Abstract

We investigate the carrier-envelope phase dynamics of octave-spanning Ti:sapphire lasers and perform a complete noise analysis of the carrier-envelope phase stabilization. We model the effect of the laser dynamics on the residual carrier-envelope phase noise by deriving a transfer function representation of the octave-spanning frequency comb. The modelled phase noise and the experimental results show excellent agreement. This greatly enhances our capability of predicting the dependence of the residual carrier-envelope phase noise on the feedback loop filter, the carrier-envelope frequency control mechanism and the pump laser used.

© 2006 Optical Society of America

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  4. R. Holzwarth, T. Udem, T.W. Hänsch, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, "Optical Frequency Synthesizer for Precision Spectroscopy," Phys. Rev. Lett. 85, 2264-2268 (2000).
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  8. A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T.W. H¨ansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
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    [CrossRef]
  22. F. X. Kärtner, I. D. Jung, and U. Keller, "Soliton Mode-Locking with Saturable Absorbers," IEEE J. Sel. Top. Quantum Electron. 2, 540-556 (1996).
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2005 (1)

2004 (2)

2003 (2)

K.W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, "Detailed Studies and Control of Intensity-Related Dynamics of Femtosecond Frequency Combs From Mode-Locked Ti:Sapphire Lasers," IEEE J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T.W. H¨ansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

2001 (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]

T. Udem, S. A. Diddams, K. R. Vogel, C.W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, and L. Hollberg, "Absolute Frequency Measurements of the Hg+ and Ca Optical Clock Transitions with a Femtosecond Laser," Phys. Rev. Lett. 86, 4996-4999 (2001).
[CrossRef] [PubMed]

H. A. Haus and E. P. Ippen, "Group velocity of solitons," Opt. Lett. 26, 1654-1656 (2001).
[CrossRef]

2000 (6)

J. Ye, J. L. Hall, and S. A. Diddams, "Precision phase control of an ultrawide-bandwidth femtosecond laser: a network of ultrastable frequency marks across the visible spectrum," Opt. Lett. 25, 1675-1677 (2000).
[CrossRef]

J. von Zanthier, T. Becker, M. Eichenseer, A.Y. Nevsky, C. Schwedes, E. Peik, H. Walther, R. Holzwarth, J. Reichert, T. Udem, T.W. H¨ansch, P.V. Pokasov, M. N. Skvortsov, and S. N. Bagayev, "Absolute frequency measurement of the In+ clock transition with a mode-locked laser," Opt. Lett. 25, 1729-1731 (2000).
[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]

R. Holzwarth, T. Udem, T.W. Hänsch, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, "Optical Frequency Synthesizer for Precision Spectroscopy," Phys. Rev. Lett. 85, 2264-2268 (2000).
[CrossRef] [PubMed]

M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T.W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, "Measurement of the Hydrogen 1S-2S Transition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock," Phys. Rev. Lett. 84, 5496-5499 (2000).
[CrossRef] [PubMed]

H. A. Haus, "Mode-Locking of Lasers," IEEE J. Sel. Top. Quantum Electron. 6, 1173-1185 (2000).
[CrossRef]

1999 (2)

1996 (2)

L. Xu, C. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T.W. Hänsch, "Route to phase control of ultrashort light pulses," Opt. Lett. 21, 2008-2010 (1996).
[CrossRef] [PubMed]

F. X. Kärtner, I. D. Jung, and U. Keller, "Soliton Mode-Locking with Saturable Absorbers," IEEE J. Sel. Top. Quantum Electron. 2, 540-556 (1996).
[CrossRef]

1995 (1)

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
[CrossRef]

1990 (1)

Abgrall, M.

M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T.W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, "Measurement of the Hydrogen 1S-2S Transition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock," Phys. Rev. Lett. 84, 5496-5499 (2000).
[CrossRef] [PubMed]

Baltuska, A.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T.W. H¨ansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Becker, T.

Bergquist, J. C.

T. Udem, S. A. Diddams, K. R. Vogel, C.W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, and L. Hollberg, "Absolute Frequency Measurements of the Hg+ and Ca Optical Clock Transitions with a Femtosecond Laser," Phys. Rev. Lett. 86, 4996-4999 (2001).
[CrossRef] [PubMed]

Birge, J. R.

Brabec, T.

Brovelli, L. R.

