Abstract

We show how to synthesize a cw, single-frequency optical field from the frequency-dispersed, pulsed field of a mode-locked laser. This process, which relies on difference-frequency generation in an optical cavity, is efficient and can be considered as an optical rectification. Quantitative estimates for the output power and amplitude noise properties of a realistic system are given. Possible applications to optical frequency synthesis and optical metrology are discussed.

© 2005 Optical Society of America

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  1. S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000).
    [CrossRef] [PubMed]
  2. T. Udem, R. Holzwarth, and T. W. Hänsch, "Optical frequency metrology," Nature 416, 233-237 (2002).
    [CrossRef] [PubMed]
  3. D. A. Jennings, C. R. Pollock, F. R. Petersen, R. E. Drullinger, K. M. Evenson, J. S. Wells, J. L. Hall, and H. P. Layer, "Direct frequency measurement of the I2-stabilized He-Ne 473-THz(633-nm) laser," Opt. Lett. 8, 136-138 (1983).
    [CrossRef] [PubMed]
  4. H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, and G. Zinner, "First phase-coherent frequency measurement of visible radiation, " Phys. Rev. Lett. 76, 18-21 (1996).
    [CrossRef] [PubMed]
  5. H. R. Telle, D. Meschede, and T. W. Hänsch, "Realization of a new concept for visible frequency division: phase locking of harmonic and sum frequencies, " Opt. Lett. 15, 532-534 (1990).
    [CrossRef] [PubMed]
  6. T. Udem, A. Huber, B. Gross, J. Reichert, M. Prevedelli, M. Weitz, and T. W. Hänsch, "Phase-coherent measurement of the hydrogen 1S-2S transition frequency with an optical frequency interval divider chain, " Phys. Rev. Lett. 79, 2646-2649 (1997).
    [CrossRef]
  7. M. Kourogi, K. Nakagawa, and M. Ohtsu, "Wide-span optical frequency comb generator for accurate optical frequency difference measurement," IEEE J. Quantum Electron. 29, 2693-2701 (1993).
    [CrossRef]
  8. 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]
  9. S. T. Cundiff, J. Ye, and J. L. Hall, "Optical frequency synthesis based on modelocked lasers, " Rev. Sci. Instrum. 72, 3749-3771 (2001), and references therein.
    [CrossRef]
  10. 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]
  11. L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, Th. Udem, H. G. Robinson, J. C. Bergquist, W. M. Itano, R. E. Drullinger, and D. J. Wineland, "Optical frequency standards and measurements," IEEE J. Quantum Electron. 37, 1502-1513 (2001).
    [CrossRef]
  12. J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 25, 25-27 (2000).
    [CrossRef]
  13. T. Ramond, S. A. Diddams, L. Hollberg, and A. Bartels, "Phase-coherent link from optical to microwave frequencies by means of the broadband continuum from a 1-GHz Ti:sapphire femtosecondoscillator," Opt. Lett. 27, 1842-1844 (2002).
    [CrossRef]
  14. I. Thomann, A. Bartels, K. L. Corwin, N. R. Newbury, L. Hollberg, S. A. Diddams, J. W. Nicholson, and M. F. Yan, "20-MHz Cr:forsterite femtosecond ring laser and continuum generation in the 1-2 µm range," Opt. Lett. 28, 1368-1370 (2003).
    [CrossRef] [PubMed]
  15. This approach requires a finesse sufficiently high to avoid the contribution of cavity modes close to unwanted resonances and may result in a cavity finesse higher than a few thousands, which can be considered a realistic value for cavities containing optical elements.
  16. The detailed spectrum of a mode-locked laser depends critically on the dispersion properties of its cavity and eventually those of the medium employed to broaden its spectrum.
  17. L. E. Myers,R. C. Eckardt, M. M. Fejer, R. L. Byer, and W. R. Bosenberg, "Multigrating quasi-phase-matched optical parametric oscillator in periodically poled LiNbO3," Opt. Lett. 21, 591-593 (1996).
    [CrossRef] [PubMed]
  18. P. De Natale, S. Borri, P. Cancio, G. Giusfredi, D. Mazzotti, M. Prevedelli, C. De Mauro, and M. Inguscio, "Extending the optical comb synthesizer to the infrared: from He at 1.083 µm to CO2 at 4.2 µm," in Proceedings of the 16th International Conference on Laser Spectroscopy, P.Hannaford, A.Sidorov, H.Bachor, and K.Baldwin, eds. (World Scientific, 2004), pp. 63-67.
  19. T. Fuji, A. Apolonski, and F. Krausz, "Self-stabilization of carrier-envelope offset phase by use of difference-frequency generation," Opt. Lett. 29, 632-634 (2004).
    [CrossRef] [PubMed]
  20. A. E. Siegman, Lasers (Oxford U. Press, 1986).
  21. R. W. Boyd, Nonlinear Optics (Academic, 1992).
  22. P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, 1993).

