Abstract

White-light generation has been used widely in single-shot f-to-2f interferometers for stabilizing the carrier-envelope (CE) phase of laser amplifiers. The accuracy of the relative phase values measured by such an interferometer is affected by fluctuations in the laser pulse energy. A simple two-step model is proposed to explain the mechanism that couples the laser energy and the CE phase. The model explains the experimentally observed dependence of the group delay between the f and the 2f pulses on the laser energy, as well as the CE phase shift caused by the pulse energy variation.

© 2009 Optical Society of America

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  1. A. Baltuška, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, and F. Krausz, “Attosecond control of electronic processes by intense light fields,” Nature 421, 611-615 (2003).
    [CrossRef] [PubMed]
  2. G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. de Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182-184 (2001).
    [CrossRef] [PubMed]
  3. M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihara, T. Homma, and H. Takahashi, “Single-shot measurement of carrier-envelope phase changes by spectral interferometry,” Opt. Lett. 26, 1436-1438 (2001).
    [CrossRef]
  4. A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovler, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972-989 (2003).
    [CrossRef]
  5. M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, “Measurements of carrier-envelope phase changes of 100 Hz amplified laser pulses,” Appl. Phys. B 74, S43-S50 (2002).
    [CrossRef]
  6. C. Li, E. Moon, H. Wang, H. Mashiko, C. M. Nakamura, J. Tackett, and Z. Chang, “Determining the phase-energy coupling coefficient in carrier-envelope phase measurements,” Opt. Lett. 32, 796-798 (2007).
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  8. Our f-to-2f interferometers are similar to the Femtosecond Phase Stabilization Unit APS800 manufactured by Menlosystems. A description of the unit can be found at http://www.menlosystems.com/home/products.html?cat=5.
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    [CrossRef]
  11. A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582-3585 (2000).
    [CrossRef] [PubMed]
  12. S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
    [CrossRef]
  13. R. W. Boyd, Nonlinear Optics (Academic, 2003).
  14. G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).
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    [CrossRef]
  16. W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215-229 (2003).
    [CrossRef]

2007

2006

2005

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

2003

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215-229 (2003).
[CrossRef]

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

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovler, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972-989 (2003).
[CrossRef]

2002

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, “Measurements of carrier-envelope phase changes of 100 Hz amplified laser pulses,” Appl. Phys. B 74, S43-S50 (2002).
[CrossRef]

F. W. Helbing, G. Steinmeyer, J. Stenger, H. R. Telle, and U. Keller, “Carrier-envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B 74, S35-S42 (2002).
[CrossRef]

2001

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. de Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihara, T. Homma, and H. Takahashi, “Single-shot measurement of carrier-envelope phase changes by spectral interferometry,” Opt. Lett. 26, 1436-1438 (2001).
[CrossRef]

2000

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582-3585 (2000).
[CrossRef] [PubMed]

1999

A. W. Albrecht, J. D. Hybl, S. M. G. Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: implications for femtosecond spectroscopy and coherent control of chemical reactions,” J. Chem. Phys. 111, 10934 (1999).
[CrossRef]

1995

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

Aközbek, N.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Albrecht, A. W.

A. W. Albrecht, J. D. Hybl, S. M. G. Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: implications for femtosecond spectroscopy and coherent control of chemical reactions,” J. Chem. Phys. 111, 10934 (1999).
[CrossRef]

Baltuška, A.

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

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovler, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972-989 (2003).
[CrossRef]

Becker, A.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215-229 (2003).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 2003).

Chang, Z.

Chériaux, G.

Chin, S. L.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215-229 (2003).
[CrossRef]

de Silvestri, S.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. de Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

Faeder, S. M. G.

A. W. Albrecht, J. D. Hybl, S. M. G. Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: implications for femtosecond spectroscopy and coherent control of chemical reactions,” J. Chem. Phys. 111, 10934 (1999).
[CrossRef]

Fujihara, Y.

Fujihira, Y.

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, “Measurements of carrier-envelope phase changes of 100 Hz amplified laser pulses,” Appl. Phys. B 74, S43-S50 (2002).
[CrossRef]

Gaeta, A. L.

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582-3585 (2000).
[CrossRef] [PubMed]

Gohle, C.

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

Golubtsov, I. S.

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215-229 (2003).
[CrossRef]

Goulielmakis, E.

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

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovler, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972-989 (2003).
[CrossRef]

Grasbon, F.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. de Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

Hänsch, T. W.

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

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovler, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972-989 (2003).
[CrossRef]

Helbing, F. W.

F. W. Helbing, G. Steinmeyer, J. Stenger, H. R. Telle, and U. Keller, “Carrier-envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B 74, S35-S42 (2002).
[CrossRef]

Hentschel, M.

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

Holzwarth, R.

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

Homma, T.