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
[CrossRef]

Calasso, I.

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
[CrossRef]

Chen, Y.

Cho, S. H.

Clairon, A.

M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T.W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, "Measurement of the Hydrogen 1S-2S Transition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock," Phys. Rev. Lett. 84, 5496-5499 (2000).
[CrossRef] [PubMed]

Cundiff, S. T.

K.W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, "Detailed Studies and Control of Intensity-Related Dynamics of Femtosecond Frequency Combs From Mode-Locked Ti:Sapphire Lasers," IEEE J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

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]

Curtis, E. A.

T. Udem, S. A. Diddams, K. R. Vogel, C.W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, and L. Hollberg, "Absolute Frequency Measurements of the Hg+ and Ca Optical Clock Transitions with a Femtosecond Laser," Phys. Rev. Lett. 86, 4996-4999 (2001).
[CrossRef] [PubMed]

Diddams, S. A.

T. Udem, S. A. Diddams, K. R. Vogel, C.W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, and L. Hollberg, "Absolute Frequency Measurements of the Hg+ and Ca Optical Clock Transitions with a Femtosecond Laser," Phys. Rev. Lett. 86, 4996-4999 (2001).
[CrossRef] [PubMed]

J. Ye, J. L. Hall, and S. A. Diddams, "Precision phase control of an ultrawide-bandwidth femtosecond laser: a network of ultrastable frequency marks across the visible spectrum," Opt. Lett. 25, 1675-1677 (2000).
[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]

Drullinger, R. E.

T. Udem, S. A. Diddams, K. R. Vogel, C.W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, and L. Hollberg, "Absolute Frequency Measurements of the Hg+ and Ca Optical Clock Transitions with a Femtosecond Laser," Phys. Rev. Lett. 86, 4996-4999 (2001).
[CrossRef] [PubMed]

Eichenseer, M.

Eikema, K. S. E.

S. Witte, R. T. Zinkstok, W. Hogervorst, K. S. E. Eikema, "Control and precise measurement of carrier-envelope phase dynamics," Appl. Phys. B 78, 5-12 (2004).
[CrossRef]

Ell, R.

Fujimoto, J. G.

Gohle, C.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T.W. H¨ansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Goulielmakis, E.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T.W. H¨ansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[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]

J. Ye, J. L. Hall, and S. A. Diddams, "Precision phase control of an ultrawide-bandwidth femtosecond laser: a network of ultrastable frequency marks across the visible spectrum," Opt. Lett. 25, 1675-1677 (2000).
[CrossRef]

Hänsch, T.W.

R. Holzwarth, T. Udem, T.W. Hänsch, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, "Optical Frequency Synthesizer for Precision Spectroscopy," Phys. Rev. Lett. 85, 2264-2268 (2000).
[CrossRef] [PubMed]

M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T.W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, "Measurement of the Hydrogen 1S-2S Transition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock," Phys. Rev. Lett. 84, 5496-5499 (2000).
[CrossRef] [PubMed]

T. Udem, J. Reichert, R. Holzwarth, and T.W. Hänsch, "Accurate measurement of large optical frequency differences with a mode-locked laser," Opt. Lett. 24, 881-883 (1999).
[CrossRef]

L. Xu, C. Spielmann, A. Poppe, T. Brabec, F. Krausz, and T.W. Hänsch, "Route to phase control of ultrashort light pulses," Opt. Lett. 21, 2008-2010 (1996).
[CrossRef] [PubMed]

Haus, H. A.

Hentschel, M.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T.W. H¨ansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Hogervorst, W.

S. Witte, R. T. Zinkstok, W. Hogervorst, K. S. E. Eikema, "Control and precise measurement of carrier-envelope phase dynamics," Appl. Phys. B 78, 5-12 (2004).
[CrossRef]

Hollberg, L.

T. Udem, S. A. Diddams, K. R. Vogel, C.W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, and L. Hollberg, "Absolute Frequency Measurements of the Hg+ and Ca Optical Clock Transitions with a Femtosecond Laser," Phys. Rev. Lett. 86, 4996-4999 (2001).
[CrossRef] [PubMed]

Holman, K.W.

