Abstract

Absolute frequency measurements, with up to 1×1011 level accuracies, are presented for 60 lines of the P and R branches for the ν1+ν3 band of C213H2 at 1.5μm (194THz). The measurements were made using cavity-enhanced, diode-laser-based saturation spectroscopy. With one laser system stabilized to the P(16) line and a second laser system stabilized to the line whose frequency was to be determined, a Cr:YAG frequency comb was employed to accurately measure the tetrahertz level frequency intervals. The results are compared with recent work from other groups and indicate that these lines would form a basis for a high-quality atlas of reference frequencies for this region of the spectrum.

© 2006 Optical Society of America

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  1. D. J. E. Knight, P. S. Hansell, H. C. Leeson, G. Duxbury, J. Meldau, and M. Lawrence, "A review of user requirements for, and practical possibilities for, frequency standards for the optical fibre communication bands," in Frequency-Stabilized Lasers and Their Applications, Y.C.Chung, ed., Proc. SPIE 1837, 106-114 (1992).
  2. C. Latrasse, M. Breton, M. Têtu, N. Cyr, R. Roberge, and B. Villeneuve, "C2HD and C213H2 absorption lines near 1530nm for semiconductor-laser frequency locking," Opt. Lett. 19, 1885-1887 (1994).
    [CrossRef]
  3. M. de Labachelerie, C. Latrasse, K. Diomandé, P. Kemssu, and P. Cerez, "A 1.5-μm absolutely stabilized extended-cavity semiconductor laser," IEEE Trans. Instrum. Meas. 40, 185-190 (1991).
    [CrossRef]
  4. M. de Labachelerie, K. Nakagawa, and M. Ohtsu, "Ultranarrow C213H2 saturated-absorption lines at 1.5μm," Opt. Lett. 19, 840-842 (1994).
    [CrossRef] [PubMed]
  5. K. Nakagawa, M. de Labachelerie, Y. Awaji, M. Kourogi, T. Enami, and M. Ohtsu, "Highly precise 1-THz optical frequency-difference measurement of 1.5-μm molecular absorption lines," Opt. Lett. 20, 410-412 (1995).
    [CrossRef]
  6. M. de Labachelerie, K. Nakagawa, Y. Awaji, and M. Ohtsu, "High-frequency-stability laser at 1.5μm using Doppler-free molecular lines," Opt. Lett. 20, 572-574 (1995).
  7. K. Nakagawa, M. de Labachelerie, Y. Awaji, and M. Kourogi, "Accurate optical frequency atlas of the 1.5-μm bands of acetylene," J. Opt. Soc. Am. B 13, 2708-2714 (1996).
    [CrossRef]
  8. A. Onae, K. Okumura, J. Yoda, K. Nakagawa, A. Yamaguchi, M. Kourogi, K. Imai, and B. Widiyatomoko, "Toward an accurate frequency standard at 1.5μm based on acetylene overtone band transition," IEEE Trans. Instrum. Meas. 48, 563-566 (1999).
    [CrossRef]
  9. A. Onae, T. Ikegami, K. Sugiyama, F.-L. Hong, K. Minoshima, H. Matsumoto, K. Nakagawa, M. Yoshida, and S. Harada, "Optical frequency link between an acetylene stabilized laser at 1542nm and an Rb stabilized laser at 778nm using a two-color mode-locked fiber laser," Opt. Commun. 183, 181-187 (2000).
    [CrossRef]
  10. A. Czajkowski, A. A. Madej, and P. Dube, "Development and study of a 1.5μm optical frequency standard referenced to the P(16) saturated absorption line in the (nu_1 + nu_3) overtone band of 13C2H2," Opt. Commun. 234, 259-268 (2004).
    [CrossRef]
  11. T. Kurosu and U. Sterr, "Frequency-stabilization of a 1.54 micrometer DFB-laser diode to Doppler-free absorption lines of acetylene," in Laser Frequency Stabilization, Standards, Measurement, and Applications, J.L.Hall and J.Ye, eds., Proc. SPIE 4269, 248-254 (2001).
  12. G. Galzerano, C. Svelto, F. Ferrario, A. Onae, M. Marano, and E. Bava, "Frequency stabilization of a 1.54-μmEr-Yb laser against Doppler-free C213H2 lines," Opt. Commun. 209, 411-416 (2002).
    [CrossRef]
  13. A. Onae, K. Okumura, K. Sugiyama, F.-L. Hong, H. Matsumoto, K. Nakagawa, R. Felder, and O. Acef, "Optical frequency standard at 1.5μm based on doppler-free acetylene absorption," in 6th Symposium on Frequency Standards and Metrology, P.Gill, ed. (World Scientific, 2002) pp. 445-452.
  14. T. J. Quinn, "Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001)," Metrologia 40, 103-133 (2003).
    [CrossRef]
  15. 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]
  16. H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, "Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327-332 (1999).
    [CrossRef]
  17. F.-L. Hong, A. Onae, J. Jiang, R. Guo, H. Inaba, K. Minoshima, T. R. Schibli, H. Matsumoto, and K. Nakagawa, "Absolute frequency measurement of an acetylene-stabilized laser at 1542nm," Opt. Lett. 28, 2324-2326 (2003).
    [PubMed]
  18. C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, G. Huang, and W. R. C. Rowley, "Absolute frequency measurement of a 1.5-μm acetylene standard by use of a combined frequency chain and femtosecond comb," Opt. Lett. 29, 566-568 (2004).
    [CrossRef] [PubMed]
  19. A. Czajkowski, J. E. Bernard, A. A. Madej, and R. S. Windeler, "Absolute frequency measurement of acetylene transitions in the region of 1540nm," Appl. Phys. B 79, 45-50 (2004).
    [CrossRef]
  20. R. Felder, "Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2003)," Metrologia 42, 323-325 (2005).
    [CrossRef]
  21. A. Onae, K. Okumura, F.-L. Hong, H. Matsumoto, and K. Nakagawa, "Accurate frequency atlas of 1.5μm band of acetylene measured by a mode-locked fiber laser," in Digest of the Conference on Precision Electromagnetic Measurements (IEEE Press, 2004), pp. 666-667.
  22. C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, and W. R. C. Rowley, "High-accuracy frequency atlas of C213H2 in the 1.5μm region," Appl. Phys. B 80, 977-983 (2005).
    [CrossRef]
  23. 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: Photophys. Laser Chem. 31, 97-105 (1983).
    [CrossRef]
  24. A. J. Alcock, S. Chepurov, J. E. Bernard, A. Czajkowski, J. M. Fraser, P. Ma, A. A. Madej, I. V. Mitchell, P. J. Poole, I. T. Sorokina, and E. Sorokin, "Ultrashort pulse, Cr4+:YAG laser for high precision, infrared frequency interval measurements," Opt. Express 13, 8837-8844 (2005).
    [CrossRef] [PubMed]
  25. J.-M. Chartier, S. Picard-Fredin, and A. Chartier, "1992 International comparison of iodine cells," BIPM Rapport CCDM92-2 (Bureau International des Poids et Mesures, 1992).
  26. G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand Reinhold, 1950), p. 104.