2004

2003

2002

2001

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

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, Th. Udem, H. G. Robinson, J. C. Bergquist, W. M. Itano, R. E. Drullinger, and D. J. Wineland, "Optical frequency standards and measurements," IEEE J. Quantum Electron. 37, 1502-1513 (2001).
[CrossRef]

2000

J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 25, 25-27 (2000).
[CrossRef]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000).
[CrossRef] [PubMed]

1999

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]

1997

T. Udem, A. Huber, B. Gross, J. Reichert, M. Prevedelli, M. Weitz, and T. W. Hänsch, "Phase-coherent measurement of the hydrogen 1S-2S transition frequency with an optical frequency interval divider chain, " Phys. Rev. Lett. 79, 2646-2649 (1997).
[CrossRef]

1996

1993

M. Kourogi, K. Nakagawa, and M. Ohtsu, "Wide-span optical frequency comb generator for accurate optical frequency difference measurement," IEEE J. Quantum Electron. 29, 2693-2701 (1993).
[CrossRef]

1990

1983

Apolonski, A.

Awaji, Y.

Bartels, A.

Bergquist, J. C.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, Th. Udem, H. G. Robinson, J. C. Bergquist, W. M. Itano, R. E. Drullinger, and D. J. Wineland, "Optical frequency standards and measurements," IEEE J. Quantum Electron. 37, 1502-1513 (2001).
[CrossRef]

Borri, S.

P. De Natale, S. Borri, P. Cancio, G. Giusfredi, D. Mazzotti, M. Prevedelli, C. De Mauro, and M. Inguscio, "Extending the optical comb synthesizer to the infrared: from He at 1.083 µm to CO2 at 4.2 µm," in Proceedings of the 16th International Conference on Laser Spectroscopy, P.Hannaford, A.Sidorov, H.Bachor, and K.Baldwin, eds. (World Scientific, 2004), pp. 63-67.

Bosenberg, W. R.

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Butcher, P. N.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, 1993).

Byer, R. L.

Cancio, P.

P. De Natale, S. Borri, P. Cancio, G. Giusfredi, D. Mazzotti, M. Prevedelli, C. De Mauro, and M. Inguscio, "Extending the optical comb synthesizer to the infrared: from He at 1.083 µm to CO2 at 4.2 µm," in Proceedings of the 16th International Conference on Laser Spectroscopy, P.Hannaford, A.Sidorov, H.Bachor, and K.Baldwin, eds. (World Scientific, 2004), pp. 63-67.

Corwin, K. L.

Cotter, D.

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, 1993).

Cundiff, S. T.

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

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000).
[CrossRef] [PubMed]

Curtis, E. A.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, Th. Udem, H. G. Robinson, J. C. Bergquist, W. M. Itano, R. E. Drullinger, and D. J. Wineland, "Optical frequency standards and measurements," IEEE J. Quantum Electron. 37, 1502-1513 (2001).
[CrossRef]

de Labachelerie, M.

De Mauro, C.

P. De Natale, S. Borri, P. Cancio, G. Giusfredi, D. Mazzotti, M. Prevedelli, C. De Mauro, and M. Inguscio, "Extending the optical comb synthesizer to the infrared: from He at 1.083 µm to CO2 at 4.2 µm," in Proceedings of the 16th International Conference on Laser Spectroscopy, P.Hannaford, A.Sidorov, H.Bachor, and K.Baldwin, eds. (World Scientific, 2004), pp. 63-67.

De Natale, P.

