Abstract

The mode number of the comb line involved in the optical frequency measurement was determined using two mode-locked, erbium-doped fiber laser combs operated at different repetition rates independently of the frequency fluctuation of the laser under measurement (LUM). A simple measurement process is presented to determine the difference in mode number between the two laser combs and the comb mode number, yielding the absolute frequency of the LUM.

© 2007 Optical Society of America

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  1. Th. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
    [CrossRef] [PubMed]
  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]
  3. S. T. Cundiff, J. Ye, and J. L. Hall, "Optical frequency synthesis based on mode-locked lasers," Rev. Sci. Instrum. 72, 3749-3771 (2001).
    [CrossRef]
  4. L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, "A new method to determine the absolute mode number of a mode-locked femtosecond laser comb used for absolute optical frequency measurements," IEEE J. Sel. Top. Quantum Electron. 9, 1066-1071 (2003).
    [CrossRef]
  5. H. Inaba, Y. Daimon, F.-L. Hong, A. Onae, K. Minoshima, T. R. Schibli, H. Matsumoto, M. Hirano, T. Okuno, M. Onishi, and M. Nakazawa, "Long-term measurement of optical frequencies using a simple, robust and low-noise fiber based frequency comb," Opt. Express 14, 5223-5231 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-12-5223.
    [CrossRef] [PubMed]
  6. 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]
  7. J.-L. Peng, H. Ahn, R.-H. Shu, H.-C. Chui, and J. W. Nicholson, "Highly stable, frequency-controlled mode-locked erbium fiber laser comb," Appl. Phys. B 86, 49-53 (2007).
    [CrossRef]
  8. H. Ahn, R.-H. Shu, R. S. Windeler, and J.-L. Peng, "Building a frequency-stabilized mode-locked femtosecond laser for optical frequency metrology," IEEE Trans. Instrum. Meas. 54, 767-770 (2005).
    [CrossRef]

2007 (1)

J.-L. Peng, H. Ahn, R.-H. Shu, H.-C. Chui, and J. W. Nicholson, "Highly stable, frequency-controlled mode-locked erbium fiber laser comb," Appl. Phys. B 86, 49-53 (2007).
[CrossRef]

2006 (1)

2005 (1)

H. Ahn, R.-H. Shu, R. S. Windeler, and J.-L. Peng, "Building a frequency-stabilized mode-locked femtosecond laser for optical frequency metrology," IEEE Trans. Instrum. Meas. 54, 767-770 (2005).
[CrossRef]

2003 (1)

L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, "A new method to determine the absolute mode number of a mode-locked femtosecond laser comb used for absolute optical frequency measurements," IEEE J. Sel. Top. Quantum Electron. 9, 1066-1071 (2003).
[CrossRef]

2002 (1)

Th. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

2001 (1)

S. T. Cundiff, J. Ye, and J. L. Hall, "Optical frequency synthesis based on mode-locked lasers," Rev. Sci. Instrum. 72, 3749-3771 (2001).
[CrossRef]

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]

1997 (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]

Ahn, H.

J.-L. Peng, H. Ahn, R.-H. Shu, H.-C. Chui, and J. W. Nicholson, "Highly stable, frequency-controlled mode-locked erbium fiber laser comb," Appl. Phys. B 86, 49-53 (2007).
[CrossRef]

H. Ahn, R.-H. Shu, R. S. Windeler, and J.-L. Peng, "Building a frequency-stabilized mode-locked femtosecond laser for optical frequency metrology," IEEE Trans. Instrum. Meas. 54, 767-770 (2005).
[CrossRef]

Chui, H.-C.

J.-L. Peng, H. Ahn, R.-H. Shu, H.-C. Chui, and J. W. Nicholson, "Highly stable, frequency-controlled mode-locked erbium fiber laser comb," Appl. Phys. B 86, 49-53 (2007).
[CrossRef]

Cundiff, S. T.

S. T. Cundiff, J. Ye, and J. L. Hall, "Optical frequency synthesis based on mode-locked lasers," Rev. Sci. Instrum. 72, 3749-3771 (2001).
[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]

Daimon, Y.

Diddams, S. 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]

Hall, J. L.

S. T. Cundiff, J. Ye, and J. L. Hall, "Optical frequency synthesis based on mode-locked lasers," Rev. Sci. Instrum. 72, 3749-3771 (2001).
[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]

Hänsch, T. W.

Th. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

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]

Hirano, M.

Holzwarth, R.

Th. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Hong, F.-L.

Inaba, H.

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]

Jones, D. J.

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]

Ma, L.-S.

L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, "A new method to determine the absolute mode number of a mode-locked femtosecond laser comb used for absolute optical frequency measurements," IEEE J. Sel. Top. Quantum Electron. 9, 1066-1071 (2003).
[CrossRef]

Matsumoto, H.

Minoshima, K.

Nakazawa, 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]

Nicholson, J. W.

J.-L. Peng, H. Ahn, R.-H. Shu, H.-C. Chui, and J. W. Nicholson, "Highly stable, frequency-controlled mode-locked erbium fiber laser comb," Appl. Phys. B 86, 49-53 (2007).
[CrossRef]

Okuno, T.

Onae, A.

Onishi, M.

Peng, J.-L.

J.-L. Peng, H. Ahn, R.-H. Shu, H.-C. Chui, and J. W. Nicholson, "Highly stable, frequency-controlled mode-locked erbium fiber laser comb," Appl. Phys. B 86, 49-53 (2007).
[CrossRef]

H. Ahn, R.-H. Shu, R. S. Windeler, and J.-L. Peng, "Building a frequency-stabilized mode-locked femtosecond laser for optical frequency metrology," IEEE Trans. Instrum. Meas. 54, 767-770 (2005).
[CrossRef]

Picard, S.

