Abstract

We introduce a new method for femtosecond pulse shape measurement. The interference of two pulses is employed rather than the second-harmonic generation (SHG). Usually, the measurements of the femtosecond pulse is realized by an interferometer in combination with a nonlinear optical material, while the measurement that we describe is realized by means of a Michelson interferometer with a Schottky junction. Only a metal–semiconductor junction (Schottky junction) is needed, and neither the nonlinear optical material nor a photodetector is included. The two-photon absorption arises when the light is strong enough, while there is only a one-photon absorption when the light is weak. And the calculations are in good agreement with the experimental results. In principle, the new technique could be used for the measuring of pulses with any duration and with very low power. Unlike the SHG scheme, in the new method the quality of optics, mechanics, and other elements of the scheme are not essential, and the measurement is easily realized, but the results are quite precise and very sensitive to the light.

© 2006 Optical Society of America

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  1. J. P. Callan, A. M.-T. Kim, C. A. D. Roeser, and E. Mazur, "Ultrafast laser-induced phase transitions in amorphous GeSb films," Phys. Rev. Lett. 86, 3650-3653 (2001).
    [CrossRef] [PubMed]
  2. J. M. Bao, L. N. Pfeiffer, K. W. West, and R. Merlin, "Ultrafast dynamic control of spin and charge density oscillations in a GaAs quantum well," Phys. Rev. Lett. 92, 236601 (2004).
    [CrossRef] [PubMed]
  3. J. Liu, H. Schroeder, S. Leang Chin, R. Li, and Z. Xu, "Ultrafast control of multiple filamentation by ultrafast laser pulses," Appl. Phys. Lett. 87, 161105 (2005).
    [CrossRef]
  4. U. Höfer, "Time-resolved coherent spectroscopy of surface states," Appl. Phys. B 68, 383-392 (1999).
    [CrossRef]
  5. T. Fujisawa, T. Hayashi, and S. Sasaki, "Time-dependent single-electron transport through quantum dots," Rep. Prog. Phys. 69, 759-796 (2006).
    [CrossRef]
  6. M. Yan, M. Yao, H. Zhang, and Q. Wu, "Ultrashort pulse measurement using interferometric autocorrelator based on two-photon-absorption detector at 1.55-μm wavelength region," in Proc. of SPIE 5633, 424-429 (2005).
    [CrossRef]
  7. A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker and M. Razeghi, "Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode," Appl. Phys. Lett. 75, 3778-3780 (1999).
    [CrossRef]
  8. S. M. Sze, Physics of Semiconductor Device, 2nd ed. (Wiley, 1981).
  9. J. I. Pankove, Optical Processes in Semiconductors (Princeton U. Press, 1973).
  10. Spectra-Physics, User's Manual of Tsunami (Spectra-Physics, 1999).
  11. J. C. Diels, Ultrashort Laser Pulse Phenomena (Academic, 1996).
  12. M. Schall and P. Uhd Jepsena, "Above-band gap two-photon absorption and its influence on ultrafast carrier dynamics in ZnTe and CdTe," Appl. Phys. Lett. 80, 4771-4773 (2002).
    [CrossRef]
  13. J.-C. M. Diels, J. J. Fontaine, I. C. McMichael, and F. Simoni, "Control and measurement of ultrashort pulse shapes (in amplitude and phase) with femtosecond accuracy," Appl. Opt. 24, 1270-1282 (1985).
    [CrossRef] [PubMed]

2006 (1)

T. Fujisawa, T. Hayashi, and S. Sasaki, "Time-dependent single-electron transport through quantum dots," Rep. Prog. Phys. 69, 759-796 (2006).
[CrossRef]

2005 (2)

M. Yan, M. Yao, H. Zhang, and Q. Wu, "Ultrashort pulse measurement using interferometric autocorrelator based on two-photon-absorption detector at 1.55-μm wavelength region," in Proc. of SPIE 5633, 424-429 (2005).
[CrossRef]

J. Liu, H. Schroeder, S. Leang Chin, R. Li, and Z. Xu, "Ultrafast control of multiple filamentation by ultrafast laser pulses," Appl. Phys. Lett. 87, 161105 (2005).
[CrossRef]