K.W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, "Detailed Studies and Control of Intensity-Related Dynamics of Femtosecond Frequency Combs From Mode-Locked Ti:Sapphire Lasers," IEEE J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

Holzwarth, R.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T.W. H¨ansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

R. Holzwarth, T. Udem, T.W. Hänsch, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, "Optical Frequency Synthesizer for Precision Spectroscopy," Phys. Rev. Lett. 85, 2264-2268 (2000).
[CrossRef] [PubMed]

M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T.W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, "Measurement of the Hydrogen 1S-2S Transition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock," Phys. Rev. Lett. 84, 5496-5499 (2000).
[CrossRef] [PubMed]

J. von Zanthier, T. Becker, M. Eichenseer, A.Y. Nevsky, C. Schwedes, E. Peik, H. Walther, R. Holzwarth, J. Reichert, T. Udem, T.W. H¨ansch, P.V. Pokasov, M. N. Skvortsov, and S. N. Bagayev, "Absolute frequency measurement of the In+ clock transition with a mode-locked laser," Opt. Lett. 25, 1729-1731 (2000).
[CrossRef]

T. Udem, J. Reichert, R. Holzwarth, and T.W. Hänsch, "Accurate measurement of large optical frequency differences with a mode-locked laser," Opt. Lett. 24, 881-883 (1999).
[CrossRef]

Ippen, E. P.

Itano, W. M.

T. Udem, S. A. Diddams, K. R. Vogel, C.W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, and L. Hollberg, "Absolute Frequency Measurements of the Hg+ and Ca Optical Clock Transitions with a Femtosecond Laser," Phys. Rev. Lett. 86, 4996-4999 (2001).
[CrossRef] [PubMed]

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]

Jones, R. J.

K.W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, "Detailed Studies and Control of Intensity-Related Dynamics of Femtosecond Frequency Combs From Mode-Locked Ti:Sapphire Lasers," IEEE J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

Jung, I. D.

F. X. Kärtner, I. D. Jung, and U. Keller, "Soliton Mode-Locking with Saturable Absorbers," IEEE J. Sel. Top. Quantum Electron. 2, 540-556 (1996).
[CrossRef]

Kaertner, F. X.

Kamp, M.

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
[CrossRef]

Kärtner, F. X.

Keller, U.

F. X. Kärtner, I. D. Jung, and U. Keller, "Soliton Mode-Locking with Saturable Absorbers," IEEE J. Sel. Top. Quantum Electron. 2, 540-556 (1996).
[CrossRef]

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
[CrossRef]

Kim, J.

Kleppner, D.

Knight, J. C.

R. Holzwarth, T. Udem, T.W. Hänsch, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, "Optical Frequency Synthesizer for Precision Spectroscopy," Phys. Rev. Lett. 85, 2264-2268 (2000).
[CrossRef] [PubMed]

Kopf, D.

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
[CrossRef]

Krausz, F.

Kuzucu, O.

Lai, Y.

Laurent, P.

M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T.W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, "Measurement of the Hydrogen 1S-2S Transition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock," Phys. Rev. Lett. 84, 5496-5499 (2000).
[CrossRef] [PubMed]

Lee, W. D.

T. Udem, S. A. Diddams, K. R. Vogel, C.W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, and L. Hollberg, "Absolute Frequency Measurements of the Hg+ and Ca Optical Clock Transitions with a Femtosecond Laser," Phys. Rev. Lett. 86, 4996-4999 (2001).
[CrossRef] [PubMed]

Lemonde, P.

M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T.W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, "Measurement of the Hydrogen 1S-2S Transition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock," Phys. Rev. Lett. 84, 5496-5499 (2000).
[CrossRef] [PubMed]

Marian, A.

K.W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, "Detailed Studies and Control of Intensity-Related Dynamics of Femtosecond Frequency Combs From Mode-Locked Ti:Sapphire Lasers," IEEE J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

Matos, L.

Morgner, U.

Mücke, O. D.

Nevsky, A.Y.

Niering, M.

M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T.W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, "Measurement of the Hydrogen 1S-2S Transition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock," Phys. Rev. Lett. 84, 5496-5499 (2000).
[CrossRef] [PubMed]

Oates, C.W.

T. Udem, S. A. Diddams, K. R. Vogel, C.W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, and L. Hollberg, "Absolute Frequency Measurements of the Hg+ and Ca Optical Clock Transitions with a Femtosecond Laser," Phys. Rev. Lett. 86, 4996-4999 (2001).
[CrossRef] [PubMed]

Peik, E.

