Abstract

The dependence of the carrier-envelope (CE) phase of the pulses from a hollow-core fiber on the input laser energy was studied using two f-to-2f interferometers. The CE phase in the in-loop f-to-2f interferometer was measured with the octave spanning white-light spectrum from the hollow-core fiber, whereas the out-of-loop interferometer was based on a sapphire plate. By modulating the input power of the in-loop interferometer and measuring the out-of-loop CE phase at the same time, the coupling coefficient between the measured CE phase and the laser energy for the hollow-core fiber was determined to be 128 mrad per 1% energy change.

© 2009 Optical Society of America

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  1. E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
    [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. A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
    [CrossRef]
  4. A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier envelope phase stability analysis," J. Phys. B 39, S257 (2006).
    [CrossRef]
  5. K. Yanane, Z. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, "Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation," Opt. Lett. 28, 2258-2260 (2003).
    [CrossRef]
  6. H. Wang, Y. Wu, C. Li, H. Mashiko, S. Gilbertson, and Z. Chang, "Generation of 0.5 mJ, few cycle laser pulses by an adaptive phase modulator," Opt. Express 16, 14449-14455 (2008).
  7. M. Kakehata, H. Takada, Y. Kobayashi, K. Torizuka, Y. Fujihira, T Homma, and H. Takahashi, "Single-shot measurement of carrier-envelope phase changes by spectral interferometry," Opt. Lett. 26, 1436-1438 (2001).
    [CrossRef]
  8. A. Baltuška, M. Uiberacker, E. Coulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W, Hänsch and F. Krausz, "Phase-controlled amplification of few-cycle laser pulses," IEEE J. Sel. Top. Quantum Electron. 9, 972-988 (2003).
    [CrossRef]
  9. H. Mashiko, C. M. Nakamura, C. Li, E. Moon, H. Wang, J. Tackett and Z. Chang, "Carrier-envelope phase stabilized 5.6 fs, 1.2 mJ pulses," Appl. Phys. Lett. 90, 161114 (2007).
    [CrossRef]
  10. A. Ishizawa, and H. Nakano, "Fluctuation of the carrier-envelope phase of a few-cycle laser pulses from a chirped-pulse amplification system with the gas pressure in a hollow fiber," Jpn. J. Appl. Phys. 44, 6039-6041 (2005).
    [CrossRef]
  11. T. M. Fortier, J. Ye, S. T. Cundiff and R. S. Windeler, "Nonlinear phase noise generated in air-silica microstructure fiber and its effect on carrier-envelope phase," Opt. Lett. 27, 445-447 (2002).
    [CrossRef]
  12. 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).
    [CrossRef] [PubMed]
  13. H. Wang, C. Li, J. Tackett, H. Mashiko, C. M. Nakamura, E. Moon, and Z. Chang, "Power locking of high-repetition-rate chirped pulse amplifiers," Appl. Phys. B 89, 275-279 (2007).
    [CrossRef]
  14. C. Li, E. Moon, H. Mashiko, H. Wang, C. M. Nakamura, J. Tackett, and Z. Chang, "Mechanism of phase-energy coupling in f-to-2f interferometry," Appl. Opt. 48, 1303-1307 (2009).
    [CrossRef] [PubMed]
  15. C. Li, E. Moon, and Z. Chang, "Carrier-envelope phase shift caused by variation of grating separation," Opt. Lett. 31, 3113-3115 (2006).
    [CrossRef] [PubMed]
  16. C. Li, H. Mashiko, H. Wang, E. Moon, S. Gilbertson and Z. Chang, "Carrier-envelope phase stabilization by controlling compressor grating separation," Appl. Phys. Lett. 92, 191114 (2008).
    [CrossRef]
  17. R. W. Boyd, Nonlinear Optics (Academic Press, Third edition, 2008).
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  19. H. J. Lehmeier, W. Leupacher and A. Penzkofer, "Nonresonant third order hyperpolarizability of rare gass and N2 determined by third harmonic generation," Opt. Commun. 56, 67-72 (1985).
    [CrossRef]
  20. R. Klingbeil, V. G. Kaveeshwar, and R. P. Hurst, "Hatree-Fock theory of third-harmonic and intensity-dependent refractive-index coefficients," Phys. Rev. A 4, 1760-1766 (1971).
    [CrossRef]