P. De Natale, S. Borri, P. Cancio, G. Giusfredi, D. Mazzotti, M. Prevedelli, C. De Mauro, and M. Inguscio, "Extending the optical comb synthesizer to the infrared: from He at 1.083 µm to CO2 at 4.2 µm," in Proceedings of the 16th International Conference on Laser Spectroscopy, P.Hannaford, A.Sidorov, H.Bachor, and K.Baldwin, eds. (World Scientific, 2004), pp. 63-67.

Diddams, S. A.

I. Thomann, A. Bartels, K. L. Corwin, N. R. Newbury, L. Hollberg, S. A. Diddams, J. W. Nicholson, and M. F. Yan, "20-MHz Cr:forsterite femtosecond ring laser and continuum generation in the 1-2 µm range," Opt. Lett. 28, 1368-1370 (2003).
[CrossRef] [PubMed]

T. Ramond, S. A. Diddams, L. Hollberg, and A. Bartels, "Phase-coherent link from optical to microwave frequencies by means of the broadband continuum from a 1-GHz Ti:sapphire femtosecondoscillator," Opt. Lett. 27, 1842-1844 (2002).
[CrossRef]

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, Th. Udem, H. G. Robinson, J. C. Bergquist, W. M. Itano, R. E. Drullinger, and D. J. Wineland, "Optical frequency standards and measurements," IEEE J. Quantum Electron. 37, 1502-1513 (2001).
[CrossRef]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000).
[CrossRef] [PubMed]

Drullinger, R. E.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, Th. Udem, H. G. Robinson, J. C. Bergquist, W. M. Itano, R. E. Drullinger, and D. J. Wineland, "Optical frequency standards and measurements," IEEE J. Quantum Electron. 37, 1502-1513 (2001).
[CrossRef]

D. A. Jennings, C. R. Pollock, F. R. Petersen, R. E. Drullinger, K. M. Evenson, J. S. Wells, J. L. Hall, and H. P. Layer, "Direct frequency measurement of the I2-stabilized He-Ne 473-THz(633-nm) laser," Opt. Lett. 8, 136-138 (1983).
[CrossRef] [PubMed]

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]

Eckardt, R. C.

Evenson, K. M.

Fejer, M. M.

Fuji, T.

Giusfredi, G.

P. De Natale, S. Borri, P. Cancio, G. Giusfredi, D. Mazzotti, M. Prevedelli, C. De Mauro, and M. Inguscio, "Extending the optical comb synthesizer to the infrared: from He at 1.083 µm to CO2 at 4.2 µm," in Proceedings of the 16th International Conference on Laser Spectroscopy, P.Hannaford, A.Sidorov, H.Bachor, and K.Baldwin, eds. (World Scientific, 2004), pp. 63-67.

Gross, B.

T. Udem, A. Huber, B. Gross, J. Reichert, M. Prevedelli, M. Weitz, and T. W. Hänsch, "Phase-coherent measurement of the hydrogen 1S-2S transition frequency with an optical frequency interval divider chain, " Phys. Rev. Lett. 79, 2646-2649 (1997).
[CrossRef]

Hall, J. L.

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

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000).
[CrossRef] [PubMed]

D. A. Jennings, C. R. Pollock, F. R. Petersen, R. E. Drullinger, K. M. Evenson, J. S. Wells, J. L. Hall, and H. P. Layer, "Direct frequency measurement of the I2-stabilized He-Ne 473-THz(633-nm) laser," Opt. Lett. 8, 136-138 (1983).
[CrossRef] [PubMed]

Hänsch, T. W.

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

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000).
[CrossRef] [PubMed]

T. Udem, A. Huber, B. Gross, J. Reichert, M. Prevedelli, M. Weitz, and T. W. Hänsch, "Phase-coherent measurement of the hydrogen 1S-2S transition frequency with an optical frequency interval divider chain, " Phys. Rev. Lett. 79, 2646-2649 (1997).
[CrossRef]

H. R. Telle, D. Meschede, and T. W. Hänsch, "Realization of a new concept for visible frequency division: phase locking of harmonic and sum frequencies, " Opt. Lett. 15, 532-534 (1990).
[CrossRef] [PubMed]

Helmcke, J.

H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, and G. Zinner, "First phase-coherent frequency measurement of visible radiation, " Phys. Rev. Lett. 76, 18-21 (1996).
[CrossRef] [PubMed]

Hollberg, L.