2004 (1)

J. M. Bao, L. N. Pfeiffer, K. W. West, and R. Merlin, "Ultrafast dynamic control of spin and charge density oscillations in a GaAs quantum well," Phys. Rev. Lett. 92, 236601 (2004).
[CrossRef] [PubMed]

2002 (1)

M. Schall and P. Uhd Jepsena, "Above-band gap two-photon absorption and its influence on ultrafast carrier dynamics in ZnTe and CdTe," Appl. Phys. Lett. 80, 4771-4773 (2002).
[CrossRef]

2001 (1)

J. P. Callan, A. M.-T. Kim, C. A. D. Roeser, and E. Mazur, "Ultrafast laser-induced phase transitions in amorphous GeSb films," Phys. Rev. Lett. 86, 3650-3653 (2001).
[CrossRef] [PubMed]

1999 (2)

U. Höfer, "Time-resolved coherent spectroscopy of surface states," Appl. Phys. B 68, 383-392 (1999).
[CrossRef]

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker and M. Razeghi, "Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode," Appl. Phys. Lett. 75, 3778-3780 (1999).
[CrossRef]

1985 (1)

Bao, J. M.

J. M. Bao, L. N. Pfeiffer, K. W. West, and R. Merlin, "Ultrafast dynamic control of spin and charge density oscillations in a GaAs quantum well," Phys. Rev. Lett. 92, 236601 (2004).
[CrossRef] [PubMed]

Callan, J. P.

J. P. Callan, A. M.-T. Kim, C. A. D. Roeser, and E. Mazur, "Ultrafast laser-induced phase transitions in amorphous GeSb films," Phys. Rev. Lett. 86, 3650-3653 (2001).
[CrossRef] [PubMed]

Chin, S. Leang

J. Liu, H. Schroeder, S. Leang Chin, R. Li, and Z. Xu, "Ultrafast control of multiple filamentation by ultrafast laser pulses," Appl. Phys. Lett. 87, 161105 (2005).
[CrossRef]

Diels, J. C.

J. C. Diels, Ultrashort Laser Pulse Phenomena (Academic, 1996).

Diels, J.-C. M.

Fontaine, J. J.

Fujisawa, T.

T. Fujisawa, T. Hayashi, and S. Sasaki, "Time-dependent single-electron transport through quantum dots," Rep. Prog. Phys. 69, 759-796 (2006).
[CrossRef]

Gaeta, A. L.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker and M. Razeghi, "Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode," Appl. Phys. Lett. 75, 3778-3780 (1999).
[CrossRef]

Hayashi, T.

T. Fujisawa, T. Hayashi, and S. Sasaki, "Time-dependent single-electron transport through quantum dots," Rep. Prog. Phys. 69, 759-796 (2006).
[CrossRef]

Höfer, U.

U. Höfer, "Time-resolved coherent spectroscopy of surface states," Appl. Phys. B 68, 383-392 (1999).
[CrossRef]

Kim, A. M.-T.

J. P. Callan, A. M.-T. Kim, C. A. D. Roeser, and E. Mazur, "Ultrafast laser-induced phase transitions in amorphous GeSb films," Phys. Rev. Lett. 86, 3650-3653 (2001).
[CrossRef] [PubMed]

Kung, P.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker and M. Razeghi, "Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode," Appl. Phys. Lett. 75, 3778-3780 (1999).
[CrossRef]

Li, R.

J. Liu, H. Schroeder, S. Leang Chin, R. Li, and Z. Xu, "Ultrafast control of multiple filamentation by ultrafast laser pulses," Appl. Phys. Lett. 87, 161105 (2005).
[CrossRef]

Liu, J.

J. Liu, H. Schroeder, S. Leang Chin, R. Li, and Z. Xu, "Ultrafast control of multiple filamentation by ultrafast laser pulses," Appl. Phys. Lett. 87, 161105 (2005).
[CrossRef]

Mazur, E.

J. P. Callan, A. M.-T. Kim, C. A. D. Roeser, and E. Mazur, "Ultrafast laser-induced phase transitions in amorphous GeSb films," Phys. Rev. Lett. 86, 3650-3653 (2001).
[CrossRef] [PubMed]

McMichael, I. C.

