Abstract

A direct measurement of the amplitude and the phase of a femtosecond light pulse is performed for the first time to our knowledge. The measurement is made in the frequency domain, and the time dependence of the field can be easily obtained by a Fourier transform. The technique relies on a pulse synthesis scheme to unravel the frequency dependence of the phase. A mask filters the spectrum, which gives rise to a pulse with a measurable temporal profile related to the frequency dependence of the phase. In particular, with a rectangular slit the time delay of the synthesized pulse is the first derivative of the phase with respect to the frequency of the original pulse at the central frequency of the filter. The amplitude of the spectrum is obtained from the power spectrum.

© 1991 Optical Society of America

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References

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  1. E. P. Ippen, C. V. Shank, in Ultrashort Light Pulses, S. L. Shapiro, ed. (Springer-Verlag, New York, 1977), pp.313–345.
  2. C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, Appl. Phys. Lett. 40, 761 (1982).
    [CrossRef]
  3. J. A. Valdmanis, R. L. Fork, IEEE J. Quantum Electron. QE-22, 112 (1986).
    [CrossRef]
  4. J. C. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, Appl. Opt. 24, 1270 (1985).
    [CrossRef] [PubMed]
  5. J. C. Diels, J. J. Fontaine, W. Rudolph, Rev. Phys. Appl. 22, 1605 (1987).
    [CrossRef]
  6. K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
    [CrossRef]
  7. J. Rothenberg, D. Grischkowsky, Opt. Lett. 12, 99(1987).
    [CrossRef] [PubMed]
  8. F. Reynaud, F. Salin, A. Barthelemy, Opt. Lett. 14, 275 (1989).
    [CrossRef] [PubMed]
  9. A. M. Weiner, J. P. Heritage, E. M. Kirschner, J. Opt. Soc. Am. B 51563 (1988).
    [CrossRef]
  10. O. E. Martinez, IEEE J. Quantum Electron. 24, 2530 (1988).
    [CrossRef]
  11. M. B. Danilov, I. P. Christov, J. Mod. Opt. 36, 725 (1989).
    [CrossRef]

1989

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

M. B. Danilov, I. P. Christov, J. Mod. Opt. 36, 725 (1989).
[CrossRef]

F. Reynaud, F. Salin, A. Barthelemy, Opt. Lett. 14, 275 (1989).
[CrossRef] [PubMed]

1988

1987

J. Rothenberg, D. Grischkowsky, Opt. Lett. 12, 99(1987).
[CrossRef] [PubMed]

J. C. Diels, J. J. Fontaine, W. Rudolph, Rev. Phys. Appl. 22, 1605 (1987).
[CrossRef]

1986

J. A. Valdmanis, R. L. Fork, IEEE J. Quantum Electron. QE-22, 112 (1986).
[CrossRef]

1985

1982

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Barthelemy, A.

Christov, I. P.

M. B. Danilov, I. P. Christov, J. Mod. Opt. 36, 725 (1989).
[CrossRef]

Danilov, M. B.

M. B. Danilov, I. P. Christov, J. Mod. Opt. 36, 725 (1989).
[CrossRef]

Diels, J. C.

J. C. Diels, J. J. Fontaine, W. Rudolph, Rev. Phys. Appl. 22, 1605 (1987).
[CrossRef]

J. C. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, Appl. Opt. 24, 1270 (1985).
[CrossRef] [PubMed]

Fontaine, J. J.

J. C. Diels, J. J. Fontaine, W. Rudolph, Rev. Phys. Appl. 22, 1605 (1987).
[CrossRef]

J. C. Diels, J. J. Fontaine, I. C. McMichael, F. Simoni, Appl. Opt. 24, 1270 (1985).
[CrossRef] [PubMed]

Fork, R. L.

J. A. Valdmanis, R. L. Fork, IEEE J. Quantum Electron. QE-22, 112 (1986).
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Grischkowsky, D.

Heritage, J. P.

Ippen, E. P.

E. P. Ippen, C. V. Shank, in Ultrashort Light Pulses, S. L. Shapiro, ed. (Springer-Verlag, New York, 1977), pp.313–345.

Kirschner, E. M.

Martinez, O. E.

O. E. Martinez, IEEE J. Quantum Electron. 24, 2530 (1988).
[CrossRef]

McMichael, I. C.

Mogi, K.

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

Naganuma, K.

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

Reynaud, F.

Rothenberg, J.

Rudolph, W.

J. C. Diels, J. J. Fontaine, W. Rudolph, Rev. Phys. Appl. 22, 1605 (1987).
[CrossRef]

Salin, F.

Shank, C. V.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

E. P. Ippen, C. V. Shank, in Ultrashort Light Pulses, S. L. Shapiro, ed. (Springer-Verlag, New York, 1977), pp.313–345.

Simoni, F.

Stolen, R. H.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Valdmanis, J. A.

J. A. Valdmanis, R. L. Fork, IEEE J. Quantum Electron. QE-22, 112 (1986).
[CrossRef]

Weiner, A. M.

Yamada, H.

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

Yen, R.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

IEEE J. Quantum Electron.

J. A. Valdmanis, R. L. Fork, IEEE J. Quantum Electron. QE-22, 112 (1986).
[CrossRef]

K. Naganuma, K. Mogi, H. Yamada, IEEE J. Quantum Electron. 25, 1225 (1989).
[CrossRef]

O. E. Martinez, IEEE J. Quantum Electron. 24, 2530 (1988).
[CrossRef]

J. Mod. Opt.

M. B. Danilov, I. P. Christov, J. Mod. Opt. 36, 725 (1989).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Rev. Phys. Appl.

J. C. Diels, J. J. Fontaine, W. Rudolph, Rev. Phys. Appl. 22, 1605 (1987).
[CrossRef]

Other

E. P. Ippen, C. V. Shank, in Ultrashort Light Pulses, S. L. Shapiro, ed. (Springer-Verlag, New York, 1977), pp.313–345.

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Figures (4)

Fig. 1
Fig. 1

Experimental setup (zero-dispersion compressor with a single slit mask). F, filter; CCR, cross correlator. The output is correlated with a pulse that comes directly from the laser. A monochromator provides the spectral position of the slit.

Fig. 2
Fig. 2

Power spectrum (upper curve) and the derivative of the phase with respect to frequency (lower curve). Experimental points are shown with error bars and a polynomial third-order fit. The cubic term that resulted is negligible.

Fig. 3
Fig. 3

Pulse shape calculated from the measured field spectrum. The FWHM is 295 fsec.

Fig. 4
Fig. 4

Autocorrelation measurements. Dashed curve, measured values; solid curve, values calculated from the pulse shape shown in Fig. 3, with a FWHM of 400 fsec; dotted curve, values calculated from the transform-limited pulse, with a FWHM of 300 fsec. The slight asymmetry in the measured curve is within the noise level of our measurement.

Equations (4)

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a out ( x 3 , t ) = b 1 - a in ( ω ) exp [ - ( χ - k β ω ) 2 a 2 / 4 α 2 ] - i k β ω x 3 / α + i χ x 3 / α + i ω t ] H ( χ ) d χ d ω .
a out ( x 3 , t ) = exp ( - x 3 2 / a 2 ) a in ( ω ) H ( ω ) exp ( i ω t ) d ω .
a in ( ω ) = a 0 exp [ i ( φ 0 + φ ω ) ] .
E ( t ) = a in ( ω ) H ( ω ) exp ( i ω t ) d ω = a 0 exp ( i φ 0 ) sinc [ s ( t + φ ) ] ,

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