Holzwarth, R.

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

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000).
[CrossRef] [PubMed]

Huber, A.

T. Udem, A. Huber, B. Gross, J. Reichert, M. Prevedelli, M. Weitz, and T. W. Hänsch, "Phase-coherent measurement of the hydrogen 1S-2S transition frequency with an optical frequency interval divider chain, " Phys. Rev. Lett. 79, 2646-2649 (1997).
[CrossRef]

Inguscio, M.

P. De Natale, S. Borri, P. Cancio, G. Giusfredi, D. Mazzotti, M. Prevedelli, C. De Mauro, and M. Inguscio, "Extending the optical comb synthesizer to the infrared: from He at 1.083 µm to CO2 at 4.2 µm," in Proceedings of the 16th International Conference on Laser Spectroscopy, P.Hannaford, A.Sidorov, H.Bachor, and K.Baldwin, eds. (World Scientific, 2004), pp. 63-67.

Itano, W. M.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, Th. Udem, H. G. Robinson, J. C. Bergquist, W. M. Itano, R. E. Drullinger, and D. J. Wineland, "Optical frequency standards and measurements," IEEE J. Quantum Electron. 37, 1502-1513 (2001).
[CrossRef]

Ivanov, E. N.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, Th. Udem, H. G. Robinson, J. C. Bergquist, W. M. Itano, R. E. Drullinger, and D. J. Wineland, "Optical frequency standards and measurements," IEEE J. Quantum Electron. 37, 1502-1513 (2001).
[CrossRef]

Jennings, D. A.

Jones, D. J.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000).
[CrossRef] [PubMed]

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]

Kourogi, M.

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. Kourogi, K. Nakagawa, and M. Ohtsu, "Wide-span optical frequency comb generator for accurate optical frequency difference measurement," IEEE J. Quantum Electron. 29, 2693-2701 (1993).
[CrossRef]

Krausz, F.

Layer, H. P.

Lipphardt, B.

H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, and G. Zinner, "First phase-coherent frequency measurement of visible radiation, " Phys. Rev. Lett. 76, 18-21 (1996).
[CrossRef] [PubMed]

Mazzotti, D.

P. De Natale, S. Borri, P. Cancio, G. Giusfredi, D. Mazzotti, M. Prevedelli, C. De Mauro, and M. Inguscio, "Extending the optical comb synthesizer to the infrared: from He at 1.083 µm to CO2 at 4.2 µm," in Proceedings of the 16th International Conference on Laser Spectroscopy, P.Hannaford, A.Sidorov, H.Bachor, and K.Baldwin, eds. (World Scientific, 2004), pp. 63-67.

Meschede, D.

Myers, L. E.

Nakagawa, K.

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. Kourogi, K. Nakagawa, and M. Ohtsu, "Wide-span optical frequency comb generator for accurate optical frequency difference measurement," IEEE J. Quantum Electron. 29, 2693-2701 (1993).
[CrossRef]

Newbury, N. R.

Nicholson, J. W.

Oates, C. W.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, Th. Udem, H. G. Robinson, J. C. Bergquist, W. M. Itano, R. E. Drullinger, and D. J. Wineland, "Optical frequency standards and measurements," IEEE J. Quantum Electron. 37, 1502-1513 (2001).
[CrossRef]

Ohtsu, M.

M. Kourogi, K. Nakagawa, and M. Ohtsu, "Wide-span optical frequency comb generator for accurate optical frequency difference measurement," IEEE J. Quantum Electron. 29, 2693-2701 (1993).
[CrossRef]

Petersen, F. R.

Pollock, C. R.

Prevedelli, M.

T. Udem, A. Huber, B. Gross, J. Reichert, M. Prevedelli, M. Weitz, and T. W. Hänsch, "Phase-coherent measurement of the hydrogen 1S-2S transition frequency with an optical frequency interval divider chain, " Phys. Rev. Lett. 79, 2646-2649 (1997).
[CrossRef]

P. De Natale, S. Borri, P. Cancio, G. Giusfredi, D. Mazzotti, M. Prevedelli, C. De Mauro, and M. Inguscio, "Extending the optical comb synthesizer to the infrared: from He at 1.083 µm to CO2 at 4.2 µm," in Proceedings of the 16th International Conference on Laser Spectroscopy, P.Hannaford, A.Sidorov, H.Bachor, and K.Baldwin, eds. (World Scientific, 2004), pp. 63-67.