2009 (1)

2008 (3)

C. Li, H. Mashiko, H. Wang, E. Moon, S. Gilbertson and Z. Chang, "Carrier-envelope phase stabilization by controlling compressor grating separation," Appl. Phys. Lett. 92, 191114 (2008).
[CrossRef]

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

H. Wang, Y. Wu, C. Li, H. Mashiko, S. Gilbertson, and Z. Chang, "Generation of 0.5 mJ, few cycle laser pulses by an adaptive phase modulator," Opt. Express 16, 14449-14455 (2008).

2007 (4)

H. Mashiko, C. M. Nakamura, C. Li, E. Moon, H. Wang, J. Tackett and Z. Chang, "Carrier-envelope phase stabilized 5.6 fs, 1.2 mJ pulses," Appl. Phys. Lett. 90, 161114 (2007).
[CrossRef]

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[CrossRef]

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).
[CrossRef] [PubMed]

H. Wang, C. Li, J. Tackett, H. Mashiko, C. M. Nakamura, E. Moon, and Z. Chang, "Power locking of high-repetition-rate chirped pulse amplifiers," Appl. Phys. B 89, 275-279 (2007).
[CrossRef]

2006 (2)

C. Li, E. Moon, and Z. Chang, "Carrier-envelope phase shift caused by variation of grating separation," Opt. Lett. 31, 3113-3115 (2006).
[CrossRef] [PubMed]

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier envelope phase stability analysis," J. Phys. B 39, S257 (2006).
[CrossRef]

2005 (1)

A. Ishizawa, and H. Nakano, "Fluctuation of the carrier-envelope phase of a few-cycle laser pulses from a chirped-pulse amplification system with the gas pressure in a hollow fiber," Jpn. J. Appl. Phys. 44, 6039-6041 (2005).
[CrossRef]

2003 (2)

K. Yanane, Z. Zhang, K. Oka, R. Morita, M. Yamashita, and A. Suguro, "Optical pulse compression to 3.4 fs in the monocycle region by feedback phase compensation," Opt. Lett. 28, 2258-2260 (2003).
[CrossRef]

A. Baltuška, M. Uiberacker, E. Coulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W, Hänsch and F. Krausz, "Phase-controlled amplification of few-cycle laser pulses," IEEE J. Sel. Top. Quantum Electron. 9, 972-988 (2003).
[CrossRef]

2002 (1)

2001 (2)

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

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]

1985 (1)

H. J. Lehmeier, W. Leupacher and A. Penzkofer, "Nonresonant third order hyperpolarizability of rare gass and N2 determined by third harmonic generation," Opt. Commun. 56, 67-72 (1985).
[CrossRef]

1971 (1)

R. Klingbeil, V. G. Kaveeshwar, and R. P. Hurst, "Hatree-Fock theory of third-harmonic and intensity-dependent refractive-index coefficients," Phys. Rev. A 4, 1760-1766 (1971).
[CrossRef]

Anscombe, M.

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier envelope phase stability analysis," J. Phys. B 39, S257 (2006).
[CrossRef]

Apolonski, A.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[CrossRef]

Aquila, A. L.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Attwood, D. T.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Baltuška, A.

A. Baltuška, M. Uiberacker, E. Coulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W, Hänsch and F. Krausz, "Phase-controlled amplification of few-cycle laser pulses," IEEE J. Sel. Top. Quantum Electron. 9, 972-988 (2003).
[CrossRef]

Biegert, J.

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier envelope phase stability analysis," J. Phys. B 39, S257 (2006).
[CrossRef]

Cavalieri, A. L.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[CrossRef]

Chang, Z.

C. Li, E. Moon, H. Mashiko, H. Wang, C. M. Nakamura, J. Tackett, and Z. Chang, "Mechanism of phase-energy coupling in f-to-2f interferometry," Appl. Opt. 48, 1303-1307 (2009).
[CrossRef] [PubMed]

C. Li, H. Mashiko, H. Wang, E. Moon, S. Gilbertson and Z. Chang, "Carrier-envelope phase stabilization by controlling compressor grating separation," Appl. Phys. Lett. 92, 191114 (2008).
[CrossRef]

H. Wang, Y. Wu, C. Li, H. Mashiko, S. Gilbertson, and Z. Chang, "Generation of 0.5 mJ, few cycle laser pulses by an adaptive phase modulator," Opt. Express 16, 14449-14455 (2008).