2005

R. Felder, "Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2003)," Metrologia 42, 323-325 (2005).
[CrossRef]

C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, and W. R. C. Rowley, "High-accuracy frequency atlas of C213H2 in the 1.5μm region," Appl. Phys. B 80, 977-983 (2005).
[CrossRef]

A. J. Alcock, S. Chepurov, J. E. Bernard, A. Czajkowski, J. M. Fraser, P. Ma, A. A. Madej, I. V. Mitchell, P. J. Poole, I. T. Sorokina, and E. Sorokin, "Ultrashort pulse, Cr4+:YAG laser for high precision, infrared frequency interval measurements," Opt. Express 13, 8837-8844 (2005).
[CrossRef] [PubMed]

2004

C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, G. Huang, and W. R. C. Rowley, "Absolute frequency measurement of a 1.5-μm acetylene standard by use of a combined frequency chain and femtosecond comb," Opt. Lett. 29, 566-568 (2004).
[CrossRef] [PubMed]

A. Czajkowski, J. E. Bernard, A. A. Madej, and R. S. Windeler, "Absolute frequency measurement of acetylene transitions in the region of 1540nm," Appl. Phys. B 79, 45-50 (2004).
[CrossRef]

A. Czajkowski, A. A. Madej, and P. Dube, "Development and study of a 1.5μm optical frequency standard referenced to the P(16) saturated absorption line in the (nu_1 + nu_3) overtone band of 13C2H2," Opt. Commun. 234, 259-268 (2004).
[CrossRef]

2003

T. J. Quinn, "Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001)," Metrologia 40, 103-133 (2003).
[CrossRef]

F.-L. Hong, A. Onae, J. Jiang, R. Guo, H. Inaba, K. Minoshima, T. R. Schibli, H. Matsumoto, and K. Nakagawa, "Absolute frequency measurement of an acetylene-stabilized laser at 1542nm," Opt. Lett. 28, 2324-2326 (2003).
[PubMed]

2002

G. Galzerano, C. Svelto, F. Ferrario, A. Onae, M. Marano, and E. Bava, "Frequency stabilization of a 1.54-μmEr-Yb laser against Doppler-free C213H2 lines," Opt. Commun. 209, 411-416 (2002).
[CrossRef]

2000

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]

A. Onae, T. Ikegami, K. Sugiyama, F.-L. Hong, K. Minoshima, H. Matsumoto, K. Nakagawa, M. Yoshida, and S. Harada, "Optical frequency link between an acetylene stabilized laser at 1542nm and an Rb stabilized laser at 778nm using a two-color mode-locked fiber laser," Opt. Commun. 183, 181-187 (2000).
[CrossRef]

1999

A. Onae, K. Okumura, J. Yoda, K. Nakagawa, A. Yamaguchi, M. Kourogi, K. Imai, and B. Widiyatomoko, "Toward an accurate frequency standard at 1.5μm based on acetylene overtone band transition," IEEE Trans. Instrum. Meas. 48, 563-566 (1999).
[CrossRef]

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, "Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327-332 (1999).
[CrossRef]

1996

1995

1994

1991

M. de Labachelerie, C. Latrasse, K. Diomandé, P. Kemssu, and P. Cerez, "A 1.5-μm absolutely stabilized extended-cavity semiconductor laser," IEEE Trans. Instrum. Meas. 40, 185-190 (1991).
[CrossRef]

1983

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: Photophys. Laser Chem. 31, 97-105 (1983).
[CrossRef]

Acef, O.