Ramond, T.

Ranka, J. K.

J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 25, 25-27 (2000).
[CrossRef]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000).
[CrossRef] [PubMed]

Reichert, J.

T. Udem, A. Huber, B. Gross, J. Reichert, M. Prevedelli, M. Weitz, and T. W. Hänsch, "Phase-coherent measurement of the hydrogen 1S-2S transition frequency with an optical frequency interval divider chain, " Phys. Rev. Lett. 79, 2646-2649 (1997).
[CrossRef]

Riehle, F.

H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, and G. Zinner, "First phase-coherent frequency measurement of visible radiation, " Phys. Rev. Lett. 76, 18-21 (1996).
[CrossRef] [PubMed]

Robinson, H. G.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, Th. Udem, H. G. Robinson, J. C. Bergquist, W. M. Itano, R. E. Drullinger, and D. J. Wineland, "Optical frequency standards and measurements," IEEE J. Quantum Electron. 37, 1502-1513 (2001).
[CrossRef]

Schnatz, H.

H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, and G. Zinner, "First phase-coherent frequency measurement of visible radiation, " Phys. Rev. Lett. 76, 18-21 (1996).
[CrossRef] [PubMed]

Siegman, A. E.

A. E. Siegman, Lasers (Oxford U. Press, 1986).

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. J.

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]

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]

H. R. Telle, D. Meschede, and T. W. Hänsch, "Realization of a new concept for visible frequency division: phase locking of harmonic and sum frequencies, " Opt. Lett. 15, 532-534 (1990).
[CrossRef] [PubMed]

Thomann, I.

Udem, T.

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

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000).
[CrossRef] [PubMed]

T. Udem, A. Huber, B. Gross, J. Reichert, M. Prevedelli, M. Weitz, and T. W. Hänsch, "Phase-coherent measurement of the hydrogen 1S-2S transition frequency with an optical frequency interval divider chain, " Phys. Rev. Lett. 79, 2646-2649 (1997).
[CrossRef]

Udem, Th.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, Th. Udem, H. G. Robinson, J. C. Bergquist, W. M. Itano, R. E. Drullinger, and D. J. Wineland, "Optical frequency standards and measurements," IEEE J. Quantum Electron. 37, 1502-1513 (2001).
[CrossRef]

Weitz, M.

T. Udem, A. Huber, B. Gross, J. Reichert, M. Prevedelli, M. Weitz, and T. W. Hänsch, "Phase-coherent measurement of the hydrogen 1S-2S transition frequency with an optical frequency interval divider chain, " Phys. Rev. Lett. 79, 2646-2649 (1997).
[CrossRef]

Wells, J. S.

Windeler, R. S.

J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 25, 25-27 (2000).
[CrossRef]

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000).
[CrossRef] [PubMed]

Wineland, D. J.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, Th. Udem, H. G. Robinson, J. C. Bergquist, W. M. Itano, R. E. Drullinger, and D. J. Wineland, "Optical frequency standards and measurements," IEEE J. Quantum Electron. 37, 1502-1513 (2001).
[CrossRef]

Yan, M. F.

Ye, J.

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

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000).
[CrossRef] [PubMed]

Zinner, G.

H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, and G. Zinner, "First phase-coherent frequency measurement of visible radiation, " Phys. Rev. Lett. 76, 18-21 (1996).
[CrossRef] [PubMed]

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]

IEEE J. Quantum Electron.

L. Hollberg, C. W. Oates, E. A. Curtis, E. N. Ivanov, S. A. Diddams, Th. Udem, H. G. Robinson, J. C. Bergquist, W. M. Itano, R. E. Drullinger, and D. J. Wineland, "Optical frequency standards and measurements," IEEE J. Quantum Electron. 37, 1502-1513 (2001).
[CrossRef]

M. Kourogi, K. Nakagawa, and M. Ohtsu, "Wide-span optical frequency comb generator for accurate optical frequency difference measurement," IEEE J. Quantum Electron. 29, 2693-2701 (1993).
[CrossRef]

J. Opt. Soc. Am. B

Nature

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

Opt. Lett.