H. Wang, C. Li, J. Tackett, H. Mashiko, C. M. Nakamura, E. Moon, and Z. Chang, "Power locking of high-repetition-rate chirped pulse amplifiers," Appl. Phys. B 89, 275-279 (2007).
[CrossRef]

H. Mashiko, C. M. Nakamura, C. Li, E. Moon, H. Wang, J. Tackett and Z. Chang, "Carrier-envelope phase stabilized 5.6 fs, 1.2 mJ pulses," Appl. Phys. Lett. 90, 161114 (2007).
[CrossRef]

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).
[CrossRef] [PubMed]

C. Li, E. Moon, and Z. Chang, "Carrier-envelope phase shift caused by variation of grating separation," Opt. Lett. 31, 3113-3115 (2006).
[CrossRef] [PubMed]

Coulielmakis, E.

A. Baltuška, M. Uiberacker, E. Coulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W, Hänsch and F. Krausz, "Phase-controlled amplification of few-cycle laser pulses," IEEE J. Sel. Top. Quantum Electron. 9, 972-988 (2003).
[CrossRef]

Cundiff, S. T.

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]

Eckle, P.

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier envelope phase stability analysis," J. Phys. B 39, S257 (2006).
[CrossRef]

Fieß, M.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[CrossRef]

Fortier, T. M.

Fujihira, Y.

Gagnon, J.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Gilbertson, S.

H. Wang, Y. Wu, C. Li, H. Mashiko, S. Gilbertson, and Z. Chang, "Generation of 0.5 mJ, few cycle laser pulses by an adaptive phase modulator," Opt. Express 16, 14449-14455 (2008).

C. Li, H. Mashiko, H. Wang, E. Moon, S. Gilbertson and Z. Chang, "Carrier-envelope phase stabilization by controlling compressor grating separation," Appl. Phys. Lett. 92, 191114 (2008).
[CrossRef]

Goulielmakis, E.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[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]

Guandalini, A.

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier envelope phase stability analysis," J. Phys. B 39, S257 (2006).
[CrossRef]

Gullikson, E. M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Helml, W.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[CrossRef]

Hofstetter, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Homma, T

Horvath, B.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[CrossRef]

Hurst, R. P.

R. Klingbeil, V. G. Kaveeshwar, and R. P. Hurst, "Hatree-Fock theory of third-harmonic and intensity-dependent refractive-index coefficients," Phys. Rev. A 4, 1760-1766 (1971).
[CrossRef]

Ishizawa, A.

A. Ishizawa, and H. Nakano, "Fluctuation of the carrier-envelope phase of a few-cycle laser pulses from a chirped-pulse amplification system with the gas pressure in a hollow fiber," Jpn. J. Appl. Phys. 44, 6039-6041 (2005).
[CrossRef]

Kakehata, M.

Kaveeshwar, V. G.

R. Klingbeil, V. G. Kaveeshwar, and R. P. Hurst, "Hatree-Fock theory of third-harmonic and intensity-dependent refractive-index coefficients," Phys. Rev. A 4, 1760-1766 (1971).
[CrossRef]

Keinberger, R.

A. Baltuška, M. Uiberacker, E. Coulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W, Hänsch and F. Krausz, "Phase-controlled amplification of few-cycle laser pulses," IEEE J. Sel. Top. Quantum Electron. 9, 972-988 (2003).
[CrossRef]

Keller, U.

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier envelope phase stability analysis," J. Phys. B 39, S257 (2006).
[CrossRef]

Kienberger, R.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[CrossRef]

Kleineberg, U.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Klingbeil, R.

R. Klingbeil, V. G. Kaveeshwar, and R. P. Hurst, "Hatree-Fock theory of third-harmonic and intensity-dependent refractive-index coefficients," Phys. Rev. A 4, 1760-1766 (1971).
[CrossRef]

Kobayashi, Y.

Krausz, F.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[CrossRef]

Lehmeier, H. J.

