodetector, signal: signal laser with isolator, pump: pump laser, AOM: acousto-optic modulator, a 25 km fiber is used as gain medium for FBA.

Fig. 2
Fig. 2

FBA in comparison to EDFAs (uni-directional and bi-directional) for different signal powers received at the output of a 25 km fiber: (a) gain (b) SNR. The spectrum analyzer bandwidth is 100 kHz.

Fig. 3
Fig. 3

Detected heterodyne beat power (RF) obtained with FBA and with EDFA, when 5 mW signal power are injected into (a) 148 km fiber (P pump = 20 mW, νB = 10.974 GHz) and (b) 332 km fiber (P pump = 40 mW, νB = 10.970 GHz).

Fig. 4
Fig. 4

(a) Phase noise of the free-running interferometer without (black line) and with a bi-directional EDFA (red ο). (b) Phase noise of 25 km spooled SMF28 fiber without (black line) and with using FBA (blue ο).

Fig. 5
Fig. 5

(a) Measurement setup for the scattered and transmitted pump power changes. The pump is injected in the opposite direction to the signal laser. CIR: circulator and OPM: optical power meter. (signal power is about 1 μW after 148 km fiber) (b).The change of the scattered pump power when the pump frequency is swept around sig + νB ) and a Gaussian fit.

Fig. 6
Fig. 6

Brillouin amplification in a frequency transfer system, AOM: Acousto-optic modulator, PD: photodetector, FM: Faraday mirror, C1: 30/70, C2: 40/60, C3:40/60, C4:30/70 simple fiber couplers (for details see text).

Fig. 7
Fig. 7

Phase noise of the out-of-loop signal (OL) before (black dashed), and after (red solid) compensation. The green curve (ο) gives the theoretical compensation limit according to [18].

Fig. 8
Fig. 8

Out-of-loop signal (OL) with compensated (red ο) and uncompensated phase noise (black ■).

Equations (2)

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P c r i t = 21 A γ L e f f ( 1 + Δ ν l a s e r Δ ν B )
g = γ L e f f P p u m p A

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