Pokasov, P.

M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T.W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, "Measurement of the Hydrogen 1S-2S Transition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock," Phys. Rev. Lett. 84, 5496-5499 (2000).
[CrossRef] [PubMed]

Poppe, A.

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]

Reichert, J.

Russell, P. St. J.

R. Holzwarth, T. Udem, T.W. Hänsch, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, "Optical Frequency Synthesizer for Precision Spectroscopy," Phys. Rev. Lett. 85, 2264-2268 (2000).
[CrossRef] [PubMed]

Salomon, C.

M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T.W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, "Measurement of the Hydrogen 1S-2S Transition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock," Phys. Rev. Lett. 84, 5496-5499 (2000).
[CrossRef] [PubMed]

Santarelli, G.

M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T.W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, "Measurement of the Hydrogen 1S-2S Transition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock," Phys. Rev. Lett. 84, 5496-5499 (2000).
[CrossRef] [PubMed]

Schibli, T. R.

Schwedes, C.

Scrinzi, A.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T.W. H¨ansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Spielmann, C.

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]

Udem, T.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T.W. H¨ansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

T. Udem, S. A. Diddams, K. R. Vogel, C.W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, and L. Hollberg, "Absolute Frequency Measurements of the Hg+ and Ca Optical Clock Transitions with a Femtosecond Laser," Phys. Rev. Lett. 86, 4996-4999 (2001).
[CrossRef] [PubMed]

R. Holzwarth, T. Udem, T.W. Hänsch, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, "Optical Frequency Synthesizer for Precision Spectroscopy," Phys. Rev. Lett. 85, 2264-2268 (2000).
[CrossRef] [PubMed]

J. von Zanthier, T. Becker, M. Eichenseer, A.Y. Nevsky, C. Schwedes, E. Peik, H. Walther, R. Holzwarth, J. Reichert, T. Udem, T.W. H¨ansch, P.V. Pokasov, M. N. Skvortsov, and S. N. Bagayev, "Absolute frequency measurement of the In+ clock transition with a mode-locked laser," Opt. Lett. 25, 1729-1731 (2000).
[CrossRef]

M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T.W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, "Measurement of the Hydrogen 1S-2S Transition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock," Phys. Rev. Lett. 84, 5496-5499 (2000).
[CrossRef] [PubMed]

T. Udem, J. Reichert, R. Holzwarth, and T.W. Hänsch, "Accurate measurement of large optical frequency differences with a mode-locked laser," Opt. Lett. 24, 881-883 (1999).
[CrossRef]

Uiberacker, M.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T.W. H¨ansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Vogel, K. R.

T. Udem, S. A. Diddams, K. R. Vogel, C.W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, and L. Hollberg, "Absolute Frequency Measurements of the Hg+ and Ca Optical Clock Transitions with a Femtosecond Laser," Phys. Rev. Lett. 86, 4996-4999 (2001).
[CrossRef] [PubMed]

von Zanthier, J.

Wadsworth, W. J.

R. Holzwarth, T. Udem, T.W. Hänsch, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, "Optical Frequency Synthesizer for Precision Spectroscopy," Phys. Rev. Lett. 85, 2264-2268 (2000).
[CrossRef] [PubMed]

Walther, H.

Weitz, M.

M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T.W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, "Measurement of the Hydrogen 1S-2S Transition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock," Phys. Rev. Lett. 84, 5496-5499 (2000).
[CrossRef] [PubMed]

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]

Winter, A.

Witte, S.

S. Witte, R. T. Zinkstok, W. Hogervorst, K. S. E. Eikema, "Control and precise measurement of carrier-envelope phase dynamics," Appl. Phys. B 78, 5-12 (2004).
[CrossRef]

Xu, L.

Yakovlev, V. S.

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T.W. H¨ansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Ye, J.

K.W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, "Detailed Studies and Control of Intensity-Related Dynamics of Femtosecond Frequency Combs From Mode-Locked Ti:Sapphire Lasers," IEEE J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

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]

J. Ye, J. L. Hall, and S. A. Diddams, "Precision phase control of an ultrawide-bandwidth femtosecond laser: a network of ultrastable frequency marks across the visible spectrum," Opt. Lett. 25, 1675-1677 (2000).
[CrossRef]

Zinkstok, R. T.