H. J. Lehmeier, W. Leupacher and A. Penzkofer, "Nonresonant third order hyperpolarizability of rare gass and N2 determined by third harmonic generation," Opt. Commun. 56, 67-72 (1985).
[CrossRef]

Leupacher, W.

H. J. Lehmeier, W. Leupacher and A. Penzkofer, "Nonresonant third order hyperpolarizability of rare gass and N2 determined by third harmonic generation," Opt. Commun. 56, 67-72 (1985).
[CrossRef]

Li, C.

C. Li, E. Moon, H. Mashiko, H. Wang, C. M. Nakamura, J. Tackett, and Z. Chang, "Mechanism of phase-energy coupling in f-to-2f interferometry," Appl. Opt. 48, 1303-1307 (2009).
[CrossRef] [PubMed]

H. Wang, Y. Wu, C. Li, H. Mashiko, S. Gilbertson, and Z. Chang, "Generation of 0.5 mJ, few cycle laser pulses by an adaptive phase modulator," Opt. Express 16, 14449-14455 (2008).

C. Li, H. Mashiko, H. Wang, E. Moon, S. Gilbertson and Z. Chang, "Carrier-envelope phase stabilization by controlling compressor grating separation," Appl. Phys. Lett. 92, 191114 (2008).
[CrossRef]

H. Wang, C. Li, J. Tackett, H. Mashiko, C. M. Nakamura, E. Moon, and Z. Chang, "Power locking of high-repetition-rate chirped pulse amplifiers," Appl. Phys. B 89, 275-279 (2007).
[CrossRef]

H. Mashiko, C. M. Nakamura, C. Li, E. Moon, H. Wang, J. Tackett and Z. Chang, "Carrier-envelope phase stabilized 5.6 fs, 1.2 mJ pulses," Appl. Phys. Lett. 90, 161114 (2007).
[CrossRef]

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).
[CrossRef] [PubMed]

C. Li, E. Moon, and Z. Chang, "Carrier-envelope phase shift caused by variation of grating separation," Opt. Lett. 31, 3113-3115 (2006).
[CrossRef] [PubMed]

Mashiko, H.

C. Li, E. Moon, H. Mashiko, H. Wang, C. M. Nakamura, J. Tackett, and Z. Chang, "Mechanism of phase-energy coupling in f-to-2f interferometry," Appl. Opt. 48, 1303-1307 (2009).
[CrossRef] [PubMed]

H. Wang, Y. Wu, C. Li, H. Mashiko, S. Gilbertson, and Z. Chang, "Generation of 0.5 mJ, few cycle laser pulses by an adaptive phase modulator," Opt. Express 16, 14449-14455 (2008).

C. Li, H. Mashiko, H. Wang, E. Moon, S. Gilbertson and Z. Chang, "Carrier-envelope phase stabilization by controlling compressor grating separation," Appl. Phys. Lett. 92, 191114 (2008).
[CrossRef]

H. Wang, C. Li, J. Tackett, H. Mashiko, C. M. Nakamura, E. Moon, and Z. Chang, "Power locking of high-repetition-rate chirped pulse amplifiers," Appl. Phys. B 89, 275-279 (2007).
[CrossRef]

H. Mashiko, C. M. Nakamura, C. Li, E. Moon, H. Wang, J. Tackett and Z. Chang, "Carrier-envelope phase stabilized 5.6 fs, 1.2 mJ pulses," Appl. Phys. Lett. 90, 161114 (2007).
[CrossRef]

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).
[CrossRef] [PubMed]

Moon, E.

C. Li, E. Moon, H. Mashiko, H. Wang, C. M. Nakamura, J. Tackett, and Z. Chang, "Mechanism of phase-energy coupling in f-to-2f interferometry," Appl. Opt. 48, 1303-1307 (2009).
[CrossRef] [PubMed]

C. Li, H. Mashiko, H. Wang, E. Moon, S. Gilbertson and Z. Chang, "Carrier-envelope phase stabilization by controlling compressor grating separation," Appl. Phys. Lett. 92, 191114 (2008).
[CrossRef]