A. Onae, K. Okumura, K. Sugiyama, F.-L. Hong, H. Matsumoto, K. Nakagawa, R. Felder, and O. Acef, "Optical frequency standard at 1.5μm based on doppler-free acetylene absorption," in 6th Symposium on Frequency Standards and Metrology, P.Gill, ed. (World Scientific, 2002) pp. 445-452.

Alcock, A. J.

Awaji, Y.

Barwood, G. P.

Bava, E.

G. Galzerano, C. Svelto, F. Ferrario, A. Onae, M. Marano, and E. Bava, "Frequency stabilization of a 1.54-μmEr-Yb laser against Doppler-free C213H2 lines," Opt. Commun. 209, 411-416 (2002).
[CrossRef]

Bernard, J. E.

Breton, M.

Cerez, P.

M. de Labachelerie, C. Latrasse, K. Diomandé, P. Kemssu, and P. Cerez, "A 1.5-μm absolutely stabilized extended-cavity semiconductor laser," IEEE Trans. Instrum. Meas. 40, 185-190 (1991).
[CrossRef]

Chartier, A.

J.-M. Chartier, S. Picard-Fredin, and A. Chartier, "1992 International comparison of iodine cells," BIPM Rapport CCDM92-2 (Bureau International des Poids et Mesures, 1992).

Chartier, J.-M.

J.-M. Chartier, S. Picard-Fredin, and A. Chartier, "1992 International comparison of iodine cells," BIPM Rapport CCDM92-2 (Bureau International des Poids et Mesures, 1992).

Chepurov, S.

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]

Cyr, N.

Czajkowski, A.

A. J. Alcock, S. Chepurov, J. E. Bernard, A. Czajkowski, J. M. Fraser, P. Ma, A. A. Madej, I. V. Mitchell, P. J. Poole, I. T. Sorokina, and E. Sorokin, "Ultrashort pulse, Cr4+:YAG laser for high precision, infrared frequency interval measurements," Opt. Express 13, 8837-8844 (2005).
[CrossRef] [PubMed]

A. Czajkowski, J. E. Bernard, A. A. Madej, and R. S. Windeler, "Absolute frequency measurement of acetylene transitions in the region of 1540nm," Appl. Phys. B 79, 45-50 (2004).
[CrossRef]

A. Czajkowski, A. A. Madej, and P. Dube, "Development and study of a 1.5μm optical frequency standard referenced to the P(16) saturated absorption line in the (nu_1 + nu_3) overtone band of 13C2H2," Opt. Commun. 234, 259-268 (2004).
[CrossRef]

de Labachelerie, M.

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]

Diomandé, K.

M. de Labachelerie, C. Latrasse, K. Diomandé, P. Kemssu, and P. Cerez, "A 1.5-μm absolutely stabilized extended-cavity semiconductor laser," IEEE Trans. Instrum. Meas. 40, 185-190 (1991).
[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: Photophys. Laser Chem. 31, 97-105 (1983).
[CrossRef]

Dube, P.

A. Czajkowski, A. A. Madej, and P. Dube, "Development and study of a 1.5μm optical frequency standard referenced to the P(16) saturated absorption line in the (nu_1 + nu_3) overtone band of 13C2H2," Opt. Commun. 234, 259-268 (2004).
[CrossRef]

Dunlop, A. E.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, "Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327-332 (1999).
[CrossRef]

Duxbury, G.

D. J. E. Knight, P. S. Hansell, H. C. Leeson, G. Duxbury, J. Meldau, and M. Lawrence, "A review of user requirements for, and practical possibilities for, frequency standards for the optical fibre communication bands," in Frequency-Stabilized Lasers and Their Applications, Y.C.Chung, ed., Proc. SPIE 1837, 106-114 (1992).

Edwards, C. S.

Enami, T.

Felder, R.

R. Felder, "Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2003)," Metrologia 42, 323-325 (2005).
[CrossRef]

A. Onae, K. Okumura, K. Sugiyama, F.-L. Hong, H. Matsumoto, K. Nakagawa, R. Felder, and O. Acef, "Optical frequency standard at 1.5μm based on doppler-free acetylene absorption," in 6th Symposium on Frequency Standards and Metrology, P.Gill, ed. (World Scientific, 2002) pp. 445-452.

Ferrario, F.

G. Galzerano, C. Svelto, F. Ferrario, A. Onae, M. Marano, and E. Bava, "Frequency stabilization of a 1.54-μmEr-Yb laser against Doppler-free C213H2 lines," Opt. Commun. 209, 411-416 (2002).
[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: Photophys. Laser Chem. 31, 97-105 (1983).
[CrossRef]

Fraser, J. M.

Galzerano, G.

G. Galzerano, C. Svelto, F. Ferrario, A. Onae, M. Marano, and E. Bava, "Frequency stabilization of a 1.54-μmEr-Yb laser against Doppler-free C213H2 lines," Opt. Commun. 209, 411-416 (2002).
[CrossRef]

Gill, P.

Guo, R.

Hall, J. L.

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]

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: Photophys. Laser Chem. 31, 97-105 (1983).
[CrossRef]

Hansell, P. S.

D. J. E. Knight, P. S. Hansell, H. C. Leeson, G. Duxbury, J. Meldau, and M. Lawrence, "A review of user requirements for, and practical possibilities for, frequency standards for the optical fibre communication bands," in Frequency-Stabilized Lasers and Their Applications, Y.C.Chung, ed., Proc. SPIE 1837, 106-114 (1992).