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, “Measurements of carrier-envelope phase changes of 100 Hz amplified laser pulses,” Appl. Phys. B 74, S43-S50 (2002).
[CrossRef]

M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihara, T. Homma, and H. Takahashi, “Single-shot measurement of carrier-envelope phase changes by spectral interferometry,” Opt. Lett. 26, 1436-1438 (2001).
[CrossRef]

Hosseini, S. A.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Hybl, J. D.

A. W. Albrecht, J. D. Hybl, S. M. G. Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: implications for femtosecond spectroscopy and coherent control of chemical reactions,” J. Chem. Phys. 111, 10934 (1999).
[CrossRef]

Iwasaki, A.

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215-229 (2003).
[CrossRef]

Joffre, M.

Jonas, D. M.

A. W. Albrecht, J. D. Hybl, S. M. G. Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: implications for femtosecond spectroscopy and coherent control of chemical reactions,” J. Chem. Phys. 111, 10934 (1999).
[CrossRef]

Kakehata, M.

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, “Measurements of carrier-envelope phase changes of 100 Hz amplified laser pulses,” Appl. Phys. B 74, S43-S50 (2002).
[CrossRef]

M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihara, T. Homma, and H. Takahashi, “Single-shot measurement of carrier-envelope phase changes by spectral interferometry,” Opt. Lett. 26, 1436-1438 (2001).
[CrossRef]

Kandidov, V. P.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215-229 (2003).
[CrossRef]

Keller, U.

F. W. Helbing, G. Steinmeyer, J. Stenger, H. R. Telle, and U. Keller, “Carrier-envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B 74, S35-S42 (2002).
[CrossRef]

Kienberger, R.

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovler, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972-989 (2003).
[CrossRef]

Kobayashi, Y.

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, “Measurements of carrier-envelope phase changes of 100 Hz amplified laser pulses,” Appl. Phys. B 74, S43-S50 (2002).
[CrossRef]

M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihara, T. Homma, and H. Takahashi, “Single-shot measurement of carrier-envelope phase changes by spectral interferometry,” Opt. Lett. 26, 1436-1438 (2001).
[CrossRef]

Kosareva, O.

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215-229 (2003).
[CrossRef]

Kosareva, O. G.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Krausz, F.

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovler, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972-989 (2003).
[CrossRef]

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

Lepetit, L.

Li, C.

Liu, W.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215-229 (2003).
[CrossRef]

Luo, Q.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Mashiko, H.

Moon, E.

Nakamura, C. M.

Nisoli, M.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. de Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

Paulus, G. G.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. de Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

Priori, E.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. de Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

Schroeder, H.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Scrinzi, A.

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

Stagira, S.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. de Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

Steinmeyer, G.

F. W. Helbing, G. Steinmeyer, J. Stenger, H. R. Telle, and U. Keller, “Carrier-envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B 74, S35-S42 (2002).
[CrossRef]

Stenger, J.

F. W. Helbing, G. Steinmeyer, J. Stenger, H. R. Telle, and U. Keller, “Carrier-envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B 74, S35-S42 (2002).
[CrossRef]

Tackett, J.

Takada, H.

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, “Measurements of carrier-envelope phase changes of 100 Hz amplified laser pulses,” Appl. Phys. B 74, S43-S50 (2002).
[CrossRef]

M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihara, T. Homma, and H. Takahashi, “Single-shot measurement of carrier-envelope phase changes by spectral interferometry,” Opt. Lett. 26, 1436-1438 (2001).
[CrossRef]

Takahashi, H.

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, “Measurements of carrier-envelope phase changes of 100 Hz amplified laser pulses,” Appl. Phys. B 74, S43-S50 (2002).
[CrossRef]

M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihara, T. Homma, and H. Takahashi, “Single-shot measurement of carrier-envelope phase changes by spectral interferometry,” Opt. Lett. 26, 1436-1438 (2001).
[CrossRef]

Telle, H. R.

F. W. Helbing, G. Steinmeyer, J. Stenger, H. R. Telle, and U. Keller, “Carrier-envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B 74, S35-S42 (2002).
[CrossRef]

Théberge, F.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

Torizuka, K.

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, “Measurements of carrier-envelope phase changes of 100 Hz amplified laser pulses,” Appl. Phys. B 74, S43-S50 (2002).
[CrossRef]

M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihara, T. Homma, and H. Takahashi, “Single-shot measurement of carrier-envelope phase changes by spectral interferometry,” Opt. Lett. 26, 1436-1438 (2001).
[CrossRef]

Udem, T.

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovler, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972-989 (2003).
[CrossRef]

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

Uiberacker, M.

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

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovler, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972-989 (2003).
[CrossRef]

Villoresi, P.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. de Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

Walther, H.

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. de Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

Wang, H.

Yakovler, V. S.

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovler, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972-989 (2003).
[CrossRef]

Yakovlev, V. S.