L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, "A new method to determine the absolute mode number of a mode-locked femtosecond laser comb used for absolute optical frequency measurements," IEEE J. Sel. Top. Quantum Electron. 9, 1066-1071 (2003).
[CrossRef]

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.

L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, "A new method to determine the absolute mode number of a mode-locked femtosecond laser comb used for absolute optical frequency measurements," IEEE J. Sel. Top. Quantum Electron. 9, 1066-1071 (2003).
[CrossRef]

Schibli, T. R.

Shu, R.-H.

J.-L. Peng, H. Ahn, R.-H. Shu, H.-C. Chui, and J. W. Nicholson, "Highly stable, frequency-controlled mode-locked erbium fiber laser comb," Appl. Phys. B 86, 49-53 (2007).
[CrossRef]

H. Ahn, R.-H. Shu, R. S. Windeler, and J.-L. Peng, "Building a frequency-stabilized mode-locked femtosecond laser for optical frequency metrology," IEEE Trans. Instrum. Meas. 54, 767-770 (2005).
[CrossRef]

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]

Udem, Th.

Th. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Windeler, R. S.

H. Ahn, R.-H. Shu, R. S. Windeler, and J.-L. Peng, "Building a frequency-stabilized mode-locked femtosecond laser for optical frequency metrology," IEEE Trans. Instrum. Meas. 54, 767-770 (2005).
[CrossRef]

L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, "A new method to determine the absolute mode number of a mode-locked femtosecond laser comb used for absolute optical frequency measurements," IEEE J. Sel. Top. Quantum Electron. 9, 1066-1071 (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]

Ye, J.

S. T. Cundiff, J. Ye, and J. L. Hall, "Optical frequency synthesis based on mode-locked lasers," Rev. Sci. Instrum. 72, 3749-3771 (2001).
[CrossRef]

Zucco, M.

L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, "A new method to determine the absolute mode number of a mode-locked femtosecond laser comb used for absolute optical frequency measurements," IEEE J. Sel. Top. Quantum Electron. 9, 1066-1071 (2003).
[CrossRef]

Appl. Phys. B (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]

J.-L. Peng, H. Ahn, R.-H. Shu, H.-C. Chui, and J. W. Nicholson, "Highly stable, frequency-controlled mode-locked erbium fiber laser comb," Appl. Phys. B 86, 49-53 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

L.-S. Ma, M. Zucco, S. Picard, L. Robertsson, and R. S. Windeler, "A new method to determine the absolute mode number of a mode-locked femtosecond laser comb used for absolute optical frequency measurements," IEEE J. Sel. Top. Quantum Electron. 9, 1066-1071 (2003).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

H. Ahn, R.-H. Shu, R. S. Windeler, and J.-L. Peng, "Building a frequency-stabilized mode-locked femtosecond laser for optical frequency metrology," IEEE Trans. Instrum. Meas. 54, 767-770 (2005).
[CrossRef]

Nature (1)

Th. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
[CrossRef] [PubMed]

Opt. Express (1)

Rev. Sci. Instrum. (1)

S. T. Cundiff, J. Ye, and J. L. Hall, "Optical frequency synthesis based on mode-locked lasers," Rev. Sci. Instrum. 72, 3749-3771 (2001).
[CrossRef]

Science (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]

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Figures (5)

Fig. 1.
Fig. 1.

(a) Determine the location of the LUM relative to the comb line by observing the beat frequency variation while reducing the repetition rate. (b) Identify the right CEO frequency by observing the beat frequency variation while changing the CEO frequency.

Fig. 2.
Fig. 2.

The frequency of the LUM relative to the beating comb lines of two mode-locked lasers operated at different repetition rates.

Fig. 3.
Fig. 3.

Parts (a) and (c) show the shift of the comb mode neighboring the LUM at a frequency of fL1 for the repetition rate being increased by fr1/n and decreased by fr1/(n+1), respectively. Parts (b) and (d) show the corresponding movement of the beat signals. The beat signals cross at half of the repetition frequency, pass 0 and fr1, respectively one time as indicated. One beat frequency is exactly the same as before and the other one is changed by an amount equals the change in repetition rate.

Fig. 4.
Fig. 4.

Schematic diagram of the optical frequency measurement using two mode-locked Er:fiber combs. Each laser has two branches of octave-spanning supercontinuum. One branch is for the frequency stabilization of the repetition rate and the CEO frequency, the other branch is for beating with the Nd:YAG laser. PC: polarization controller, SMF: single mode fiber

Fig. 5.
Fig. 5.

Parts (a) and (b) ( (e) and (f) ) are measured beat frequencies without (with) modulating the frequency of the Nd:YAG laser. Parts (c) and (g) are the measured beat frequency difference. Parts (d) and (h) are the calculated mode number.

Equations (6)

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

f L 1 = n f r 1 + f o 1 + f b 1
f L 1 = ( n + m ) f r 2 + f o 2 + f b 2
n = m f r 2 + f o 2 f o 1 + f b 2 f b 1 f r 1 f r 2
m = f r 1 f r 2 f r 2 n f o 2 f o 1 + f b 2 f b 1 f r 2
= f r 1 f r 2 f r 1 n + n ( f r 1 f r 2 ) 2 f r 1 f r 2 f o 2 f o 1 + f b 2 f b 1 f r 2
f r 1 f r 2 f r 1 n f o 2 f o 1 + f b 2 f b 1 f r 2 if n ( f r 1 f r 2 ) 2 f r 1 f r 2 1

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