Harada, S.

A. Onae, T. Ikegami, K. Sugiyama, F.-L. Hong, K. Minoshima, H. Matsumoto, K. Nakagawa, M. Yoshida, and S. Harada, "Optical frequency link between an acetylene stabilized laser at 1542nm and an Rb stabilized laser at 778nm using a two-color mode-locked fiber laser," Opt. Commun. 183, 181-187 (2000).
[CrossRef]

Herzberg, G.

G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand Reinhold, 1950), p. 104.

Hong, F.-L.

F.-L. Hong, A. Onae, J. Jiang, R. Guo, H. Inaba, K. Minoshima, T. R. Schibli, H. Matsumoto, and K. Nakagawa, "Absolute frequency measurement of an acetylene-stabilized laser at 1542nm," Opt. Lett. 28, 2324-2326 (2003).
[PubMed]

A. Onae, T. Ikegami, K. Sugiyama, F.-L. Hong, K. Minoshima, H. Matsumoto, K. Nakagawa, M. Yoshida, and S. Harada, "Optical frequency link between an acetylene stabilized laser at 1542nm and an Rb stabilized laser at 778nm using a two-color mode-locked fiber laser," Opt. Commun. 183, 181-187 (2000).
[CrossRef]

A. Onae, K. Okumura, K. Sugiyama, F.-L. Hong, H. Matsumoto, K. Nakagawa, R. Felder, and O. Acef, "Optical frequency standard at 1.5μm based on doppler-free acetylene absorption," in 6th Symposium on Frequency Standards and Metrology, P.Gill, ed. (World Scientific, 2002) pp. 445-452.

A. Onae, K. Okumura, F.-L. Hong, H. Matsumoto, and K. Nakagawa, "Accurate frequency atlas of 1.5μm band of acetylene measured by a mode-locked fiber laser," in Digest of the Conference on Precision Electromagnetic Measurements (IEEE Press, 2004), pp. 666-667.

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: Photophys. Laser Chem. 31, 97-105 (1983).
[CrossRef]

Huang, G.

Ikegami, T.

A. Onae, T. Ikegami, K. Sugiyama, F.-L. Hong, K. Minoshima, H. Matsumoto, K. Nakagawa, M. Yoshida, and S. Harada, "Optical frequency link between an acetylene stabilized laser at 1542nm and an Rb stabilized laser at 778nm using a two-color mode-locked fiber laser," Opt. Commun. 183, 181-187 (2000).
[CrossRef]

Imai, K.

A. Onae, K. Okumura, J. Yoda, K. Nakagawa, A. Yamaguchi, M. Kourogi, K. Imai, and B. Widiyatomoko, "Toward an accurate frequency standard at 1.5μm based on acetylene overtone band transition," IEEE Trans. Instrum. Meas. 48, 563-566 (1999).
[CrossRef]

Inaba, H.

Jiang, J.

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]

Keller, U.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, "Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327-332 (1999).
[CrossRef]

Kemssu, P.

M. de Labachelerie, C. Latrasse, K. Diomandé, P. Kemssu, and P. Cerez, "A 1.5-μm absolutely stabilized extended-cavity semiconductor laser," IEEE Trans. Instrum. Meas. 40, 185-190 (1991).
[CrossRef]

Knight, D. J. E.

D. J. E. Knight, P. S. Hansell, H. C. Leeson, G. Duxbury, J. Meldau, and M. Lawrence, "A review of user requirements for, and practical possibilities for, frequency standards for the optical fibre communication bands," in Frequency-Stabilized Lasers and Their Applications, Y.C.Chung, ed., Proc. SPIE 1837, 106-114 (1992).

Kourogi, M.

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: Photophys. Laser Chem. 31, 97-105 (1983).
[CrossRef]

Kurosu, T.

T. Kurosu and U. Sterr, "Frequency-stabilization of a 1.54 micrometer DFB-laser diode to Doppler-free absorption lines of acetylene," in Laser Frequency Stabilization, Standards, Measurement, and Applications, J.L.Hall and J.Ye, eds., Proc. SPIE 4269, 248-254 (2001).

Latrasse, C.

C. Latrasse, M. Breton, M. Têtu, N. Cyr, R. Roberge, and B. Villeneuve, "C2HD and C213H2 absorption lines near 1530nm for semiconductor-laser frequency locking," Opt. Lett. 19, 1885-1887 (1994).
[CrossRef]

M. de Labachelerie, C. Latrasse, K. Diomandé, P. Kemssu, and P. Cerez, "A 1.5-μm absolutely stabilized extended-cavity semiconductor laser," IEEE Trans. Instrum. Meas. 40, 185-190 (1991).
[CrossRef]

Lawrence, M.

D. J. E. Knight, P. S. Hansell, H. C. Leeson, G. Duxbury, J. Meldau, and M. Lawrence, "A review of user requirements for, and practical possibilities for, frequency standards for the optical fibre communication bands," in Frequency-Stabilized Lasers and Their Applications, Y.C.Chung, ed., Proc. SPIE 1837, 106-114 (1992).

Lea, S. N.

Leeson, H. C.

D. J. E. Knight, P. S. Hansell, H. C. Leeson, G. Duxbury, J. Meldau, and M. Lawrence, "A review of user requirements for, and practical possibilities for, frequency standards for the optical fibre communication bands," in Frequency-Stabilized Lasers and Their Applications, Y.C.Chung, ed., Proc. SPIE 1837, 106-114 (1992).