H. Wang, C. Li, J. Tackett, H. Mashiko, C. M. Nakamura, E. Moon, and Z. Chang, "Power locking of high-repetition-rate chirped pulse amplifiers," Appl. Phys. B 89, 275-279 (2007).
[CrossRef]

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).
[CrossRef] [PubMed]

H. Mashiko, C. M. Nakamura, C. Li, E. Moon, H. Wang, J. Tackett and Z. Chang, "Carrier-envelope phase stabilized 5.6 fs, 1.2 mJ pulses," Appl. Phys. Lett. 90, 161114 (2007).
[CrossRef]

C. Li, E. Moon, and Z. Chang, "Carrier-envelope phase shift caused by variation of grating separation," Opt. Lett. 31, 3113-3115 (2006).
[CrossRef] [PubMed]

Morita, R.

Nakamura, C. M.

C. Li, E. Moon, H. Mashiko, H. Wang, C. M. Nakamura, J. Tackett, and Z. Chang, "Mechanism of phase-energy coupling in f-to-2f interferometry," Appl. Opt. 48, 1303-1307 (2009).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

H. Wang, C. Li, J. Tackett, H. Mashiko, C. M. Nakamura, E. Moon, and Z. Chang, "Power locking of high-repetition-rate chirped pulse amplifiers," Appl. Phys. B 89, 275-279 (2007).
[CrossRef]

H. Mashiko, C. M. Nakamura, C. Li, E. Moon, H. Wang, J. Tackett and Z. Chang, "Carrier-envelope phase stabilized 5.6 fs, 1.2 mJ pulses," Appl. Phys. Lett. 90, 161114 (2007).
[CrossRef]

Nakano, H.

A. Ishizawa, and H. Nakano, "Fluctuation of the carrier-envelope phase of a few-cycle laser pulses from a chirped-pulse amplification system with the gas pressure in a hollow fiber," Jpn. J. Appl. Phys. 44, 6039-6041 (2005).
[CrossRef]

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]

Oka, K.

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]

Penzkofer, A.

H. J. Lehmeier, W. Leupacher and A. Penzkofer, "Nonresonant third order hyperpolarizability of rare gass and N2 determined by third harmonic generation," Opt. Commun. 56, 67-72 (1985).
[CrossRef]

Pervak, V.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[CrossRef]

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]

Schlup, P.

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier envelope phase stability analysis," J. Phys. B 39, S257 (2006).
[CrossRef]

Schultze, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[CrossRef]

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]

Suguro, A.

Tackett, J.

C. Li, E. Moon, H. Mashiko, H. Wang, C. M. Nakamura, J. Tackett, and Z. Chang, "Mechanism of phase-energy coupling in f-to-2f interferometry," Appl. Opt. 48, 1303-1307 (2009).
[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

H. Wang, C. Li, J. Tackett, H. Mashiko, C. M. Nakamura, E. Moon, and Z. Chang, "Power locking of high-repetition-rate chirped pulse amplifiers," Appl. Phys. B 89, 275-279 (2007).
[CrossRef]

H. Mashiko, C. M. Nakamura, C. Li, E. Moon, H. Wang, J. Tackett and Z. Chang, "Carrier-envelope phase stabilized 5.6 fs, 1.2 mJ pulses," Appl. Phys. Lett. 90, 161114 (2007).
[CrossRef]

Takada, H.

Takahashi, H.

Torizuka, K.

Udem, T.

A. Baltuška, M. Uiberacker, E. Coulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W, Hänsch and F. Krausz, "Phase-controlled amplification of few-cycle laser pulses," IEEE J. Sel. Top. Quantum Electron. 9, 972-988 (2003).
[CrossRef]

Uiberacker, M.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[CrossRef]

A. Baltuška, M. Uiberacker, E. Coulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W, Hänsch and F. Krausz, "Phase-controlled amplification of few-cycle laser pulses," IEEE J. Sel. Top. Quantum Electron. 9, 972-988 (2003).
[CrossRef]

Veisz, L.

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[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.

C. Li, E. Moon, H. Mashiko, H. Wang, C. M. Nakamura, J. Tackett, and Z. Chang, "Mechanism of phase-energy coupling in f-to-2f interferometry," Appl. Opt. 48, 1303-1307 (2009).
[CrossRef] [PubMed]

H. Wang, Y. Wu, C. Li, H. Mashiko, S. Gilbertson, and Z. Chang, "Generation of 0.5 mJ, few cycle laser pulses by an adaptive phase modulator," Opt. Express 16, 14449-14455 (2008).