L. E. Myers,R. C. Eckardt, M. M. Fejer, R. L. Byer, and W. R. Bosenberg, "Multigrating quasi-phase-matched optical parametric oscillator in periodically poled LiNbO3," Opt. Lett. 21, 591-593 (1996).
[CrossRef] [PubMed]

H. R. Telle, D. Meschede, and T. W. Hänsch, "Realization of a new concept for visible frequency division: phase locking of harmonic and sum frequencies, " Opt. Lett. 15, 532-534 (1990).
[CrossRef] [PubMed]

T. Ramond, S. A. Diddams, L. Hollberg, and A. Bartels, "Phase-coherent link from optical to microwave frequencies by means of the broadband continuum from a 1-GHz Ti:sapphire femtosecondoscillator," Opt. Lett. 27, 1842-1844 (2002).
[CrossRef]

I. Thomann, A. Bartels, K. L. Corwin, N. R. Newbury, L. Hollberg, S. A. Diddams, J. W. Nicholson, and M. F. Yan, "20-MHz Cr:forsterite femtosecond ring laser and continuum generation in the 1-2 µm range," Opt. Lett. 28, 1368-1370 (2003).
[CrossRef] [PubMed]

T. Fuji, A. Apolonski, and F. Krausz, "Self-stabilization of carrier-envelope offset phase by use of difference-frequency generation," Opt. Lett. 29, 632-634 (2004).
[CrossRef] [PubMed]

J. K. Ranka, R. S. Windeler, and A. J. Stentz, "Visible continuum generation in air silica microstructure optical fibers with anomalous dispersion at 800 nm," Opt. Lett. 25, 25-27 (2000).
[CrossRef]

D. A. Jennings, C. R. Pollock, F. R. Petersen, R. E. Drullinger, K. M. Evenson, J. S. Wells, J. L. Hall, and H. P. Layer, "Direct frequency measurement of the I2-stabilized He-Ne 473-THz(633-nm) laser," Opt. Lett. 8, 136-138 (1983).
[CrossRef] [PubMed]

Phys. Rev. Lett.

S. A. Diddams, D. J. Jones, J. Ye, S. T. Cundiff, J. L. Hall, J. K. Ranka, R. S. Windeler, R. Holzwarth, T. Udem, and T. W. Hänsch, "Direct link between microwave and optical frequencies with a 300 THz femtosecond laser comb," Phys. Rev. Lett. 84, 5102-5105 (2000).
[CrossRef] [PubMed]

H. Schnatz, B. Lipphardt, J. Helmcke, F. Riehle, and G. Zinner, "First phase-coherent frequency measurement of visible radiation, " Phys. Rev. Lett. 76, 18-21 (1996).
[CrossRef] [PubMed]

T. Udem, A. Huber, B. Gross, J. Reichert, M. Prevedelli, M. Weitz, and T. W. Hänsch, "Phase-coherent measurement of the hydrogen 1S-2S transition frequency with an optical frequency interval divider chain, " Phys. Rev. Lett. 79, 2646-2649 (1997).
[CrossRef]

Rev. Sci. Instrum.

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

Other

This approach requires a finesse sufficiently high to avoid the contribution of cavity modes close to unwanted resonances and may result in a cavity finesse higher than a few thousands, which can be considered a realistic value for cavities containing optical elements.

The detailed spectrum of a mode-locked laser depends critically on the dispersion properties of its cavity and eventually those of the medium employed to broaden its spectrum.

P. De Natale, S. Borri, P. Cancio, G. Giusfredi, D. Mazzotti, M. Prevedelli, C. De Mauro, and M. Inguscio, "Extending the optical comb synthesizer to the infrared: from He at 1.083 µm to CO2 at 4.2 µm," in Proceedings of the 16th International Conference on Laser Spectroscopy, P.Hannaford, A.Sidorov, H.Bachor, and K.Baldwin, eds. (World Scientific, 2004), pp. 63-67.

A. E. Siegman, Lasers (Oxford U. Press, 1986).

R. W. Boyd, Nonlinear Optics (Academic, 1992).

P. N. Butcher and D. Cotter, The Elements of Nonlinear Optics (Cambridge U. Press, 1993).

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Figures (2)

Fig. 1
Fig. 1

Experimental setup of the optical rectifier for mode-locked lasers. A nonlinear medium, chosen for DFG between two spectral regions of a mode-locked laser, is placed into an optical cavity resonant with one frequency component ω ¯ generated by DFG. The M 1 , 2 , 3 mirrors are highly reflective at the frequencies generated by DFG and highly transmitting for all the other frequencies. The output mirror M 4 is chosen to be slightly transmitting for the circulating light. MSE, mode-selective etalons.

