Abstract

We developed a new radio frequency dissemination system based on an optical fiber link. A 1.55 μm mode-locked fiber laser was used as optical transmitter in the system. To actively reduce the phase fluctuation induced by the fiber length variations with high resolution, we proposed a novel compensation technique. In our technique, we directly control the phase of optical pulses generated by the laser to compensate the fluctuation. The phase-controlling method is based on both pump power modulation and cavity length adjusting. We performed the transfer in a 22-km outdoor fiber link, with a transfer stability of 3.7 × 10−14 at 1 s and 6.6 × 10−18 at 16000 s. The integrated timing jitter in 24 hours was reduced from 14 ps to 35 fs.

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References

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  1. J. Levine, “A review of time and frequency transfer methods,” Metrologia45(6), S162–S174 (2008).
    [CrossRef]
  2. S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum.78(2), 021101 (2007).
    [CrossRef] [PubMed]
  3. K. Minoshima and H. Matsumoto, “In-situ measurements of shapes and thickness of optical parts by femtosecond two-color interferometry,” Opt. Commun.138(1-3), 6–10 (1997).
    [CrossRef]
  4. J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications (Kluwer Academic Publishers / Springer, 2004).
  5. J. F. Cliche and B. Shillue, “Precision timing control for radioastronomy: maintaining femtosecond synchronization in the Atacama Large Millimeter Array,” IEEE Contr. Syst. Mag.26(1), 19–26 (2006).
    [CrossRef]
  6. Y. F. Chen, J. Jiang, and D. J. Jones, “Remote distribution of a mode-locked pulse train with sub 40-as jitter,” Opt. Express14(25), 12134–12144 (2006).
    [CrossRef] [PubMed]
  7. E. Allaria, C. Callegari, D. Cocco, W. M. Fawley, M. Kiskinova, C. Masciovecchio, and F. Parmigiani, “The FERMI@Elettra free-electron-laser source for coherent x-ray physics: photon properties, beam transport system and applications,” New J. Phys.12(7), 075002 (2010).
    [CrossRef]
  8. P. R. Bolton, “Noninvasive laser probing of ultrashort single electron bunches for accelerator and light source development,” Int. J. Mod. Phys. B21(03n04), 527–539 (2007).
    [CrossRef]
  9. L. S. Ma, P. Jungner, J. Ye, and J. L. Hall, “Delivering the same optical frequency at two places: accurate cancellation of phase noise introduced by an optical fiber or other time-varying path,” Opt. Lett.19(21), 1777–1779 (1994).
    [CrossRef] [PubMed]
  10. K. W. Holman, D. J. Jones, D. D. Hudson, and J. Ye, “Precise frequency transfer through a fiber network by use of 1.5-microm mode-locked sources,” Opt. Lett.29(13), 1554–1556 (2004).
    [CrossRef] [PubMed]
  11. K. W. Holman, D. D. Hudson, J. Ye, and D. J. Jones, “Remote transfer of a high-stability and ultralow-jitter timing signal,” Opt. Lett.30(10), 1225–1227 (2005).
    [CrossRef] [PubMed]
  12. J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett.32(9), 1044–1046 (2007).
    [CrossRef] [PubMed]
  13. J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics2(12), 733–736 (2008).
    [CrossRef]
  14. G. Marra, H. S. Margolis, S. N. Lea, and P. Gill, “High-stability microwave frequency transfer by propagation of an optical frequency comb over 50 km of optical fiber,” Opt. Lett.35(7), 1025–1027 (2010).
    [CrossRef] [PubMed]
  15. G. Marra, R. Slavík, H. S. Margolis, S. N. Lea, P. Petropoulos, D. J. Richardson, and P. Gill, “High-resolution microwave frequency transfer over an 86-km-long optical fiber network using a mode-locked laser,” Opt. Lett.36(4), 511–513 (2011).
    [CrossRef] [PubMed]
  16. D. Hou, P. Li, C. Liu, J. Zhao, and Z. Zhang, “Long-term stable frequency transfer over an urban fiber link using microwave phase stabilization,” Opt. Express19(2), 506–511 (2011).
    [CrossRef] [PubMed]
  17. D. D. Hudson, S. M. Foreman, S. T. Cundiff, and J. Ye, “Synchronization of mode-locked femtosecond lasers through a fiber link,” Opt. Lett.31(13), 1951–1953 (2006).
    [CrossRef] [PubMed]
  18. A. Yariv, Quantum Electronics Third Edition (John Wiley & Sons, 1989).
  19. A. Maitland and M. H. Dumn, Laser Physics (North-Holland Publishing Company, 1969).
  20. N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B78(3-4), 321–324 (2004).
    [CrossRef]
  21. W. K. Tan, H. Y. Wong, A. E. Kelly, M. Sorel, J. H. Marsh, and A. C. Bryce, “Temperature behaviour of pulse repetition frequency in passively mode-locked InGaAsP/InP laser diode - Experimental results and simple model,” IEEE J. Sel. Top. Quantum Electron.13(5), 1209–1214 (2007).
    [CrossRef]
  22. E. N. Ivanov, S. A. Diddams, and L. Hollberg, “Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a femtosecond laser,” IEEE J. Sel. Top. Quantum Electron.9(4), 1059–1065 (2003).
    [CrossRef]
  23. 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]