S. Witte, R. T. Zinkstok, W. Hogervorst, K. S. E. Eikema, "Control and precise measurement of carrier-envelope phase dynamics," Appl. Phys. B 78, 5-12 (2004).
[CrossRef]

Appl. Phys. B (1)

S. Witte, R. T. Zinkstok, W. Hogervorst, K. S. E. Eikema, "Control and precise measurement of carrier-envelope phase dynamics," Appl. Phys. B 78, 5-12 (2004).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (3)

K.W. Holman, R. J. Jones, A. Marian, S. T. Cundiff, and J. Ye, "Detailed Studies and Control of Intensity-Related Dynamics of Femtosecond Frequency Combs From Mode-Locked Ti:Sapphire Lasers," IEEE J. Sel. Top. Quantum Electron. 9, 1018-1024 (2003).
[CrossRef]

H. A. Haus, "Mode-Locking of Lasers," IEEE J. Sel. Top. Quantum Electron. 6, 1173-1185 (2000).
[CrossRef]

F. X. Kärtner, I. D. Jung, and U. Keller, "Soliton Mode-Locking with Saturable Absorbers," IEEE J. Sel. Top. Quantum Electron. 2, 540-556 (1996).
[CrossRef]

J. Opt. Soc. Am. B (2)

Nature (1)

A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T.W. H¨ansch, and F. Krausz, "Attosecond control of electronic processes by intense light fields," Nature 421, 611-615 (2003).
[CrossRef] [PubMed]

Opt. Eng. (1)

F. X. Kärtner, L. R. Brovelli, D. Kopf, M. Kamp, I. Calasso, and U. Keller, "Control of solid state laser dynamics by semiconductor devices," Opt. Eng. 34, 2024-2036 (1995).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Phys. Rev. Lett. (3)

R. Holzwarth, T. Udem, T.W. Hänsch, J. C. Knight, W. J. Wadsworth, P. St. J. Russell, "Optical Frequency Synthesizer for Precision Spectroscopy," Phys. Rev. Lett. 85, 2264-2268 (2000).
[CrossRef] [PubMed]

M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T.W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, "Measurement of the Hydrogen 1S-2S Transition Frequency by Phase Coherent Comparison with a Microwave Cesium Fountain Clock," Phys. Rev. Lett. 84, 5496-5499 (2000).
[CrossRef] [PubMed]

T. Udem, S. A. Diddams, K. R. Vogel, C.W. Oates, E. A. Curtis, W. D. Lee, W. M. Itano, R. E. Drullinger, J. C. Bergquist, and L. Hollberg, "Absolute Frequency Measurements of the Hg+ and Ca Optical Clock Transitions with a Femtosecond Laser," Phys. Rev. Lett. 86, 4996-4999 (2001).
[CrossRef] [PubMed]

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]

Other (3)

G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback control of dynamic systems (Addison-Wesley, 3rd edition, Reading, MA, 1994).

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 3rd edition, San Diego, 2001).

F. M. Gardner, Phaselock Techniques (John Wiley, 3rd edition, Hoboken, NJ, 2005).
[CrossRef]

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Figures (12)

Fig. 1.
Fig. 1.

(a) Carrier-envelope frequency shift (left axis) and relative change in intracavity power (right axis) as a function of pump power. Both curves make evident the presence of a cw breakthrough for pump powers above 6.3W, which is confirmed by the appearance of a cw component in the optical spectrum shown in (b). For clarity, the spectra are vertically offset by 10 dB.

Fig. 2.
Fig. 2.

Relative intensity noise (RIN) of a Coherent Verdi-V6 (red curve) and a Spectra-Physics Millennia Xs (blue curve). The measurement noise floor is given by the black curve.

Fig. 3.
Fig. 3.

Comparison of the carrier-envelope phase noise of a self-referenced 200MHz Ti:sapphire frequency comb pumped by a Coherent Verdi-V6 (red and green curves) and by a Spectra-Physics Millennia Xs (blue and orange curves).

Fig. 4.
Fig. 4.

Block diagram of the phase-lock loop (PLL) composed of the f CE-stabilized laser. The voltage-controlled oscillator (VCO) is depicted in the dashed box.

Fig. 5.
Fig. 5.

