Abstract

Distortions in pulsed laser fields are analyzed by means of the root mean square of intensity-weighted spectral phase deviations. This method quantifies pulse errors independently of pulse duration and can be applied to both simple, transform-limited and complex, shaped pulses. A good linear relationship exists (fit correlation=0.95) between the analyzed phase deviations and temporal pulse distortion measures. In contrast, a common Taylor series analysis showed a fit correlation of only 0.5 with temporal measures. Alternative methods examined, such as the pulse FWHM, were determined to be less general measures of pulse distortion and, in modeling of spectral phase errors, were shown to have the potential of being misleading.

© 1999 Optical Society of America

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  1. See, for example, M. Schnurer, C. Spielmann, P. Wobrauschek, C. Streli, N. H. Burnett, C. Kan, K. Ferencz, R. Koppitsch, Z. Cheng, T. Brabec, and F. Krausz, “Coherent 0.5-keV x-ray emission from helium driven by a sub-10-fs laser,” Phys. Rev. Lett. 80, 3236–3239 (1998); D. Umstader, S.-Y. Chen, A. Maksimchuk, G. Mourou, and R. Wagner, “Nonlinear optics in relativistic plasmas and laser wake field acceleration of electrons,” Science 273, 472–475 (1996); B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchick, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B JOBPDE 13, 459–468 (1996); P. Y. Cheng, D. Zhong, and A. H. Zewail, “Femtosecond real-time probing of reactions. XXI. Direct observation of transition state dynamics and structure in charge-transfer reactions,” J. Chem. Phys. JCPSA6 105, 6216–6248 (1996); B. Walker, M. Kaluza, B. Sheehy, P. Agostini, and L. F. DiMauro, “Observation of continuum–continuum Autler–Townes splitting,” Phys. Rev. Lett. PRLTAO 75, 633–636 (1995).
    [CrossRef] [PubMed]
  2. S. Sartania, Z. Cheng, M. Lenzner, G. Tempea, C. Spielmann, F. Krausz, and K. Ferencz, “Generation of 0.1-TW 5-fs optical pulses at a 1-kHz repetition rate,” Opt. Lett. 22, 1562–1564 (1997).
    [CrossRef]
  3. J. S. Melinger, D. McMorrow, C. Hillegas, and W. S. Warren, “Selective excitation of vibrational overtones in an anharmonic ladder with frequency- and amplitude-modulated laser pulses,” Phys. Rev. A 51, 3366–3369 (1995).
    [CrossRef] [PubMed]
  4. J. Piasecki, B. Colombeou, M. Vampouille, C. Froehly, and J. A. Arnaud, “New method for measuring the impulse response of optical fibers,” Appl. Opt. 19, 3749–3755 (1980).
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  5. R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time–frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
    [CrossRef]
  6. D. N. Fittinghoff, B. C. Walker, J. A. Squier, Cs. Tóth, C. Rose-Petruck, and C. P. J. Barty, “Dispersion considerations in ultrafast CPA systems,” IEEE J. Sel. Top. Quantum Electron. 4, 430–440 (1998); D. N. Christodoulides, E. Bourkoff, R. I. Joseph, and T. Simos, “Reflection of femtosecond optical pulses from multiple-layer dielectric mirrors—analysis,” IEEE J. Quantum Electron. 22, 186–191 (1986); K. E. Oughstun and H. Xiao, “Failure of the quasimonochromatic approximation for ultrashort pulse propagation in a dispersive medium,” Phys. Rev. Lett. PRLTAO 78, 642–645 (1997).
    [CrossRef]
  7. A. Sullivan, W. E. White, K. C. Chu, J. P. Heritage, K. W. Delong, and R. Trebino, “Quantitative investigation of optical phase measuring techniques for ultrashort pulse lasers,” J. Opt. Soc. Am. B 13, 1965–1978 (1996).
    [CrossRef]
  8. C. P. J. Barty, T. Guo, C. LeBlanc, F. Raski, C. Rose-Petruck, J. Squier, K. R. Wilson, V. V. Yakovlev, and K. Yamakawa, “Generation of 18-fs, multiterawatt pulses by regenerative pulse shaping and chirped-pulse amplification,” Opt. Lett. 21, 668–670 (1996).
    [CrossRef] [PubMed]