2012 (1)

2011 (2)

2010 (2)

E. Allaria, C. Callegari, D. Cocco, W. M. Fawley, M. Kiskinova, C. Masciovecchio, and F. Parmigiani, “The FERMI@Elettra free-electron-laser source for coherent x-ray physics: photon properties, beam transport system and applications,” New J. Phys.12(7), 075002 (2010).
[CrossRef]

G. Marra, H. S. Margolis, S. N. Lea, and P. Gill, “High-stability microwave frequency transfer by propagation of an optical frequency comb over 50 km of optical fiber,” Opt. Lett.35(7), 1025–1027 (2010).
[CrossRef] [PubMed]

2008 (2)

J. Levine, “A review of time and frequency transfer methods,” Metrologia45(6), S162–S174 (2008).
[CrossRef]

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics2(12), 733–736 (2008).
[CrossRef]

2007 (4)

J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett.32(9), 1044–1046 (2007).
[CrossRef] [PubMed]

W. K. Tan, H. Y. Wong, A. E. Kelly, M. Sorel, J. H. Marsh, and A. C. Bryce, “Temperature behaviour of pulse repetition frequency in passively mode-locked InGaAsP/InP laser diode - Experimental results and simple model,” IEEE J. Sel. Top. Quantum Electron.13(5), 1209–1214 (2007).
[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]

P. R. Bolton, “Noninvasive laser probing of ultrashort single electron bunches for accelerator and light source development,” Int. J. Mod. Phys. B21(03n04), 527–539 (2007).
[CrossRef]

2006 (3)

2005 (1)

2004 (2)

K. W. Holman, D. J. Jones, D. D. Hudson, and J. Ye, “Precise frequency transfer through a fiber network by use of 1.5-microm mode-locked sources,” Opt. Lett.29(13), 1554–1556 (2004).
[CrossRef] [PubMed]

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B78(3-4), 321–324 (2004).
[CrossRef]

2003 (1)

E. N. Ivanov, S. A. Diddams, and L. Hollberg, “Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a femtosecond laser,” IEEE J. Sel. Top. Quantum Electron.9(4), 1059–1065 (2003).
[CrossRef]

1997 (1)

K. Minoshima and H. Matsumoto, “In-situ measurements of shapes and thickness of optical parts by femtosecond two-color interferometry,” Opt. Commun.138(1-3), 6–10 (1997).
[CrossRef]

1994 (1)

Allaria, E.

E. Allaria, C. Callegari, D. Cocco, W. M. Fawley, M. Kiskinova, C. Masciovecchio, and F. Parmigiani, “The FERMI@Elettra free-electron-laser source for coherent x-ray physics: photon properties, beam transport system and applications,” New J. Phys.12(7), 075002 (2010).
[CrossRef]

Bolton, P. R.

P. R. Bolton, “Noninvasive laser probing of ultrashort single electron bunches for accelerator and light source development,” Int. J. Mod. Phys. B21(03n04), 527–539 (2007).
[CrossRef]

Bryce, A. C.

W. K. Tan, H. Y. Wong, A. E. Kelly, M. Sorel, J. H. Marsh, and A. C. Bryce, “Temperature behaviour of pulse repetition frequency in passively mode-locked InGaAsP/InP laser diode - Experimental results and simple model,” IEEE J. Sel. Top. Quantum Electron.13(5), 1209–1214 (2007).
[CrossRef]

Callegari, C.

E. Allaria, C. Callegari, D. Cocco, W. M. Fawley, M. Kiskinova, C. Masciovecchio, and F. Parmigiani, “The FERMI@Elettra free-electron-laser source for coherent x-ray physics: photon properties, beam transport system and applications,” New J. Phys.12(7), 075002 (2010).
[CrossRef]

Chen, J.

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics2(12), 733–736 (2008).
[CrossRef]

J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett.32(9), 1044–1046 (2007).
[CrossRef] [PubMed]

Chen, Y. F.

Cliche, J. F.