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

Appl. Phys. B

M. Kakehata, Y. Fujihira, H. Takada, Y. Kobayashi, K. Torizuka, T. Homma, and H. Takahashi, “Measurements of carrier-envelope phase changes of 100 Hz amplified laser pulses,” Appl. Phys. B 74, S43-S50 (2002).
[CrossRef]

F. W. Helbing, G. Steinmeyer, J. Stenger, H. R. Telle, and U. Keller, “Carrier-envelope-offset dynamics and stabilization of femtosecond pulses,” Appl. Phys. B 74, S35-S42 (2002).
[CrossRef]

W. Liu, O. Kosareva, I. S. Golubtsov, A. Iwasaki, A. Becker, V. P. Kandidov, and S. L. Chin, “Femtosecond laser pulse filamentation versus optical breakdown in H2O,” Appl. Phys. B 76, 215-229 (2003).
[CrossRef]

Can. J. Phys.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications, and new challenges,” Can. J. Phys. 83, 863-905 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

A. Baltuška, M. Uiberacker, E. Goulielmakis, R. Kienberger, V. S. Yakovler, T. Udem, T. W. Hänsch, and F. Krausz, “Phase-controlled amplification of few-cycle laser pulses,” IEEE J. Sel. Top. Quantum Electron. 9, 972-989 (2003).
[CrossRef]

J. Chem. Phys.

A. W. Albrecht, J. D. Hybl, S. M. G. Faeder, and D. M. Jonas, “Experimental distinction between phase shifts and time delays: implications for femtosecond spectroscopy and coherent control of chemical reactions,” J. Chem. Phys. 111, 10934 (1999).
[CrossRef]

J. Opt. Soc. Am. B

Nature

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

G. G. Paulus, F. Grasbon, H. Walther, P. Villoresi, M. Nisoli, S. Stagira, E. Priori, and S. de Silvestri, “Absolute-phase phenomena in photoionization with few-cycle laser pulses,” Nature 414, 182-184 (2001).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. Lett.

A. L. Gaeta, “Catastrophic collapse of ultrashort pulses,” Phys. Rev. Lett. 84, 3582-3585 (2000).
[CrossRef] [PubMed]

Other

R. W. Boyd, Nonlinear Optics (Academic, 2003).

G. P. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Academic, 2001).

Our f-to-2f interferometers are similar to the Femtosecond Phase Stabilization Unit APS800 manufactured by Menlosystems. A description of the unit can be found at http://www.menlosystems.com/home/products.html?cat=5.

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Figures (4)

Fig. 1
Fig. 1

(a) Collinear f-to- 2 f interferometer. Inset: Formation of a single filament by self-focusing. D, diameter of the laser beam; f, focal length of the focusing lens; ω 0 , radius of the focal spot; z sf , self-focusing distance; z fila , length of the filament. (b) Calculated dependence of the self-focusing distance on the laser energy.

Fig. 2
Fig. 2

Comparison between the experimental and the calculated results. (a) Relative group delay between the green pulses and the infrared pulses as a function of laser energy. (b) Intercept of the Φ ( ω ) plot, i.e., Φ ( 0 ) as a function of laser energy.

Fig. 3
Fig. 3

Comparison between the experimental and the calculated results of the CE phase shift as a result of the laser energy change.

Fig. 4
Fig. 4

(a) Relative group delay with different focus length. (b) Calculated relative CE phase.

Equations (10)

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S ( ω ) = I SHG ( ω ) + I G ( ω ) + 2 I SHG ( ω ) I G ( ω ) cos [ ϕ SHG ( ω ) ϕ G ( ω ) ] ,
z sf ( ε ) = 2 n 0 w 0 2 λ 0 1 P / P c 1 = 2 n 0 w 0 2 λ 0 1 ε / ( τ p P c ) 1 ,
ϕ spm = 0 z sf 2 π λ 0 n 2 2 ε τ p π w 2 ( z ) d z 2 π 2 λ 0 2 n 2 ε τ p ,
ϕ G , sf ( ω ) = φ CE + Δ φ n 0 + Δ φ n 2 + ϕ spm ϕ G . sf ( ω G ) ,
ϕ IR , sf ( ω ) = φ CE + Δ φ n o + Δ φ n 2 + ϕ spm ϕ IR , sf ( ω IR ) ,
ϕ G ( ω ) = ϕ G , sf [ β G + β G ( ω ω G ) ] z fila ,
ϕ IR ( ω ) = ϕ IR , sf [ β IR + β IR ( ω ω IR ) ] z fila ,
ϕ SHG ( ω ) = 2 ϕ IR , sf ( ω IR ) [ 2 β IR + β IR ( ω ω G ) ] z fila .
Φ ( ω ) = φ CE + Δ φ n 2 + ϕ spm + ω 0 Δ τ 0 + ω G Δ τ ph ( ω G ω ) Δ τ g .
d Δ φ err d ε d z sf d ε w 0 2 P 3 / 2 ,

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