  9. C. G. Durfee III, S. Backus, M. Murnane, and H. Kapteyn, “Design and implementation of a TW-class high average power laser system,” IEEE J. Sel. Top. Quantum Electron. 4, 395–406 (1998); S. Backus, C. G. Durfee III, M. Murnane, and H. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207–1223 (1998).
    [CrossRef]
  10. S. Backus, G. Durfee, H. C. Kapteyn, and M. M. Murnane, “0.27-TW, sub-17-fs laser system at 1 kHz,” in Conference on Lasers and Electro-Optics (CLEO/U.S.), Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 362–363; E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, and G. Vdovin, “Pulse compression by use of deformable mirrors,” Opt. Lett. 24, 493–495 (1999).
    [CrossRef]
  11. V. Bagnoud and F. Salin, “Global optimization of pulse compression in chirped pulse amplification,” IEEE J. Sel. Top. Quantum Electron. 4, 445–448 (1998).
    [CrossRef]
  12. C. Bardeen, V. Yakovlev, K. R. Wilson, S. Carpenter, P. Weber, and W. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
    [CrossRef]
  13. This situation is in contrast to the microwave spectral region, where determination of the field as a function of time is possible, and, for this case, distortions can and are quantified in time; e.g., white noise on the temporal profile is commonly quantified as a time-integrated rms.
  14. For all calculations in this paper, I includes a spectral truncation window of 74 THz such as would occur in experimental systems, for example, at frequencies beyond the edges of the stretcher and compressor gratings.
  15. The n time moment is defined as ∫|t|nIdt/∫Idt.
  16. D. Sutter, I. Jung, F. Kartner, N. Matuschek, F. M. Genoud, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Self starting 6.5 fs pulses from a Ti:sapphire laser using a semiconductor saturable absorber and double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 169–178 (1998).
    [CrossRef]
  17. C. J. Bardeen, V. V. Yakovlev, J. A. Squier, and K. R. Wilson, “Quantum control of population transfer in green flourescent protein by using chirped femtosecond pulses,” J. Am. Chem. Soc. 120, 13023–13027 (1998).
    [CrossRef]
  18. B. C. Walker, Cs. Tóth, D. Fittinghoff, J. Squier, T. Guo, K. R. Wilson, and C. P. T. Barty, “Ultrafast, relativistic intensities: generation, characterization, and application to photoionization,” in Conference on Lasers and Electro-Optics, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 71.
  19. M. D. Perry, T. Ditmire, and B. C. Stuart, “Self-phase modulation in chirped-pulse amplification” Opt. Lett. 19, 2149–2151 (1994).
    [CrossRef] [PubMed]
  20. M. D. Perry and G. Mourou, “Terawatt to petawatt subpicosecond lasers,” Science 264, 917–924 (1994); D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
    [CrossRef] [PubMed]
  21. G. Tempea, F. Krausz, C. Spielmann, and K. Ferencz, “Dispersion control over 150 THz with chirped dielectric mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 193–196 (1998); N. Matuschek, F. Kartner, and U. Keller, “Theory of double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
    [CrossRef]
  22. C. Spielmann, University Wien, Vienna, Austria (personal communication, 1998).
  23. G. Cheriaux, P. Rousseau, F. Salin, J. P. Chambaret, B. Walker, and L. F. DiMauro, “Aberration-free stretcher design for ultrashort-pulse amplification,” Opt. Lett. 21, 414–416 (1996).
    [CrossRef] [PubMed]
  24. Thin Film, Broad Band, Plate Polarizer, from Alpine Research Optics, Boulder, Colo., 80301.
  25. The Taylor series expansion was truncated at n=4. This truncation is commonly required when one is representing experimental data owing to convergence and term orthogonality problems, and it results in a significant filtering of high-frequency phase-dispersion information. For example, the value of øerr is different for the experimental phase data and the Taylor series representation of that data.
  26. The Pearson r is r=∑xy/[(∑x2)(∑y2)]1/2. |r| is 1 for a perfectly linear relationship. See N. Downie and R. Heath, Basic Statistical Methods, 2nd ed (Harper & Row, New York, 1965), p. 78.