J. F. Cliche and B. Shillue, “Precision timing control for radioastronomy: maintaining femtosecond synchronization in the Atacama Large Millimeter Array,” IEEE Contr. Syst. Mag.26(1), 19–26 (2006).
[CrossRef]

Cocco, D.

E. Allaria, C. Callegari, D. Cocco, W. M. Fawley, M. Kiskinova, C. Masciovecchio, and F. Parmigiani, “The FERMI@Elettra free-electron-laser source for coherent x-ray physics: photon properties, beam transport system and applications,” New J. Phys.12(7), 075002 (2010).
[CrossRef]

Cox, J. A.

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics2(12), 733–736 (2008).
[CrossRef]

Cundiff, S. T.

Diddams, S. A.

E. N. Ivanov, S. A. Diddams, and L. Hollberg, “Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a femtosecond laser,” IEEE J. Sel. Top. Quantum Electron.9(4), 1059–1065 (2003).
[CrossRef]

Fallnich, C.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B78(3-4), 321–324 (2004).
[CrossRef]

Fawley, W. M.

E. Allaria, C. Callegari, D. Cocco, W. M. Fawley, M. Kiskinova, C. Masciovecchio, and F. Parmigiani, “The FERMI@Elettra free-electron-laser source for coherent x-ray physics: photon properties, beam transport system and applications,” New J. Phys.12(7), 075002 (2010).
[CrossRef]

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]

D. D. Hudson, S. M. Foreman, S. T. Cundiff, and J. Ye, “Synchronization of mode-locked femtosecond lasers through a fiber link,” Opt. Lett.31(13), 1951–1953 (2006).
[CrossRef] [PubMed]

Gill, P.

Hall, J. L.

Haverkamp, N.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B78(3-4), 321–324 (2004).
[CrossRef]

Hollberg, L.

E. N. Ivanov, S. A. Diddams, and L. Hollberg, “Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a femtosecond laser,” IEEE J. Sel. Top. Quantum Electron.9(4), 1059–1065 (2003).
[CrossRef]

Holman, K. W.

Hou, D.

Hudson, D. D.

Hundertmark, H.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B78(3-4), 321–324 (2004).
[CrossRef]

Ivanov, E. N.

E. N. Ivanov, S. A. Diddams, and L. Hollberg, “Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a femtosecond laser,” IEEE J. Sel. Top. Quantum Electron.9(4), 1059–1065 (2003).
[CrossRef]

Jiang, J.

Jones, D. J.

Jungner, P.

Kartner, F. X.

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics2(12), 733–736 (2008).
[CrossRef]

Kärtner, F. X.

Kelly, A. E.

W. K. Tan, H. Y. Wong, A. E. Kelly, M. Sorel, J. H. Marsh, and A. C. Bryce, “Temperature behaviour of pulse repetition frequency in passively mode-locked InGaAsP/InP laser diode - Experimental results and simple model,” IEEE J. Sel. Top. Quantum Electron.13(5), 1209–1214 (2007).
[CrossRef]

Kim, J.

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics2(12), 733–736 (2008).
[CrossRef]

J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett.32(9), 1044–1046 (2007).
[CrossRef] [PubMed]

Kiskinova, M.

E. Allaria, C. Callegari, D. Cocco, W. M. Fawley, M. Kiskinova, C. Masciovecchio, and F. Parmigiani, “The FERMI@Elettra free-electron-laser source for coherent x-ray physics: photon properties, beam transport system and applications,” New J. Phys.12(7), 075002 (2010).
[CrossRef]

Lea, S. N.

Levine, J.

J. Levine, “A review of time and frequency transfer methods,” Metrologia45(6), S162–S174 (2008).
[CrossRef]

Li, P.

Liu, C.

Loehl, F.

Ma, L. S.

Margolis, H. S.

Marra, G.

Marsh, J. H.

W. K. Tan, H. Y. Wong, A. E. Kelly, M. Sorel, J. H. Marsh, and A. C. Bryce, “Temperature behaviour of pulse repetition frequency in passively mode-locked InGaAsP/InP laser diode - Experimental results and simple model,” IEEE J. Sel. Top. Quantum Electron.13(5), 1209–1214 (2007).
[CrossRef]

Masciovecchio, C.

E. Allaria, C. Callegari, D. Cocco, W. M. Fawley, M. Kiskinova, C. Masciovecchio, and F. Parmigiani, “The FERMI@Elettra free-electron-laser source for coherent x-ray physics: photon properties, beam transport system and applications,” New J. Phys.12(7), 075002 (2010).
[CrossRef]

Matsumoto, H.