Mode locking related energy-dependent loss q ml(E). At point 1, where dq ml=dE<0, mode locking stability is reduced. Stable mode locking occurs at operating point 2, where dq ml=dE > 0 or equal to 0, if the pulse energy is not yet too high leading to cw breakthrough or to multiple pulse operation.

Fig. 6.
Fig. 6.

Calculated amplitude and phase response of intracavity power with pump power for cw operation (red) and for different values of saturable absorption: q E s P s = 10 r τ L ( blue ) , q E s P s = 50 r τ L ( green ) , and q E s P s = 150 r τ L ( orange ) .

Fig. 7.
Fig. 7.

Schematic of the transfer function measurement setup. In order to measure only the contribution from the OSFC laser itself, a first calibration measurement is performed with PD1 measuring the AOM and AOM driver response (PD1 and PD2 are the same photo detector). The OSFC laser transfer function is measured by detecting with PD2 the reflection from one intracavity BaF2 plate and subtracting the AOM and AOM driver response.

Fig. 8.
Fig. 8.

Measured (red and blue, measurement setup in Fig. 7) and modelled (green and orange) amplitude and phase response of OSFC laser, in cw and mode-locked operation.

Fig. 9.
Fig. 9.

Block diagram describing the addition of intensity noise to the laser PLL.

Fig. 10.
Fig. 10.

Measured (blue) and calculated (red) transfer functions for loop filter (top) and AOM (bottom). Amplitude response is on the left and phase response on the right.

Fig. 11.
Fig. 11.

Carrier-envelope phase noise spectrum of the Millennia-Xs-pumped OSFC. The red curve is the calculated spectrum, the blue curve is the measurement for phase locked carrier-envelope frequency.

Fig. 12.
Fig. 12.

Amplitude (top) and phase (bottom) of open-loop transfer function of the laser PLL (red curves) corresponding to Fig. 9. The contribution from the loop filter (green), AOM (blue) and laser dynamics (orange) to the open-loop phase are also shown. The zoomed plots on the right-hand side confirm that the PLL satisfies the Nyquist stability criterion (gain margin 2 dB, phase margin 12°).

Tables (1)

Tables Icon

Table 1. Transfer functions of the Ti:sapphire laser, phase detector, loop filter, and AOM.

Equations (22)

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

f CE = Δ ϕ CE 2 π T R .
e i 2 π f c ( t z v p ) ,
Δ ϕ CE = 2 π f c ( 1 v g ( f c ) v p ( f c ) ) T R
f CE = f c ( 1 v g ( f c ) v p ( f c ) ) .
T R A T = D irrev A i D 2 2 t 2 A A 2 A ,
A ( T , t ) = A 0 sech ( t τ ) e i ϕ s T T R ,
ϕ s = 1 2 δ A 0 2 .
L pert = δ ω c t ( A 2 A ) .
T R Δ t ( T ) T | self steep = Δ ( 1 v g ) = δ ω c A 0 2 = 2 ϕ s ω c .
f CE = f R 2 π Δ ϕ CE = f R ϕ s 2 π + f c T Δ t ( T ) self steep + f c ( 1 v g ( f c ) v p ( f c ) )
= f R 4 π δA 0 2 + 2 f R 4 π δA 0 2 + f c ( 1 v g ( f c ) v p ( f c ) ) .
f CE = f R 4 π δ A 0 2 + f c ( 1 v g ( f c ) v p ( f c ) ) .
c f P intra = Δ f CE Δ P intra ,
Δ f CE Δ P intra = L n 2 4 λ c A eff τ ,
T R d E d T = ( g l q ( E ) ) E
T R d g d T = g g 0 τ L T R g E E sat ,
T R E d T = q E s E s Δ E + E s Δ g
T R g d T = T R τ stim Δ g g s E sat Δ E + T R τ L Δ g 0 ,
Δ E ˜ = P s K 0 τ L s 2 + ( R τ L + q E s P s ) s + P s q E s R τ L + R 1 τ L τ p ( 1 + q s L ) Δ P ˜ p ,
H CL ( s ) = H Tisa ( s ) 1 + H Tisa ( s ) H PD ( s ) H LF ( s ) H AOM ( s ) .
S ϕ ( s ) = H CL ( s ) 2 S P ( s ) .
H CL wn ( s ) = 1 1 + H Tisa ( s ) H PD ( s ) H LF ( s ) H AOM ( s ) ,

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