Abstract

Remote transfer of an ultralow-jitter microwave frequency reference signal is demonstrated using the pulse trains generated by a mode-locked fiber laser. The timing jitter in a ~ 30-m fiber link is reduced to 38 attoseconds (as) integrated over a bandwidth from 1 Hz to 10 MHz via active stabilization which represents a significant improvement over previously reported jitter performance. Our approach uses an all-optical generation of the synchronization error signal and an accompanying out-of-loop optical detection technique to verify the jitter performance.

© 2006 Optical Society of America

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References

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  1. J. Levine, "Introduction to time and frequency metrology," Rev. Sci. Instrum. 70, 2567-2596 (1999).
    [CrossRef]
  2. 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, 1318-1324 (2004).
    [CrossRef] [PubMed]
  3. A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, "Systematic study of the 87Sr clock transition in an optical lattice," Phys. Rev. Lett. 96, 033003 (2006).
    [CrossRef] [PubMed]
  4. M. Calhoun, R. Sydnor, and W. Diener, "A stabilized 100-Megahertz and 1-Gigahertz reference frequency distribution for Cassini radio science," Interplanetary Network Progress Rep. 42-148, Jet Propulsion Laboratory, Pasadena, California (2002).
  5. "Linac Coherent Light Source - LCLS," http://www-ssrl.slac.stanford.edu/lcls/index.html.
  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. (to be published).
    [PubMed]
  7. 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, 1225-1227 (2005).
    [CrossRef] [PubMed]
  8. T. R. Schibli, J. Kim, O. Kuzucu, G. J. T., S. N. Tandon, G. S. Petrich, L. A. Kolodziejski, J. G. Fujimoto, E. P. Ippen, and F. X. Kaertner, "Attosecond active synchronization of passively mode-locked lasers by balanced cross correlation," Opt. Lett. 28, 947-949 (2003).
    [CrossRef] [PubMed]
  9. A. Bartels, S. A. Diddams, T. M. Ramond, and L. Hollberg, "Mode-locked laser pulse trains with subfemtosecond timing jitter synchronized to an optical reference oscillator," Opt. Lett. 28, 663-665 (2003).
    [CrossRef] [PubMed]
  10. 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]
  11. J. Ye and S. T. Cundiff, "Femtosecond Optical Frequency Comb Technology: Principle, Operation, and Applications," in Optical frequency combs and their applications, J. Ye and S. T. Cundiff, eds., pp. 12-53 (Springer, 2005).
  12. R. K. Shelton, S. M. Foreman, L.-S. Ma, J. L. Hall, H. C. Kapteyn, M. M. Murnane, M. Notcutt, and J. Ye, "Subfemtosecond timing jitter between two independent, actively synchronized, mode-locked lasers," Opt. Lett. 27, 312-314 (2002).
    [CrossRef]
  13. L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, "Ultrashort-pulse fiber ring lasers," Appl. Phys. B 65, 277-294 (1997).
    [CrossRef]
  14. K. W. Holman, "Distribution of an Ultrastable Frequency Reference Using Optical Frequency Combs," Ph.D. thesis, University of Colorado (2004).
  15. J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques, and Applications on a Femtosecond Time Scale, Optics and Photonics (Academic Press, San Diego, 1996).
  16. K. Kikuchi, "Highly sensitive interferometric autocorrelator using Si avalanche photodiode as two-photon absorber," Electron. Lett. 34, 123-125 (1997).
    [CrossRef]
  17. D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
    [CrossRef] [PubMed]

2006 (1)

A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, "Systematic study of the 87Sr clock transition in an optical lattice," Phys. Rev. Lett. 96, 033003 (2006).
[CrossRef] [PubMed]

2005 (1)

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, 1318-1324 (2004).
[CrossRef] [PubMed]

2003 (3)

2002 (1)

2000 (1)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

1999 (1)

J. Levine, "Introduction to time and frequency metrology," Rev. Sci. Instrum. 70, 2567-2596 (1999).
[CrossRef]

1997 (2)

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, "Ultrashort-pulse fiber ring lasers," Appl. Phys. B 65, 277-294 (1997).
[CrossRef]

K. Kikuchi, "Highly sensitive interferometric autocorrelator using Si avalanche photodiode as two-photon absorber," Electron. Lett. 34, 123-125 (1997).
[CrossRef]

Bartels, A.

Bergquist, J. C.

Bize, S.

Blatt, S.

A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, "Systematic study of the 87Sr clock transition in an optical lattice," Phys. Rev. Lett. 96, 033003 (2006).
[CrossRef] [PubMed]

Boyd, M. M.

A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, "Systematic study of the 87Sr clock transition in an optical lattice," Phys. Rev. Lett. 96, 033003 (2006).
[CrossRef] [PubMed]

Cundiff, S. T.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

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, 1318-1324 (2004).
[CrossRef] [PubMed]

A. Bartels, S. A. Diddams, T. M. Ramond, and L. Hollberg, "Mode-locked laser pulse trains with subfemtosecond timing jitter synchronized to an optical reference oscillator," Opt. Lett. 28, 663-665 (2003).
[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]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Foreman, S. M.