Ma, P.

Madej, A. A.

A. J. Alcock, S. Chepurov, J. E. Bernard, A. Czajkowski, J. M. Fraser, P. Ma, A. A. Madej, I. V. Mitchell, P. J. Poole, I. T. Sorokina, and E. Sorokin, "Ultrashort pulse, Cr4+:YAG laser for high precision, infrared frequency interval measurements," Opt. Express 13, 8837-8844 (2005).
[CrossRef] [PubMed]

A. Czajkowski, J. E. Bernard, A. A. Madej, and R. S. Windeler, "Absolute frequency measurement of acetylene transitions in the region of 1540nm," Appl. Phys. B 79, 45-50 (2004).
[CrossRef]

A. Czajkowski, A. A. Madej, and P. Dube, "Development and study of a 1.5μm optical frequency standard referenced to the P(16) saturated absorption line in the (nu_1 + nu_3) overtone band of 13C2H2," Opt. Commun. 234, 259-268 (2004).
[CrossRef]

Marano, M.

G. Galzerano, C. Svelto, F. Ferrario, A. Onae, M. Marano, and E. Bava, "Frequency stabilization of a 1.54-μmEr-Yb laser against Doppler-free C213H2 lines," Opt. Commun. 209, 411-416 (2002).
[CrossRef]

Margolis, H. S.

Matsumoto, H.

F.-L. Hong, A. Onae, J. Jiang, R. Guo, H. Inaba, K. Minoshima, T. R. Schibli, H. Matsumoto, and K. Nakagawa, "Absolute frequency measurement of an acetylene-stabilized laser at 1542nm," Opt. Lett. 28, 2324-2326 (2003).
[PubMed]

A. Onae, T. Ikegami, K. Sugiyama, F.-L. Hong, K. Minoshima, H. Matsumoto, K. Nakagawa, M. Yoshida, and S. Harada, "Optical frequency link between an acetylene stabilized laser at 1542nm and an Rb stabilized laser at 778nm using a two-color mode-locked fiber laser," Opt. Commun. 183, 181-187 (2000).
[CrossRef]

A. Onae, K. Okumura, K. Sugiyama, F.-L. Hong, H. Matsumoto, K. Nakagawa, R. Felder, and O. Acef, "Optical frequency standard at 1.5μm based on doppler-free acetylene absorption," in 6th Symposium on Frequency Standards and Metrology, P.Gill, ed. (World Scientific, 2002) pp. 445-452.

A. Onae, K. Okumura, F.-L. Hong, H. Matsumoto, and K. Nakagawa, "Accurate frequency atlas of 1.5μm band of acetylene measured by a mode-locked fiber laser," in Digest of the Conference on Precision Electromagnetic Measurements (IEEE Press, 2004), pp. 666-667.

Meldau, J.

D. J. E. Knight, P. S. Hansell, H. C. Leeson, G. Duxbury, J. Meldau, and M. Lawrence, "A review of user requirements for, and practical possibilities for, frequency standards for the optical fibre communication bands," in Frequency-Stabilized Lasers and Their Applications, Y.C.Chung, ed., Proc. SPIE 1837, 106-114 (1992).

Minoshima, K.

F.-L. Hong, A. Onae, J. Jiang, R. Guo, H. Inaba, K. Minoshima, T. R. Schibli, H. Matsumoto, and K. Nakagawa, "Absolute frequency measurement of an acetylene-stabilized laser at 1542nm," Opt. Lett. 28, 2324-2326 (2003).
[PubMed]

A. Onae, T. Ikegami, K. Sugiyama, F.-L. Hong, K. Minoshima, H. Matsumoto, K. Nakagawa, M. Yoshida, and S. Harada, "Optical frequency link between an acetylene stabilized laser at 1542nm and an Rb stabilized laser at 778nm using a two-color mode-locked fiber laser," Opt. Commun. 183, 181-187 (2000).
[CrossRef]

Mitchell, I. V.

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: Photophys. Laser Chem. 31, 97-105 (1983).
[CrossRef]

Nakagawa, K.

F.-L. Hong, A. Onae, J. Jiang, R. Guo, H. Inaba, K. Minoshima, T. R. Schibli, H. Matsumoto, and K. Nakagawa, "Absolute frequency measurement of an acetylene-stabilized laser at 1542nm," Opt. Lett. 28, 2324-2326 (2003).
[PubMed]

A. Onae, T. Ikegami, K. Sugiyama, F.-L. Hong, K. Minoshima, H. Matsumoto, K. Nakagawa, M. Yoshida, and S. Harada, "Optical frequency link between an acetylene stabilized laser at 1542nm and an Rb stabilized laser at 778nm using a two-color mode-locked fiber laser," Opt. Commun. 183, 181-187 (2000).
[CrossRef]

A. Onae, K. Okumura, J. Yoda, K. Nakagawa, A. Yamaguchi, M. Kourogi, K. Imai, and B. Widiyatomoko, "Toward an accurate frequency standard at 1.5μm based on acetylene overtone band transition," IEEE Trans. Instrum. Meas. 48, 563-566 (1999).
[CrossRef]

K. Nakagawa, M. de Labachelerie, Y. Awaji, and M. Kourogi, "Accurate optical frequency atlas of the 1.5-μm bands of acetylene," J. Opt. Soc. Am. B 13, 2708-2714 (1996).
[CrossRef]

M. de Labachelerie, K. Nakagawa, Y. Awaji, and M. Ohtsu, "High-frequency-stability laser at 1.5μm using Doppler-free molecular lines," Opt. Lett. 20, 572-574 (1995).