1998 (3)

V. Bagnoud and F. Salin, “Global optimization of pulse compression in chirped pulse amplification,” IEEE J. Sel. Top. Quantum Electron. 4, 445–448 (1998).
[CrossRef]

D. Sutter, I. Jung, F. Kartner, N. Matuschek, F. M. Genoud, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Self starting 6.5 fs pulses from a Ti:sapphire laser using a semiconductor saturable absorber and double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 169–178 (1998).
[CrossRef]

C. J. Bardeen, V. V. Yakovlev, J. A. Squier, and K. R. Wilson, “Quantum control of population transfer in green flourescent protein by using chirped femtosecond pulses,” J. Am. Chem. Soc. 120, 13023–13027 (1998).
[CrossRef]

1997 (3)

C. Bardeen, V. Yakovlev, K. R. Wilson, S. Carpenter, P. Weber, and W. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time–frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

S. Sartania, Z. Cheng, M. Lenzner, G. Tempea, C. Spielmann, F. Krausz, and K. Ferencz, “Generation of 0.1-TW 5-fs optical pulses at a 1-kHz repetition rate,” Opt. Lett. 22, 1562–1564 (1997).
[CrossRef]

1996 (3)

1995 (1)

J. S. Melinger, D. McMorrow, C. Hillegas, and W. S. Warren, “Selective excitation of vibrational overtones in an anharmonic ladder with frequency- and amplitude-modulated laser pulses,” Phys. Rev. A 51, 3366–3369 (1995).
[CrossRef] [PubMed]

1994 (1)

1980 (1)

Arnaud, J. A.

Bagnoud, V.

V. Bagnoud and F. Salin, “Global optimization of pulse compression in chirped pulse amplification,” IEEE J. Sel. Top. Quantum Electron. 4, 445–448 (1998).
[CrossRef]

Bardeen, C.

C. Bardeen, V. Yakovlev, K. R. Wilson, S. Carpenter, P. Weber, and W. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Bardeen, C. J.

C. J. Bardeen, V. V. Yakovlev, J. A. Squier, and K. R. Wilson, “Quantum control of population transfer in green flourescent protein by using chirped femtosecond pulses,” J. Am. Chem. Soc. 120, 13023–13027 (1998).
[CrossRef]

Barty, C. P. J.

Carpenter, S.

C. Bardeen, V. Yakovlev, K. R. Wilson, S. Carpenter, P. Weber, and W. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Chambaret, J. P.

Cheng, Z.

Cheriaux, G.

Chu, K. C.

Colombeou, B.

Delong, K. W.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time–frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

A. Sullivan, W. E. White, K. C. Chu, J. P. Heritage, K. W. Delong, and R. Trebino, “Quantitative investigation of optical phase measuring techniques for ultrashort pulse lasers,” J. Opt. Soc. Am. B 13, 1965–1978 (1996).
[CrossRef]

DiMauro, L. F.

Ditmire, T.

Ferencz, K.

Fittinghoff, D. N.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time–frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Froehly, C.

Genoud, F. M.

D. Sutter, I. Jung, F. Kartner, N. Matuschek, F. M. Genoud, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Self starting 6.5 fs pulses from a Ti:sapphire laser using a semiconductor saturable absorber and double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 169–178 (1998).
[CrossRef]

Guo, T.

Heritage, J. P.

Hillegas, C.

J. S. Melinger, D. McMorrow, C. Hillegas, and W. S. Warren, “Selective excitation of vibrational overtones in an anharmonic ladder with frequency- and amplitude-modulated laser pulses,” Phys. Rev. A 51, 3366–3369 (1995).
[CrossRef] [PubMed]

Jung, I.

D. Sutter, I. Jung, F. Kartner, N. Matuschek, F. M. Genoud, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Self starting 6.5 fs pulses from a Ti:sapphire laser using a semiconductor saturable absorber and double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 169–178 (1998).
[CrossRef]

Kane, D. J.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time–frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Kartner, F.