A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, "Systematic study of the 87Sr clock transition in an optical lattice," Phys. Rev. Lett. 96, 033003 (2006).
[CrossRef] [PubMed]

R. K. Shelton, S. M. Foreman, L.-S. Ma, J. L. Hall, H. C. Kapteyn, M. M. Murnane, M. Notcutt, and J. Ye, "Subfemtosecond timing jitter between two independent, actively synchronized, mode-locked lasers," Opt. Lett. 27, 312-314 (2002).
[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. (to be published).
[PubMed]

Hall, J. L.

Haus, H. A.

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, "Ultrashort-pulse fiber ring lasers," Appl. Phys. B 65, 277-294 (1997).
[CrossRef]

Hollberg, L.

Hollberg, L. W.

Holman, K. W.

Hudson, D. D.

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, 1225-1227 (2005).
[CrossRef] [PubMed]

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. (to be published).
[PubMed]

Ido, T.

A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, "Systematic study of the 87Sr clock transition in an optical lattice," Phys. Rev. Lett. 96, 033003 (2006).
[CrossRef] [PubMed]

Ippen, E. P.

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, "Ultrashort-pulse fiber ring lasers," Appl. Phys. B 65, 277-294 (1997).
[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, 1318-1324 (2004).
[CrossRef] [PubMed]

Jones, D. J.

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, 1225-1227 (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]

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, "Ultrashort-pulse fiber ring lasers," Appl. Phys. B 65, 277-294 (1997).
[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. (to be published).
[PubMed]

Jones, R. J.

Kapteyn, H. C.

Kikuchi, K.

K. Kikuchi, "Highly sensitive interferometric autocorrelator using Si avalanche photodiode as two-photon absorber," Electron. Lett. 34, 123-125 (1997).
[CrossRef]

Kim, J.

Kitching, J.

Kuzucu, O.

Levine, J.

J. Levine, "Introduction to time and frequency metrology," Rev. Sci. Instrum. 70, 2567-2596 (1999).
[CrossRef]

Ludlow, A. D.

A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, "Systematic study of the 87Sr clock transition in an optical lattice," Phys. Rev. Lett. 96, 033003 (2006).
[CrossRef] [PubMed]

Ma, L.-S.

Murnane, M. M.

Nelson, L. E.

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, "Ultrashort-pulse fiber ring lasers," Appl. Phys. B 65, 277-294 (1997).
[CrossRef]

Notcutt, M.

A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, "Systematic study of the 87Sr clock transition in an optical lattice," Phys. Rev. Lett. 96, 033003 (2006).
[CrossRef] [PubMed]

R. K. Shelton, S. M. Foreman, L.-S. Ma, J. L. Hall, H. C. Kapteyn, M. M. Murnane, M. Notcutt, and J. Ye, "Subfemtosecond timing jitter between two independent, actively synchronized, mode-locked lasers," Opt. Lett. 27, 312-314 (2002).
[CrossRef]

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, 1318-1324 (2004).
[CrossRef] [PubMed]

Peng, J. L.

Ramond, T. M.

Ranka, J. K.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Robertsson, L.

Schibli, T. R.

Shelton, R. K.

Stentz, A.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Tamura, K.

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, "Ultrashort-pulse fiber ring lasers," Appl. Phys. B 65, 277-294 (1997).
[CrossRef]

Windeler, R. S.

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

Ye, J.

Zelevinsky, T.

A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, "Systematic study of the 87Sr clock transition in an optical lattice," Phys. Rev. Lett. 96, 033003 (2006).
[CrossRef] [PubMed]

Appl. Phys. B (1)

L. E. Nelson, D. J. Jones, K. Tamura, H. A. Haus, and E. P. Ippen, "Ultrashort-pulse fiber ring lasers," Appl. Phys. B 65, 277-294 (1997).
[CrossRef]

Electron. Lett. (1)

K. Kikuchi, "Highly sensitive interferometric autocorrelator using Si avalanche photodiode as two-photon absorber," Electron. Lett. 34, 123-125 (1997).
[CrossRef]

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

Opt. Lett. (4)

Phys. Rev. Lett. (1)

A. D. Ludlow, M. M. Boyd, T. Zelevinsky, S. M. Foreman, S. Blatt, M. Notcutt, T. Ido, and J. Ye, "Systematic study of the 87Sr clock transition in an optical lattice," Phys. Rev. Lett. 96, 033003 (2006).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (2)

J. Levine, "Introduction to time and frequency metrology," Rev. Sci. Instrum. 70, 2567-2596 (1999).
[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. (to be published).
[PubMed]

Science (2)

D. J. Jones, S. A. Diddams, J. K. Ranka, A. Stentz, R. S. Windeler, J. L. Hall, and S. T. Cundiff, "Carrier-envelope phase control of femtosecond mode-locked lasers and direct optical frequency synthesis," Science 288, 635-639 (2000).
[CrossRef] [PubMed]

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, 1318-1324 (2004).
[CrossRef] [PubMed]

Other (5)

M. Calhoun, R. Sydnor, and W. Diener, "A stabilized 100-Megahertz and 1-Gigahertz reference frequency distribution for Cassini radio science," Interplanetary Network Progress Rep. 42-148, Jet Propulsion Laboratory, Pasadena, California (2002).