K. Nakagawa, M. de Labachelerie, Y. Awaji, M. Kourogi, T. Enami, and M. Ohtsu, "Highly precise 1-THz optical frequency-difference measurement of 1.5-μm molecular absorption lines," Opt. Lett. 20, 410-412 (1995).
[CrossRef]

M. de Labachelerie, K. Nakagawa, and M. Ohtsu, "Ultranarrow C213H2 saturated-absorption lines at 1.5μm," Opt. Lett. 19, 840-842 (1994).
[CrossRef] [PubMed]

A. Onae, K. Okumura, K. Sugiyama, F.-L. Hong, H. Matsumoto, K. Nakagawa, R. Felder, and O. Acef, "Optical frequency standard at 1.5μm based on doppler-free acetylene absorption," in 6th Symposium on Frequency Standards and Metrology, P.Gill, ed. (World Scientific, 2002) pp. 445-452.

A. Onae, K. Okumura, F.-L. Hong, H. Matsumoto, and K. Nakagawa, "Accurate frequency atlas of 1.5μm band of acetylene measured by a mode-locked fiber laser," in Digest of the Conference on Precision Electromagnetic Measurements (IEEE Press, 2004), pp. 666-667.

Ohtsu, M.

Okumura, K.

A. Onae, K. Okumura, J. Yoda, K. Nakagawa, A. Yamaguchi, M. Kourogi, K. Imai, and B. Widiyatomoko, "Toward an accurate frequency standard at 1.5μm based on acetylene overtone band transition," IEEE Trans. Instrum. Meas. 48, 563-566 (1999).
[CrossRef]

A. Onae, K. Okumura, K. Sugiyama, F.-L. Hong, H. Matsumoto, K. Nakagawa, R. Felder, and O. Acef, "Optical frequency standard at 1.5μm based on doppler-free acetylene absorption," in 6th Symposium on Frequency Standards and Metrology, P.Gill, ed. (World Scientific, 2002) pp. 445-452.

A. Onae, K. Okumura, F.-L. Hong, H. Matsumoto, and K. Nakagawa, "Accurate frequency atlas of 1.5μm band of acetylene measured by a mode-locked fiber laser," in Digest of the Conference on Precision Electromagnetic Measurements (IEEE Press, 2004), pp. 666-667.

Onae, A.

F.-L. Hong, A. Onae, J. Jiang, R. Guo, H. Inaba, K. Minoshima, T. R. Schibli, H. Matsumoto, and K. Nakagawa, "Absolute frequency measurement of an acetylene-stabilized laser at 1542nm," Opt. Lett. 28, 2324-2326 (2003).
[PubMed]

G. Galzerano, C. Svelto, F. Ferrario, A. Onae, M. Marano, and E. Bava, "Frequency stabilization of a 1.54-μmEr-Yb laser against Doppler-free C213H2 lines," Opt. Commun. 209, 411-416 (2002).
[CrossRef]

A. Onae, T. Ikegami, K. Sugiyama, F.-L. Hong, K. Minoshima, H. Matsumoto, K. Nakagawa, M. Yoshida, and S. Harada, "Optical frequency link between an acetylene stabilized laser at 1542nm and an Rb stabilized laser at 778nm using a two-color mode-locked fiber laser," Opt. Commun. 183, 181-187 (2000).
[CrossRef]

A. Onae, K. Okumura, J. Yoda, K. Nakagawa, A. Yamaguchi, M. Kourogi, K. Imai, and B. Widiyatomoko, "Toward an accurate frequency standard at 1.5μm based on acetylene overtone band transition," IEEE Trans. Instrum. Meas. 48, 563-566 (1999).
[CrossRef]

A. Onae, K. Okumura, K. Sugiyama, F.-L. Hong, H. Matsumoto, K. Nakagawa, R. Felder, and O. Acef, "Optical frequency standard at 1.5μm based on doppler-free acetylene absorption," in 6th Symposium on Frequency Standards and Metrology, P.Gill, ed. (World Scientific, 2002) pp. 445-452.

A. Onae, K. Okumura, F.-L. Hong, H. Matsumoto, and K. Nakagawa, "Accurate frequency atlas of 1.5μm band of acetylene measured by a mode-locked fiber laser," in Digest of the Conference on Precision Electromagnetic Measurements (IEEE Press, 2004), pp. 666-667.

Picard-Fredin, S.

J.-M. Chartier, S. Picard-Fredin, and A. Chartier, "1992 International comparison of iodine cells," BIPM Rapport CCDM92-2 (Bureau International des Poids et Mesures, 1992).

Poole, P. J.

Quinn, T. J.

T. J. Quinn, "Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001)," Metrologia 40, 103-133 (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]

Roberge, R.

Rowley, W. R. C.

Schibli, T. R.

Sorokin, E.

Sorokina, I. T.

Steinmeyer, G.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, "Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327-332 (1999).
[CrossRef]

Stenger, J.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, "Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327-332 (1999).
[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]

Sterr, U.