C. Li, H. Mashiko, H. Wang, E. Moon, S. Gilbertson and Z. Chang, "Carrier-envelope phase stabilization by controlling compressor grating separation," Appl. Phys. Lett. 92, 191114 (2008).
[CrossRef]

H. Wang, C. Li, J. Tackett, H. Mashiko, C. M. Nakamura, E. Moon, and Z. Chang, "Power locking of high-repetition-rate chirped pulse amplifiers," Appl. Phys. B 89, 275-279 (2007).
[CrossRef]

H. Mashiko, C. M. Nakamura, C. Li, E. Moon, H. Wang, J. Tackett and Z. Chang, "Carrier-envelope phase stabilized 5.6 fs, 1.2 mJ pulses," Appl. Phys. Lett. 90, 161114 (2007).
[CrossRef]

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).
[CrossRef] [PubMed]

Windeler, R. S.

Wu, Y.

H. Wang, Y. Wu, C. Li, H. Mashiko, S. Gilbertson, and Z. Chang, "Generation of 0.5 mJ, few cycle laser pulses by an adaptive phase modulator," Opt. Express 16, 14449-14455 (2008).

Yakovlev, V. S.

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[CrossRef]

A. Baltuška, M. Uiberacker, E. Coulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W, Hänsch and F. Krausz, "Phase-controlled amplification of few-cycle laser pulses," IEEE J. Sel. Top. Quantum Electron. 9, 972-988 (2003).
[CrossRef]

Yamashita, M.

Yanane, K.

Ye, J.

Zhang, Z.

Appl. Opt. (1)

Appl. Phys. B (1)

H. Wang, C. Li, J. Tackett, H. Mashiko, C. M. Nakamura, E. Moon, and Z. Chang, "Power locking of high-repetition-rate chirped pulse amplifiers," Appl. Phys. B 89, 275-279 (2007).
[CrossRef]

Appl. Phys. Lett. (2)

C. Li, H. Mashiko, H. Wang, E. Moon, S. Gilbertson and Z. Chang, "Carrier-envelope phase stabilization by controlling compressor grating separation," Appl. Phys. Lett. 92, 191114 (2008).
[CrossRef]

H. Mashiko, C. M. Nakamura, C. Li, E. Moon, H. Wang, J. Tackett and Z. Chang, "Carrier-envelope phase stabilized 5.6 fs, 1.2 mJ pulses," Appl. Phys. Lett. 90, 161114 (2007).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Baltuška, M. Uiberacker, E. Coulielmakis, R. Keinberger, V. S. Yakovlev, T. Udem, T. W, Hänsch and F. Krausz, "Phase-controlled amplification of few-cycle laser pulses," IEEE J. Sel. Top. Quantum Electron. 9, 972-988 (2003).
[CrossRef]

J. Phys. B (1)

A. Guandalini, P. Eckle, M. Anscombe, P. Schlup, J. Biegert, and U. Keller, "5.1 fs pulses generated by filamentation and carrier envelope phase stability analysis," J. Phys. B 39, S257 (2006).
[CrossRef]

Jpn. J. Appl. Phys. (1)

A. Ishizawa, and H. Nakano, "Fluctuation of the carrier-envelope phase of a few-cycle laser pulses from a chirped-pulse amplification system with the gas pressure in a hollow fiber," Jpn. J. Appl. Phys. 44, 6039-6041 (2005).
[CrossRef]

Nature (1)

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]

New J. Phys. (1)

A. L. Cavalieri, E. Goulielmakis, B. Horvath, W. Helml, M. Schultze, M. Fieß, V. Pervak, L. Veisz, V. S. Yakovlev, M. Uiberacker, A. Apolonski, F. Krausz, and R. Kienberger, "Intense 1.5-cycle near infrared laser waveforms and their use for the generation of ultra-broadband soft-x-ray harmonic continua," New J. Phys. 9, 242 (2007).
[CrossRef]

Opt. Commun. (1)

H. J. Lehmeier, W. Leupacher and A. Penzkofer, "Nonresonant third order hyperpolarizability of rare gass and N2 determined by third harmonic generation," Opt. Commun. 56, 67-72 (1985).
[CrossRef]

Opt. Express (1)

H. Wang, Y. Wu, C. Li, H. Mashiko, S. Gilbertson, and Z. Chang, "Generation of 0.5 mJ, few cycle laser pulses by an adaptive phase modulator," Opt. Express 16, 14449-14455 (2008).