"Linac Coherent Light Source - LCLS," http://www-ssrl.slac.stanford.edu/lcls/index.html.

J. Ye and S. T. Cundiff, "Femtosecond Optical Frequency Comb Technology: Principle, Operation, and Applications," in Optical frequency combs and their applications, J. Ye and S. T. Cundiff, eds., pp. 12-53 (Springer, 2005).

K. W. Holman, "Distribution of an Ultrastable Frequency Reference Using Optical Frequency Combs," Ph.D. thesis, University of Colorado (2004).

J.-C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques, and Applications on a Femtosecond Time Scale, Optics and Photonics (Academic Press, San Diego, 1996).

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Figures (7)

Fig. 1.
Fig. 1.

A graphical representation of the three terms in Eq. (3) in the frequency domain. (a) 1st term, which shows the local pulse train; (b) 2nd term, which shows the transmitted pulse train (δf r is exaggerated for clarity); (c) 3rd term, which shows the interference between the two pulse trains, where m+1≈m

Fig. 2.
Fig. 2.

Experimental setup of optical heterodyne jitter cancellation and interferometric cross-correlation (ICC) measurement. Scheme 1 uses optical heterodyne detection at spectral extremes, while scheme 2 is single optical heterodyne. EDFL, mode-locked Erbiumdoped fiber laser; BS, beam splitter; DCF, dispersion compensating fiber; SMF-28, single mode fiber; PZT, piezoelectric transducer; PBS, polarizing beam splitter; HWP, half-wave plate; QWP, quarter-wave plate; FPD, free-space photodiode; CPD, fiber-coupled photodiode; BPF, band-pass filter; Amp, radio frequency amplifier; OSA, optical spectrum analyzer; PLL, phase-locked loop; APD, avalanche photodiode.

Fig. 3.
Fig. 3.

A frequency domain diagram showing the mixing procedures to obtain the optically leveraged noise sidebands by scheme 1 & 2. Optical heterodyne beat detected (a) at the low optical frequency region and (b) at the high optical frequency region in scheme 1; (c) Optically leveraged noise sidebands at baseband produced at the output of mixer in scheme 1; (d) Detected harmonic of repetition rate in scheme 2; (e) Detected optical heterodyne beat in scheme 2; (f) Optically leveraged noise sidebands at baseband produced the output of mixer in scheme 2.

Fig. 4.
Fig. 4.

The green and purple curves show the spectra of reference and transmission paths, respectively. The self-phase modulation due to transmission through the ~60-m fiber results in the slightly wider spectrum in the transmission arm with respect to the reference arm. The blue and red curves are the spectra of the received signals at two spectral extremes. Each spectral slice has a bandwidth of ~1.8 nm. The black curve is the stable interference pattern of combined signal when PLL is activated.

Fig. 5.
Fig. 5.

Time domain traces of the interferometric cross correlation signal between the reference and transmitted pulses. The green and blue curves show the noise measured respectively for 10 s and 1 ms intervals when it is actively canceled by the approach of spectral leveraging (scheme 1). The equivalent time scale is shown on the right axis. The red curve is the free-running (unlocked) case.

Fig. 6.
Fig. 6.

Power spectral density (solid curves referring to left axis) and integrated jitter (dashed curves referring to right axis) of APD’s noise floor and noise when actively canceled by scheme 1 and 2.

Fig. 7.
Fig. 7.

Power spectral density (solid curve referring to left axis) and integrated jitter (dashed curve referring to right axis) of unlocked noise, noise floor of microwave detection and that of optical detection. Microwave detection is conducted at 1822.46 MHz, the 37th harmonic of the repetition rate of the mode-locked fiber laser.

Equations (7)

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

E ˜ 1 = n = n 1 n 2 A n exp [ i ( n f rep 1 + f o 1 ) t ] & E ˜ 2 = m = m 1 m 2 A m exp [ i ( m f rep 2 + f o 2 ) t ]
i ~ 2 k = 0 n 2 n 1 ( n 2 n 1 + 1 k ) cos ( k f rep 1 t ) + 2 l 0 m 2 m 1 ( m 2 m 1 + 1 l ) cos ( l f rep 2 t )
+ 2 n = n 1 n 2 m = m 1 m 2 cos ( n f rep 1 + f o 1 m f rep 2 f o 2 ) t
i ~ 2 k = 0 n 2 n 1 ( n 2 n 1 + 1 k ) cos ( k f rep 1 t ) + 2 l 0 m 2 m 1 ( m 2 m 1 + 1 l ) cos ( l f rep 1 + l δ f r ) t
+ 2 n = n 1 n 2 m = m 1 m 2 cos [ ( n m ) f rep 1 m δ f r + δ f o ] t
δ T ˜ ( f ) = δ ϕ ˜ ( f ) 2 π ν 0 = A ˜ ( f ) 2 π ν 0 A 0 [ second Hz 1 / 2 ]
T rms = { f 1 f h [ δ T ˜ ( f ) ] 2 d f } 1 / 2 [ second ]

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