T. Kurosu and U. Sterr, "Frequency-stabilization of a 1.54 micrometer DFB-laser diode to Doppler-free absorption lines of acetylene," in Laser Frequency Stabilization, Standards, Measurement, and Applications, J.L.Hall and J.Ye, eds., Proc. SPIE 4269, 248-254 (2001).

Sugiyama, K.

A. Onae, T. Ikegami, K. Sugiyama, F.-L. Hong, K. Minoshima, H. Matsumoto, K. Nakagawa, M. Yoshida, and S. Harada, "Optical frequency link between an acetylene stabilized laser at 1542nm and an Rb stabilized laser at 778nm using a two-color mode-locked fiber laser," Opt. Commun. 183, 181-187 (2000).
[CrossRef]

A. Onae, K. Okumura, K. Sugiyama, F.-L. Hong, H. Matsumoto, K. Nakagawa, R. Felder, and O. Acef, "Optical frequency standard at 1.5μm based on doppler-free acetylene absorption," in 6th Symposium on Frequency Standards and Metrology, P.Gill, ed. (World Scientific, 2002) pp. 445-452.

Sutter, D. H.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, "Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327-332 (1999).
[CrossRef]

Svelto, C.

G. Galzerano, C. Svelto, F. Ferrario, A. Onae, M. Marano, and E. Bava, "Frequency stabilization of a 1.54-μmEr-Yb laser against Doppler-free C213H2 lines," Opt. Commun. 209, 411-416 (2002).
[CrossRef]

Telle, H. R.

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, "Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327-332 (1999).
[CrossRef]

Têtu, M.

Villeneuve, B.

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: Photophys. Laser Chem. 31, 97-105 (1983).
[CrossRef]

Widiyatomoko, B.

A. Onae, K. Okumura, J. Yoda, K. Nakagawa, A. Yamaguchi, M. Kourogi, K. Imai, and B. Widiyatomoko, "Toward an accurate frequency standard at 1.5μm based on acetylene overtone band transition," IEEE Trans. Instrum. Meas. 48, 563-566 (1999).
[CrossRef]

Windeler, R. S.

A. Czajkowski, J. E. Bernard, A. A. Madej, and R. S. Windeler, "Absolute frequency measurement of acetylene transitions in the region of 1540nm," Appl. Phys. B 79, 45-50 (2004).
[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]

Yamaguchi, A.

A. Onae, K. Okumura, J. Yoda, K. Nakagawa, A. Yamaguchi, M. Kourogi, K. Imai, and B. Widiyatomoko, "Toward an accurate frequency standard at 1.5μm based on acetylene overtone band transition," IEEE Trans. Instrum. Meas. 48, 563-566 (1999).
[CrossRef]

Yoda, J.

A. Onae, K. Okumura, J. Yoda, K. Nakagawa, A. Yamaguchi, M. Kourogi, K. Imai, and B. Widiyatomoko, "Toward an accurate frequency standard at 1.5μm based on acetylene overtone band transition," IEEE Trans. Instrum. Meas. 48, 563-566 (1999).
[CrossRef]

Yoshida, M.

A. Onae, T. Ikegami, K. Sugiyama, F.-L. Hong, K. Minoshima, H. Matsumoto, K. Nakagawa, M. Yoshida, and S. Harada, "Optical frequency link between an acetylene stabilized laser at 1542nm and an Rb stabilized laser at 778nm using a two-color mode-locked fiber laser," Opt. Commun. 183, 181-187 (2000).
[CrossRef]

Appl. Phys. B

H. R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, and U. Keller, "Carrier-envelope offset phase control: a novel concept for absolute optical frequency measurement and ultrashort pulse generation," Appl. Phys. B 69, 327-332 (1999).
[CrossRef]

C. S. Edwards, H. S. Margolis, G. P. Barwood, S. N. Lea, P. Gill, and W. R. C. Rowley, "High-accuracy frequency atlas of C213H2 in the 1.5μm region," Appl. Phys. B 80, 977-983 (2005).
[CrossRef]

A. Czajkowski, J. E. Bernard, A. A. Madej, and R. S. Windeler, "Absolute frequency measurement of acetylene transitions in the region of 1540nm," Appl. Phys. B 79, 45-50 (2004).
[CrossRef]

Appl. Phys. B: Photophys. Laser Chem.

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: Photophys. Laser Chem. 31, 97-105 (1983).
[CrossRef]

IEEE Trans. Instrum. Meas.

M. de Labachelerie, C. Latrasse, K. Diomandé, P. Kemssu, and P. Cerez, "A 1.5-μm absolutely stabilized extended-cavity semiconductor laser," IEEE Trans. Instrum. Meas. 40, 185-190 (1991).
[CrossRef]

A. Onae, K. Okumura, J. Yoda, K. Nakagawa, A. Yamaguchi, M. Kourogi, K. Imai, and B. Widiyatomoko, "Toward an accurate frequency standard at 1.5μm based on acetylene overtone band transition," IEEE Trans. Instrum. Meas. 48, 563-566 (1999).
[CrossRef]

J. Opt. Soc. Am. B

Metrologia

R. Felder, "Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2003)," Metrologia 42, 323-325 (2005).
[CrossRef]

T. J. Quinn, "Practical realization of the definition of the metre, including recommended radiations of other optical frequency standards (2001)," Metrologia 40, 103-133 (2003).
[CrossRef]

Opt. Commun.