D. Sutter, I. Jung, F. Kartner, N. Matuschek, F. M. Genoud, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Self starting 6.5 fs pulses from a Ti:sapphire laser using a semiconductor saturable absorber and double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 169–178 (1998).
[CrossRef]

Keller, U.

D. Sutter, I. Jung, F. Kartner, N. Matuschek, F. M. Genoud, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Self starting 6.5 fs pulses from a Ti:sapphire laser using a semiconductor saturable absorber and double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 169–178 (1998).
[CrossRef]

Krausz, F.

Krumbugel, M. A.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time–frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

LeBlanc, C.

Lenzner, M.

Matuschek, N.

D. Sutter, I. Jung, F. Kartner, N. Matuschek, F. M. Genoud, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Self starting 6.5 fs pulses from a Ti:sapphire laser using a semiconductor saturable absorber and double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 169–178 (1998).
[CrossRef]

McMorrow, D.

J. S. Melinger, D. McMorrow, C. Hillegas, and W. S. Warren, “Selective excitation of vibrational overtones in an anharmonic ladder with frequency- and amplitude-modulated laser pulses,” Phys. Rev. A 51, 3366–3369 (1995).
[CrossRef] [PubMed]

Melinger, J. S.

J. S. Melinger, D. McMorrow, C. Hillegas, and W. S. Warren, “Selective excitation of vibrational overtones in an anharmonic ladder with frequency- and amplitude-modulated laser pulses,” Phys. Rev. A 51, 3366–3369 (1995).
[CrossRef] [PubMed]

Perry, M. D.

Piasecki, J.

Raski, F.

Richman, B. A.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time–frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Rose-Petruck, C.

Rousseau, P.

Salin, F.

V. Bagnoud and F. Salin, “Global optimization of pulse compression in chirped pulse amplification,” IEEE J. Sel. Top. Quantum Electron. 4, 445–448 (1998).
[CrossRef]

G. Cheriaux, P. Rousseau, F. Salin, J. P. Chambaret, B. Walker, and L. F. DiMauro, “Aberration-free stretcher design for ultrashort-pulse amplification,” Opt. Lett. 21, 414–416 (1996).
[CrossRef] [PubMed]

Sartania, S.

Scheuer, V.

D. Sutter, I. Jung, F. Kartner, N. Matuschek, F. M. Genoud, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Self starting 6.5 fs pulses from a Ti:sapphire laser using a semiconductor saturable absorber and double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 169–178 (1998).
[CrossRef]

Spielmann, C.

Squier, J.

Squier, J. A.

C. J. Bardeen, V. V. Yakovlev, J. A. Squier, and K. R. Wilson, “Quantum control of population transfer in green flourescent protein by using chirped femtosecond pulses,” J. Am. Chem. Soc. 120, 13023–13027 (1998).
[CrossRef]

Stuart, B. C.

Sullivan, A.

Sutter, D.

D. Sutter, I. Jung, F. Kartner, N. Matuschek, F. M. Genoud, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Self starting 6.5 fs pulses from a Ti:sapphire laser using a semiconductor saturable absorber and double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 169–178 (1998).
[CrossRef]

Sweetser, J. N.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time–frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Tempea, G.

Tilsch, M.

D. Sutter, I. Jung, F. Kartner, N. Matuschek, F. M. Genoud, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Self starting 6.5 fs pulses from a Ti:sapphire laser using a semiconductor saturable absorber and double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 169–178 (1998).
[CrossRef]

Trebino, R.

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time–frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

A. Sullivan, W. E. White, K. C. Chu, J. P. Heritage, K. W. Delong, and R. Trebino, “Quantitative investigation of optical phase measuring techniques for ultrashort pulse lasers,” J. Opt. Soc. Am. B 13, 1965–1978 (1996).
[CrossRef]

Tschudi, T.

D. Sutter, I. Jung, F. Kartner, N. Matuschek, F. M. Genoud, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Self starting 6.5 fs pulses from a Ti:sapphire laser using a semiconductor saturable absorber and double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 169–178 (1998).
[CrossRef]

Vampouille, M.

Walker, B.

Warren, W.