Opt. Lett. (5)

Phys. Rev. A (1)

R. Klingbeil, V. G. Kaveeshwar, and R. P. Hurst, "Hatree-Fock theory of third-harmonic and intensity-dependent refractive-index coefficients," Phys. Rev. A 4, 1760-1766 (1971).
[CrossRef]

Science (1)

E. Goulielmakis, M. Schultze, M. Hofstetter, V. S. Yakovlev, J. Gagnon, M. Uiberacker, A. L. Aquila, E. M. Gullikson, D. T. Attwood, R. Kienberger, F. Krausz, and U. Kleineberg, "Single-cycle nonlinear optics," Science 320, 1614-1617 (2008).
[CrossRef] [PubMed]

Other (2)

R. W. Boyd, Nonlinear Optics (Academic Press, Third edition, 2008).

E. Hecht, Optics (Addison Wesley, Forth edition, 2001).

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Figures (5)

Fig. 1.
Fig. 1.

Experimental setup for determining the energy to CE phase coupling. VND: variable neutral density filter; L: focusing lens; SP: Sapphire plate; BBO: frequency doubling crystal; P: polarizers; FS: fused silica; Spec.: spectrometer and computer. In stretcher, G1 and G2: gratings; PZT: piezoelectric transducer; M1and M2: mirrors; BS: beam splitter.

Fig. 2.
Fig. 2.

The output spectrum of the octave-spanning white-light from the hollow-core fiber with 2 mJ input and 2 bar Ne pressure.

Fig. 3.
Fig. 3.

In-loop CE phase stabilized by a sapphire plate based f-to-2f interferometer (left) and out-of-loop CE phase measured by a hollow-core fiber based f-to-2f interferometer (right).

Fig. 4.
Fig. 4.

In-loop CE phase stabilized by a hollow-core fiber based f-to-2f interferometer (left) and Out-of-loop CE phase measured by a sapphire plate based f-to-2f interferometer (right).

Fig. 5.
Fig. 5.

(a) In-loop CE phase locked by a hollow-core fiber based f-to-2f interferometer; (b) Out-of-loop CE phase measured by a sapphire plate based f-to-2f interferometer and the in-loop power modulation; (c) CE phase change to laser power coupling coefficient by a least-square fitting.

Equations (15)

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

ΔϕCE=2 π L dndλ ,
n=n0+n2I,
ΔϕCE=2 π L (dn0dλ+dn2dλI) .
n2=32n02ε0cχ(3),
δΔϕCE=2πLdn2dλΔI=2 π L Δ I (3χ(3)n03ε0cdn0dλ+32n02ε0cdχ(3)dλ)
=2 π L Δ I n2 (2dn0n0dλ+dχ(3)χ(3)dλ)
n(ω)=1+Nqe2ε0me(1ω02ω2).
χ(3)(ω)ω0ωaω0ωχ(3)(ωa),
I=Wπr2τ=2×103Jπ×(200×106m)2×30×1015s=5.3×1017Wm2.
ϕ1(Lpro)=ϕNL1+ϕL1(Lpro)+ϕCE,
ϕ2(Lpro)=ϕNL2+ϕL2(Lpro)+ϕCE.
φ2(Lpro)=2ϕ2(Lpro)=2ϕNL2+2ϕL2(Lpro)+2ϕCE.
Φ=φ2(Lpro)ϕ1(Lpro)=[2ϕNL2ϕNL1]+[2ϕL2(Lpro)ϕL1(Lpro)]+ϕCE.
ΔLpro=Δl=l100L100=9 mm ,
ΔΦ=2πΔLpro[2n(λ2)λ2n(λ1)λ1]=2 π Δ L [n(λ2)λ1n(λ1)λ1]120 mrad .

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