G. Galzerano, C. Svelto, F. Ferrario, A. Onae, M. Marano, and E. Bava, "Frequency stabilization of a 1.54-μmEr-Yb laser against Doppler-free C213H2 lines," Opt. Commun. 209, 411-416 (2002).
[CrossRef]

A. Onae, T. Ikegami, K. Sugiyama, F.-L. Hong, K. Minoshima, H. Matsumoto, K. Nakagawa, M. Yoshida, and S. Harada, "Optical frequency link between an acetylene stabilized laser at 1542nm and an Rb stabilized laser at 778nm using a two-color mode-locked fiber laser," Opt. Commun. 183, 181-187 (2000).
[CrossRef]

A. Czajkowski, A. A. Madej, and P. Dube, "Development and study of a 1.5μm optical frequency standard referenced to the P(16) saturated absorption line in the (nu_1 + nu_3) overtone band of 13C2H2," Opt. Commun. 234, 259-268 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Science

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]

Other

D. J. E. Knight, P. S. Hansell, H. C. Leeson, G. Duxbury, J. Meldau, and M. Lawrence, "A review of user requirements for, and practical possibilities for, frequency standards for the optical fibre communication bands," in Frequency-Stabilized Lasers and Their Applications, Y.C.Chung, ed., Proc. SPIE 1837, 106-114 (1992).

A. Onae, K. Okumura, K. Sugiyama, F.-L. Hong, H. Matsumoto, K. Nakagawa, R. Felder, and O. Acef, "Optical frequency standard at 1.5μm based on doppler-free acetylene absorption," in 6th Symposium on Frequency Standards and Metrology, P.Gill, ed. (World Scientific, 2002) pp. 445-452.

T. Kurosu and U. Sterr, "Frequency-stabilization of a 1.54 micrometer DFB-laser diode to Doppler-free absorption lines of acetylene," in Laser Frequency Stabilization, Standards, Measurement, and Applications, J.L.Hall and J.Ye, eds., Proc. SPIE 4269, 248-254 (2001).

J.-M. Chartier, S. Picard-Fredin, and A. Chartier, "1992 International comparison of iodine cells," BIPM Rapport CCDM92-2 (Bureau International des Poids et Mesures, 1992).

G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand Reinhold, 1950), p. 104.

A. Onae, K. Okumura, F.-L. Hong, H. Matsumoto, and K. Nakagawa, "Accurate frequency atlas of 1.5μm band of acetylene measured by a mode-locked fiber laser," in Digest of the Conference on Precision Electromagnetic Measurements (IEEE Press, 2004), pp. 666-667.

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Figures (7)

Fig. 1
Fig. 1

(Color online) Schematic diagram of the acetylene-stabilized optical frequency standard. EOM, electro-optic modulator, PBS, polarizing beamsplitter; λ 4 , quarter-wave plate; Det., Photodetector.

Fig. 2
Fig. 2

Allan deviation of the frequency of the heterodyne beat between laser systems 1 and 2, with both systems locked to P ( 16 ) transition.

Fig. 3
Fig. 3

Schematic diagram of the mode-locked Cr : YAG laser.

Fig. 4
Fig. 4

Diagram of the setup used to measure frequency differences between laser systems 1 and 2 using a mode-locked Cr : YAG laser.

Fig. 5
Fig. 5

(a) A sample record of the counter readings obtained in the measurement of the frequency difference between laser systems 1 and 2. (b) Allan deviation plot of the frequency readings shown in (a).

Fig. 6
Fig. 6

Plotted differences in the measured frequencies of the ν 1 + ν 3 band C 2 13 H 2 lines determined in this work and those obtained in Reference [21].

Fig. 7
Fig. 7

Plotted differences in the measured frequencies of the ν 1 + ν 3 band C 2 13 H 2 lines determined in this work and those obtained in Reference [22].

Tables (1)

Tables Icon

Table 1 Summary of the Measured Frequency Differences and Absolute Frequencies of the ν 1 + ν 3 Band Transitions in C 2 13 H 2 a

Equations (8)

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

ν 2 [ P ( 16 ) ] = 194 369 569 382 500 ± 1350 Hz ( 1 σ )
ν 1 [ P ( 16 ) ] = 194 369 569 384 036 ± 500 Hz ( 1 σ ) .
f beat 1 = ± { f 1 ( X ) [ f o ( t ) + n * f rep ] } ,
f beat 2 = ± { f 2 [ P ( 16 ) ] [ f o ( t ) + m * f rep ] } ,
f beat 1 f beat 2 = ± ( { f 1 ( X ) f 2 [ P ( 16 ) ] } ( n m ) * f rep ) .
f 1 ( X ) f 2 [ P ( 16 ) ] = ( n m ) * f rep ± ( f track + 20 MHz ) .
E ( J ) h c = B J ( J + 1 ) D J 2 ( J + 1 ) 2 + H J 3 ( J + 1 ) 3 + L J 4 ( J + 1 ) 4 + . . . .
Δ 2 F = ν R ( J 1 ) ν P ( J + 1 ) = ( 4 B 6 D + 27 4 H + 27 4 L ) ( J + 1 2 ) + ( 8 D + 34 H + 75 L ) ( J + 1 2 ) 3 + ( 12 H + 100 L ) ( J + 1 2 ) 5 + 16 L ( J + 1 2 ) 7 ,

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