C. Bardeen, V. Yakovlev, K. R. Wilson, S. Carpenter, P. Weber, and W. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Warren, W. S.

J. S. Melinger, D. McMorrow, C. Hillegas, and W. S. Warren, “Selective excitation of vibrational overtones in an anharmonic ladder with frequency- and amplitude-modulated laser pulses,” Phys. Rev. A 51, 3366–3369 (1995).
[CrossRef] [PubMed]

Weber, P.

C. Bardeen, V. Yakovlev, K. R. Wilson, S. Carpenter, P. Weber, and W. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

White, W. E.

Wilson, K. R.

C. J. Bardeen, V. V. Yakovlev, J. A. Squier, and K. R. Wilson, “Quantum control of population transfer in green flourescent protein by using chirped femtosecond pulses,” J. Am. Chem. Soc. 120, 13023–13027 (1998).
[CrossRef]

C. Bardeen, V. Yakovlev, K. R. Wilson, S. Carpenter, P. Weber, and W. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

C. P. J. Barty, T. Guo, C. LeBlanc, F. Raski, C. Rose-Petruck, J. Squier, K. R. Wilson, V. V. Yakovlev, and K. Yamakawa, “Generation of 18-fs, multiterawatt pulses by regenerative pulse shaping and chirped-pulse amplification,” Opt. Lett. 21, 668–670 (1996).
[CrossRef] [PubMed]

Yakovlev, V.

C. Bardeen, V. Yakovlev, K. R. Wilson, S. Carpenter, P. Weber, and W. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

Yakovlev, V. V.

C. J. Bardeen, V. V. Yakovlev, J. A. Squier, and K. R. Wilson, “Quantum control of population transfer in green flourescent protein by using chirped femtosecond pulses,” J. Am. Chem. Soc. 120, 13023–13027 (1998).
[CrossRef]

C. P. J. Barty, T. Guo, C. LeBlanc, F. Raski, C. Rose-Petruck, J. Squier, K. R. Wilson, V. V. Yakovlev, and K. Yamakawa, “Generation of 18-fs, multiterawatt pulses by regenerative pulse shaping and chirped-pulse amplification,” Opt. Lett. 21, 668–670 (1996).
[CrossRef] [PubMed]

Yamakawa, K.

Appl. Opt. (1)

Chem. Phys. Lett. (1)

C. Bardeen, V. Yakovlev, K. R. Wilson, S. Carpenter, P. Weber, and W. Warren, “Feedback quantum control of molecular electronic population transfer,” Chem. Phys. Lett. 280, 151–158 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

D. Sutter, I. Jung, F. Kartner, N. Matuschek, F. M. Genoud, V. Scheuer, M. Tilsch, T. Tschudi, and U. Keller, “Self starting 6.5 fs pulses from a Ti:sapphire laser using a semiconductor saturable absorber and double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 169–178 (1998).
[CrossRef]

V. Bagnoud and F. Salin, “Global optimization of pulse compression in chirped pulse amplification,” IEEE J. Sel. Top. Quantum Electron. 4, 445–448 (1998).
[CrossRef]

J. Am. Chem. Soc. (1)

C. J. Bardeen, V. V. Yakovlev, J. A. Squier, and K. R. Wilson, “Quantum control of population transfer in green flourescent protein by using chirped femtosecond pulses,” J. Am. Chem. Soc. 120, 13023–13027 (1998).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (4)

Phys. Rev. A (1)

J. S. Melinger, D. McMorrow, C. Hillegas, and W. S. Warren, “Selective excitation of vibrational overtones in an anharmonic ladder with frequency- and amplitude-modulated laser pulses,” Phys. Rev. A 51, 3366–3369 (1995).
[CrossRef] [PubMed]

Rev. Sci. Instrum. (1)

R. Trebino, K. W. Delong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbugel, B. A. Richman, and D. J. Kane, “Measuring ultrashort laser pulses in the time–frequency domain using frequency resolved optical gating,” Rev. Sci. Instrum. 68, 3277–3295 (1997).
[CrossRef]

Other (14)