K. Minoshima and H. Matsumoto, “In-situ measurements of shapes and thickness of optical parts by femtosecond two-color interferometry,” Opt. Commun.138(1-3), 6–10 (1997).
[CrossRef]

Minoshima, K.

K. Minoshima and H. Matsumoto, “In-situ measurements of shapes and thickness of optical parts by femtosecond two-color interferometry,” Opt. Commun.138(1-3), 6–10 (1997).
[CrossRef]

Parmigiani, F.

E. Allaria, C. Callegari, D. Cocco, W. M. Fawley, M. Kiskinova, C. Masciovecchio, and F. Parmigiani, “The FERMI@Elettra free-electron-laser source for coherent x-ray physics: photon properties, beam transport system and applications,” New J. Phys.12(7), 075002 (2010).
[CrossRef]

Petropoulos, P.

Richardson, D. J.

Schlarb, H.

Shillue, B.

J. F. Cliche and B. Shillue, “Precision timing control for radioastronomy: maintaining femtosecond synchronization in the Atacama Large Millimeter Array,” IEEE Contr. Syst. Mag.26(1), 19–26 (2006).
[CrossRef]

Slavík, R.

Sorel, M.

W. K. Tan, H. Y. Wong, A. E. Kelly, M. Sorel, J. H. Marsh, and A. C. Bryce, “Temperature behaviour of pulse repetition frequency in passively mode-locked InGaAsP/InP laser diode - Experimental results and simple model,” IEEE J. Sel. Top. Quantum Electron.13(5), 1209–1214 (2007).
[CrossRef]

Tan, W. K.

W. K. Tan, H. Y. Wong, A. E. Kelly, M. Sorel, J. H. Marsh, and A. C. Bryce, “Temperature behaviour of pulse repetition frequency in passively mode-locked InGaAsP/InP laser diode - Experimental results and simple model,” IEEE J. Sel. Top. Quantum Electron.13(5), 1209–1214 (2007).
[CrossRef]

Telle, H. R.

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B78(3-4), 321–324 (2004).
[CrossRef]

Wong, F. N. C.

Wong, H. Y.

W. K. Tan, H. Y. Wong, A. E. Kelly, M. Sorel, J. H. Marsh, and A. C. Bryce, “Temperature behaviour of pulse repetition frequency in passively mode-locked InGaAsP/InP laser diode - Experimental results and simple model,” IEEE J. Sel. Top. Quantum Electron.13(5), 1209–1214 (2007).
[CrossRef]

Ye, J.

Zhang, Z.

Zhao, J.

Appl. Phys. B (1)

N. Haverkamp, H. Hundertmark, C. Fallnich, and H. R. Telle, “Frequency stabilization of mode-locked Erbium fiber lasers using pump power control,” Appl. Phys. B78(3-4), 321–324 (2004).
[CrossRef]

IEEE Contr. Syst. Mag. (1)

J. F. Cliche and B. Shillue, “Precision timing control for radioastronomy: maintaining femtosecond synchronization in the Atacama Large Millimeter Array,” IEEE Contr. Syst. Mag.26(1), 19–26 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

W. K. Tan, H. Y. Wong, A. E. Kelly, M. Sorel, J. H. Marsh, and A. C. Bryce, “Temperature behaviour of pulse repetition frequency in passively mode-locked InGaAsP/InP laser diode - Experimental results and simple model,” IEEE J. Sel. Top. Quantum Electron.13(5), 1209–1214 (2007).
[CrossRef]

E. N. Ivanov, S. A. Diddams, and L. Hollberg, “Analysis of noise mechanisms limiting the frequency stability of microwave signals generated with a femtosecond laser,” IEEE J. Sel. Top. Quantum Electron.9(4), 1059–1065 (2003).
[CrossRef]

Int. J. Mod. Phys. B (1)

P. R. Bolton, “Noninvasive laser probing of ultrashort single electron bunches for accelerator and light source development,” Int. J. Mod. Phys. B21(03n04), 527–539 (2007).
[CrossRef]

Metrologia (1)

J. Levine, “A review of time and frequency transfer methods,” Metrologia45(6), S162–S174 (2008).
[CrossRef]

Nat. Photonics (1)

J. Kim, J. A. Cox, J. Chen, and F. X. Kartner, “Drift-free femtosecond timing synchronization of remote optical and microwave sources,” Nat. Photonics2(12), 733–736 (2008).
[CrossRef]

New J. Phys. (1)

E. Allaria, C. Callegari, D. Cocco, W. M. Fawley, M. Kiskinova, C. Masciovecchio, and F. Parmigiani, “The FERMI@Elettra free-electron-laser source for coherent x-ray physics: photon properties, beam transport system and applications,” New J. Phys.12(7), 075002 (2010).
[CrossRef]

