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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  1. 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).
  2. 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).
  3. 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]
  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).
    [CrossRef]
  5. 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).
  6. 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]
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    [CrossRef]
  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).
  9. L. Matos, D. Kleppner, O. Kuzucu, T. R. Schibli, J. Kim, E. P. Ippen, and F. X. Kaertner, "Direct frequency comb generation from an octave-spanning, prismless Ti:sapphire laser," Opt. Lett. 29, 1683-1685 (2004).
    [CrossRef]
  10. O. D. Mücke, R. Ell, A. Winter, J. Kim, J. R. Birge, L. Matos, and F. X. Kärtner, "Self-Referenced 200 MHz Octave-Spanning Ti:Sapphire Laser with 50 Attosecond Carrier-Envelope Phase Jitter," Opt. Express 13, 5163-5169 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-13-5163.
    [CrossRef]
  11. 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).
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    [CrossRef]
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  14. H. A. Haus and E. P. Ippen, "Group velocity of solitons," Opt. Lett. 26, 1654-1656 (2001).
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  16. Y. Chen, F. X. Kärtner, U. Morgner, S. H. Cho, H. A. Haus, E. P. Ippen, and J. G. Fujimoto, "Dispersion-managed mode locking," J. Opt. Soc. Am. B 16, 1999-2004 (1999).
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    [CrossRef]
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  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).
  23. G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback control of dynamic systems (Addison-Wesley, 3rd edition, Reading, MA, 1994).

2005

2004

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]

L. Matos, D. Kleppner, O. Kuzucu, T. R. Schibli, J. Kim, E. P. Ippen, and F. X. Kaertner, "Direct frequency comb generation from an octave-spanning, prismless Ti:sapphire laser," Opt. Lett. 29, 1683-1685 (2004).
[CrossRef]

2003

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).

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).

2001

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

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]

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

2000

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).

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. 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]

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).

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]

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

1999

1996

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).

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).

1995

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).

1990

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]

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).

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]

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).

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).

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]

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).

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]

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]

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]

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).

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]

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]

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).

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).

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]

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).

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]

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]

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).

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).

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).

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]

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).

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).

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]

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]

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).

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).

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]

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]

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).

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).

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).

Kärtner, F. X.

O. D. Mücke, R. Ell, A. Winter, J. Kim, J. R. Birge, L. Matos, and F. X. Kärtner, "Self-Referenced 200 MHz Octave-Spanning Ti:Sapphire Laser with 50 Attosecond Carrier-Envelope Phase Jitter," Opt. Express 13, 5163-5169 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-13-5163.
[CrossRef]

Y. Chen, F. X. Kärtner, U. Morgner, S. H. Cho, H. A. Haus, E. P. Ippen, and J. G. Fujimoto, "Dispersion-managed mode locking," J. Opt. Soc. Am. B 16, 1999-2004 (1999).

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).

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).

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).

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).

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]

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).

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]

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]

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]

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).

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]

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]

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]

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]

Reichert, J.

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).

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]

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).

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]

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]

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]

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).

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]

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).

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]

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]

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).

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]

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).

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).

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]

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]

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]

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]

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).

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).

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).

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

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.

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).

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

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).

J. Opt. Soc. Am. B

Nature

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).

Opt. Eng.

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).

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

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]

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]

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]

Rev. Sci. Instrum.

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

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

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).

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