D. N. Fittinghoff, B. C. Walker, J. A. Squier, Cs. Tóth, C. Rose-Petruck, and C. P. J. Barty, “Dispersion considerations in ultrafast CPA systems,” IEEE J. Sel. Top. Quantum Electron. 4, 430–440 (1998); D. N. Christodoulides, E. Bourkoff, R. I. Joseph, and T. Simos, “Reflection of femtosecond optical pulses from multiple-layer dielectric mirrors—analysis,” IEEE J. Quantum Electron. 22, 186–191 (1986); K. E. Oughstun and H. Xiao, “Failure of the quasimonochromatic approximation for ultrashort pulse propagation in a dispersive medium,” Phys. Rev. Lett. PRLTAO 78, 642–645 (1997).
[CrossRef]

C. G. Durfee III, S. Backus, M. Murnane, and H. Kapteyn, “Design and implementation of a TW-class high average power laser system,” IEEE J. Sel. Top. Quantum Electron. 4, 395–406 (1998); S. Backus, C. G. Durfee III, M. Murnane, and H. Kapteyn, “High power ultrafast lasers,” Rev. Sci. Instrum. 69, 1207–1223 (1998).
[CrossRef]

S. Backus, G. Durfee, H. C. Kapteyn, and M. M. Murnane, “0.27-TW, sub-17-fs laser system at 1 kHz,” in Conference on Lasers and Electro-Optics (CLEO/U.S.), Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 362–363; E. Zeek, K. Maginnis, S. Backus, U. Russek, M. Murnane, G. Mourou, H. Kapteyn, and G. Vdovin, “Pulse compression by use of deformable mirrors,” Opt. Lett. 24, 493–495 (1999).
[CrossRef]

This situation is in contrast to the microwave spectral region, where determination of the field as a function of time is possible, and, for this case, distortions can and are quantified in time; e.g., white noise on the temporal profile is commonly quantified as a time-integrated rms.

For all calculations in this paper, I includes a spectral truncation window of 74 THz such as would occur in experimental systems, for example, at frequencies beyond the edges of the stretcher and compressor gratings.

The n time moment is defined as ∫|t|nIdt/∫Idt.

B. C. Walker, Cs. Tóth, D. Fittinghoff, J. Squier, T. Guo, K. R. Wilson, and C. P. T. Barty, “Ultrafast, relativistic intensities: generation, characterization, and application to photoionization,” in Conference on Lasers and Electro-Optics, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 71.

M. D. Perry and G. Mourou, “Terawatt to petawatt subpicosecond lasers,” Science 264, 917–924 (1994); D. Strickland and G. Mourou, “Compression of amplified chirped optical pulses,” Opt. Commun. 56, 219–221 (1985).
[CrossRef] [PubMed]

G. Tempea, F. Krausz, C. Spielmann, and K. Ferencz, “Dispersion control over 150 THz with chirped dielectric mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 193–196 (1998); N. Matuschek, F. Kartner, and U. Keller, “Theory of double chirped mirrors,” IEEE J. Sel. Top. Quantum Electron. 4, 197–208 (1998).
[CrossRef]

C. Spielmann, University Wien, Vienna, Austria (personal communication, 1998).

Thin Film, Broad Band, Plate Polarizer, from Alpine Research Optics, Boulder, Colo., 80301.

The Taylor series expansion was truncated at n=4. This truncation is commonly required when one is representing experimental data owing to convergence and term orthogonality problems, and it results in a significant filtering of high-frequency phase-dispersion information. For example, the value of øerr is different for the experimental phase data and the Taylor series representation of that data.

The Pearson r is r=∑xy/[(∑x2)(∑y2)]1/2. |r| is 1 for a perfectly linear relationship. See N. Downie and R. Heath, Basic Statistical Methods, 2nd ed (Harper & Row, New York, 1965), p. 78.