Opt. Commun. (1)

K. Minoshima and H. Matsumoto, “In-situ measurements of shapes and thickness of optical parts by femtosecond two-color interferometry,” Opt. Commun.138(1-3), 6–10 (1997).
[CrossRef]

Opt. Express (3)

Opt. Lett. (7)

D. D. Hudson, S. M. Foreman, S. T. Cundiff, and J. Ye, “Synchronization of mode-locked femtosecond lasers through a fiber link,” Opt. Lett.31(13), 1951–1953 (2006).
[CrossRef] [PubMed]

G. Marra, H. S. Margolis, S. N. Lea, and P. Gill, “High-stability microwave frequency transfer by propagation of an optical frequency comb over 50 km of optical fiber,” Opt. Lett.35(7), 1025–1027 (2010).
[CrossRef] [PubMed]

G. Marra, R. Slavík, H. S. Margolis, S. N. Lea, P. Petropoulos, D. J. Richardson, and P. Gill, “High-resolution microwave frequency transfer over an 86-km-long optical fiber network using a mode-locked laser,” Opt. Lett.36(4), 511–513 (2011).
[CrossRef] [PubMed]

L. S. Ma, P. Jungner, J. Ye, and J. L. Hall, “Delivering the same optical frequency at two places: accurate cancellation of phase noise introduced by an optical fiber or other time-varying path,” Opt. Lett.19(21), 1777–1779 (1994).
[CrossRef] [PubMed]

K. W. Holman, D. J. Jones, D. D. Hudson, and J. Ye, “Precise frequency transfer through a fiber network by use of 1.5-microm mode-locked sources,” Opt. Lett.29(13), 1554–1556 (2004).
[CrossRef] [PubMed]

K. W. Holman, D. D. Hudson, J. Ye, and D. J. Jones, “Remote transfer of a high-stability and ultralow-jitter timing signal,” Opt. Lett.30(10), 1225–1227 (2005).
[CrossRef] [PubMed]

J. Kim, J. Chen, Z. Zhang, F. N. C. Wong, F. X. Kärtner, F. Loehl, and H. Schlarb, “Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator,” Opt. Lett.32(9), 1044–1046 (2007).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

S. M. Foreman, K. W. Holman, D. D. Hudson, D. J. Jones, and J. Ye, “Remote transfer of ultrastable frequency references via fiber networks,” Rev. Sci. Instrum.78(2), 021101 (2007).
[CrossRef] [PubMed]

Other (3)

J. Ye and S. T. Cundiff, Femtosecond Optical Frequency Comb: Principle, Operation, and Applications (Kluwer Academic Publishers / Springer, 2004).

A. Yariv, Quantum Electronics Third Edition (John Wiley & Sons, 1989).

A. Maitland and M. H. Dumn, Laser Physics (North-Holland Publishing Company, 1969).

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Figures (4)

Fig. 1
Fig. 1

Phase shift generated by different methods in 1 ms. Blue filled square: physically control the cavity length; red filled circle: modulate pump power.

Fig. 2
Fig. 2

Experimental setup of the compensation technique. PD: photodiode; EDFA: erbium-doped fiber amplifier; BPF: band-pass filter; LPF: low-pass filter; RF amp: radio frequency amplifier; LF amp:low frequency amplifier; AGC: automatic gain control; OC: optical circulator; BF: back-reflector; PZT: piezo-electric transducer; CM: collimator; SMF: single-mode fiber; WP: wave plate; EDF: erbium-doped fiber; PBS: polarization beam splitter; WDM: wavelength division multiplexer.

Fig. 3
Fig. 3

Phase fluctuation (a) and phase noise (b) of the 21st harmonic of frep at the remote end. a) blue: phase fluctuation not compensated; red: phase fluctuation suppressed; black: background fluctuation measured by applying the same radio-frequency signal . b) blue: phase noise not suppressed; red: phase noise suppressed; grey: measurement noise ñoor, measured when 22-km SMF is replaced by 0.5-m fiber.

Fig. 4
Fig. 4

Frequency stability of the 21st harmonic of frep measured at the remote end. Filled blue circle: phase fluctuation not compensated; filled red square: phase fluctuation suppressed. Open grey square: measurement noise ñoor, measured when 22-km SMF is replaced by 0.5-m fiber.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

[ c n L 0 c n( L 0 +0.6nm) ] τ 100MHz 300fs,
φ return = φ 0 + φ c +2 φ p ,
φ ir = φ c +2 φ p φ pr =2 φ p .
φ c = φ p .

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