Fig. 2
Fig. 2

Output power spectrum of the rectifier discussed in the text. Each point corresponds to the frequency component of the polarization at f p = ω p 2 π . The power is normalized to the single-pass conversion efficiency of the nonlinear crystal at the center frequency f ¯ ; the dashed curve corresponds to the emission that one would have in a single-pass DFG. The inset represents a magnification of the same spectrum around the resonant mode (filled circle), with the frequency expressed in gigahertz. The polarization is here considered to have a 1 cosh profile centered at f ¯ with a FWHM of 6.4 THz (dashed line). The graph shows the increase of the power available on the resonant frequency component and the corresponding reduction of the power on all the nonresonant components.

Equations (17)

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E ( t ) = n E 0 ( t n τ ) exp ( i n ϕ 0 ) ,
E ̃ ( ω ) = 2 π E ̃ 0 ( ω ) n = δ ( ω τ + ϕ 0 2 π n )
P 2 ( z , t ) = χ ( 2 ) j , m E ̃ * ( ω m ) E ̃ ( ω j ) exp [ i ( k j k m ) z ] exp [ i ( ω j ω m ) t ] ,
E ̃ int ( ω p ) = 1 ( 1 T ) 1 2 exp ( i ω p L eff c ) exp ( i k NL z 1 ) exp ( i ω p z 1 c ) 4 π ω p 2 n ( ω p ) 1 2 c 2 × j m = p exp { i [ k NL ( j , m ) k p ] l } 1 k p 2 k NL ( j , m ) 2 χ ( 2 ) E * ( ω m ) E ( ω j ) ,
E ̃ out ( ω p ) = T 1 ( 1 T ) 1 2 exp ( i ω p L eff c ) E ̃ sp ( ω p ) .
N c π l ω r 1 v g ( ω ¯ 1 ) 1 v g ( ω ¯ 2 ) 1 = Δ ω acc ω r .
E fs ( z ) = E ¯ fs exp ( i ω p z c ) .
E fs ( 1 , 2 ) ( z ) = E ¯ fs ( 1 , 2 ) exp ( i ω p z c ) ,
P 2 ( z ) = P NL exp ( i k NL z ) ,
[ 2 z 2 + ϵ ( ω p ) ω p 2 c 2 ] E ( z ) = 4 π ω p 2 c 2 P NL exp ( i k NL z ) .
E med ( z ) = 4 π c 2 ω p 2 P NL k p 2 k NL 2 exp ( i k NL z ) + E ¯ med exp ( i k p z ) ,
E ¯ med ( z 1 ) = ϵ ( ω p ) 1 4 E ¯ fs ( 1 ) ( z 1 ) ,
E ¯ med ( z 1 + l ) = ϵ ( ω p ) 1 4 E ¯ fs ( 2 ) ( z 1 + l ) .
E ¯ fs ( 1 ) ( 0 ) = 1 T E ¯ fs ( 2 ) ( L ) ,
E fs ( 2 ) ( L ) = E ¯ fs ( 2 ) exp ( i ω p L c ) = 4 π ω p 2 ϵ ( ω p ) 1 4 c 2 exp ( i k NL z 1 ) exp ( i ω p z 1 c ) ( 1 T ) 1 2 exp ( i ω p L eff c ) exp [ i ( k NL k p ) l ] 1 k p 2 k NL 2 P NL ,
E med ( z 1 + l ) = 4 π ω p 2 P NL c 2 1 exp [ i ( k NL k p ) l ] k p 2 k NL 2 exp ( i k p l ) exp ( i k NL z 1 ) ,
E fs ( 2 , sp ) ( L ) = 4 π ω p 2 ϵ ( ω p ) 1 4 c 2 exp ( i k p l ) exp ( i k NL z 1 ) exp [ i ( L l z 1 ) ] ω p c 1 exp [ i ( k NL k p ) l ] k p 2 k NL 2 P NL .

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