See, for example, M. Schnurer, C. Spielmann, P. Wobrauschek, C. Streli, N. H. Burnett, C. Kan, K. Ferencz, R. Koppitsch, Z. Cheng, T. Brabec, and F. Krausz, “Coherent 0.5-keV x-ray emission from helium driven by a sub-10-fs laser,” Phys. Rev. Lett. 80, 3236–3239 (1998); D. Umstader, S.-Y. Chen, A. Maksimchuk, G. Mourou, and R. Wagner, “Nonlinear optics in relativistic plasmas and laser wake field acceleration of electrons,” Science 273, 472–475 (1996); B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchick, B. W. Shore, and M. D. Perry, “Optical ablation by high-power short-pulse lasers,” J. Opt. Soc. Am. B JOBPDE 13, 459–468 (1996); P. Y. Cheng, D. Zhong, and A. H. Zewail, “Femtosecond real-time probing of reactions. XXI. Direct observation of transition state dynamics and structure in charge-transfer reactions,” J. Chem. Phys. JCPSA6 105, 6216–6248 (1996); B. Walker, M. Kaluza, B. Sheehy, P. Agostini, and L. F. DiMauro, “Observation of continuum–continuum Autler–Townes splitting,” Phys. Rev. Lett. PRLTAO 75, 633–636 (1995).
[CrossRef] [PubMed]

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Figures (8)

Fig. 1
Fig. 1

(a) Gaussian pulse spectrum for an 18-fs FWHM transform-limited pulse. (b) Three sample phase errors, each with ϕerr of 0.5 rad for the pulse spectrum in (a). The distortions are, dashed curve, quadratic; solid curve, cubic; dotted curve, sidusoidal.

Fig. 2
Fig. 2

Temporal pulse profile characteristics for a Gaussian spectrum as a function of ϕerr from (a) quadratic and (b) sinusoidal phase distortions. The calculated points are shown with a fit to guide the eye. The following measures are plotted (symbol, fit): (cross, solid curve) standard deviation, (filled circle, long-dashed curve) first moment, (square, lower dotted curve) FWHM, (filled triangle, light dashed curve) 50% energy, (open triangle, upper dotted curve), 99.9% energy.

Fig. 3
Fig. 3

(a) Temporal profile of a two-peaked pulse for ϕerr of zero and the evolution of the pulse for ϕerr of (b) 0.25, (c) 0.5, (d) 0.75 rad with a pure quadratic phase dispersion.

Fig. 4
Fig. 4

Spectral phase distortions caused by optical components with ϕerr=0.5 rad for an 18-fs Gaussian pulse. The distortions shown are, solid curve, dielectric mirrors; light dashed curve, grating compressor; short-and-long-dashed curve, self-phase modulation; bold dashed curve, o-KDP (5.5-mm path); dotted curve, e-sapphire (2.8-mm path).

Fig. 5
Fig. 5

(a) Phases distortions minimized by Taylor series and ϕerr approaches (a) (the frequency is defined relative to the carrier used 2.36 rad/fs.) (b) Relative temporal profile of the Ig spectral distribution with the phase errors in (a). (c) Comparison of normalized intensity profiles. Light solid curve, transform limit; dotted curve, ϕerr; bold solid curve, Taylor series.

Fig. 6
Fig. 6

Examples of three different experimental phase measurements (b)–(d) for the pulse spectrum in (a). The error bars represent one standard deviation about the mean of 7–11 single-shot, full spectral phase measurements.

Fig. 7
Fig. 7

Correlation of the spectral FOM ϕerr and the temporal observables, including (filled square) the pulse FWHM duration, (open triangle) 50% energy width, and (filled circle) the first and (cross) second temporal moments.

Fig. 8
Fig. 8

Correlation of the magnitudes of (filled square) c2, (cross) c3, and (open triangle) c4 with (a) the measured pulse FWHM and (b) the temporal second moment. The error bars represent one standard deviation of fluctuations in c2 for (a). The error bars for c3 (c4) are, on average, 15% (1000%) larger.

Equations (5)

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ϕTaylor(ω)=c0+c1(ω-ω0)+c2(ω-ω0)2+c3(ω-ω0)3+,
ϕerr2=I[ϕ-ϕr-ϕp-ϕ¯]2dωIdω.
ϕp[Id(ϕ-ϕr)/dω¯/I¯]ω.
ϕ¯I(ϕ-ϕr-ϕp)¯/I¯.
Itp(t)=exp-(t+a)2b2+exp-(t-a)2b2+2 exp-[(t+a)2+(t-a)2]2b2,

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