Merlin, R.

J. M. Bao, L. N. Pfeiffer, K. W. West, and R. Merlin, "Ultrafast dynamic control of spin and charge density oscillations in a GaAs quantum well," Phys. Rev. Lett. 92, 236601 (2004).
[CrossRef] [PubMed]

Moll, K. D.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker and M. Razeghi, "Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode," Appl. Phys. Lett. 75, 3778-3780 (1999).
[CrossRef]

Pankove, J. I.

J. I. Pankove, Optical Processes in Semiconductors (Princeton U. Press, 1973).

Pfeiffer, L. N.

J. M. Bao, L. N. Pfeiffer, K. W. West, and R. Merlin, "Ultrafast dynamic control of spin and charge density oscillations in a GaAs quantum well," Phys. Rev. Lett. 92, 236601 (2004).
[CrossRef] [PubMed]

Razeghi, M.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker and M. Razeghi, "Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode," Appl. Phys. Lett. 75, 3778-3780 (1999).
[CrossRef]

Roeser, C. A. D.

J. P. Callan, A. M.-T. Kim, C. A. D. Roeser, and E. Mazur, "Ultrafast laser-induced phase transitions in amorphous GeSb films," Phys. Rev. Lett. 86, 3650-3653 (2001).
[CrossRef] [PubMed]

Sasaki, S.

T. Fujisawa, T. Hayashi, and S. Sasaki, "Time-dependent single-electron transport through quantum dots," Rep. Prog. Phys. 69, 759-796 (2006).
[CrossRef]

Schall, M.

M. Schall and P. Uhd Jepsena, "Above-band gap two-photon absorption and its influence on ultrafast carrier dynamics in ZnTe and CdTe," Appl. Phys. Lett. 80, 4771-4773 (2002).
[CrossRef]

Schroeder, H.

J. Liu, H. Schroeder, S. Leang Chin, R. Li, and Z. Xu, "Ultrafast control of multiple filamentation by ultrafast laser pulses," Appl. Phys. Lett. 87, 161105 (2005).
[CrossRef]

Simoni, F.

Streltsov, A. M.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker and M. Razeghi, "Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode," Appl. Phys. Lett. 75, 3778-3780 (1999).
[CrossRef]

Sze, S. M.

S. M. Sze, Physics of Semiconductor Device, 2nd ed. (Wiley, 1981).

Uhd Jepsena, P.

M. Schall and P. Uhd Jepsena, "Above-band gap two-photon absorption and its influence on ultrafast carrier dynamics in ZnTe and CdTe," Appl. Phys. Lett. 80, 4771-4773 (2002).
[CrossRef]

Walker, D.

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker and M. Razeghi, "Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode," Appl. Phys. Lett. 75, 3778-3780 (1999).
[CrossRef]

West, K. W.

J. M. Bao, L. N. Pfeiffer, K. W. West, and R. Merlin, "Ultrafast dynamic control of spin and charge density oscillations in a GaAs quantum well," Phys. Rev. Lett. 92, 236601 (2004).
[CrossRef] [PubMed]

Wu, Q.

M. Yan, M. Yao, H. Zhang, and Q. Wu, "Ultrashort pulse measurement using interferometric autocorrelator based on two-photon-absorption detector at 1.55-μm wavelength region," in Proc. of SPIE 5633, 424-429 (2005).
[CrossRef]

Xu, Z.

J. Liu, H. Schroeder, S. Leang Chin, R. Li, and Z. Xu, "Ultrafast control of multiple filamentation by ultrafast laser pulses," Appl. Phys. Lett. 87, 161105 (2005).
[CrossRef]

Yan, M.

M. Yan, M. Yao, H. Zhang, and Q. Wu, "Ultrashort pulse measurement using interferometric autocorrelator based on two-photon-absorption detector at 1.55-μm wavelength region," in Proc. of SPIE 5633, 424-429 (2005).
[CrossRef]

Yao, M.

M. Yan, M. Yao, H. Zhang, and Q. Wu, "Ultrashort pulse measurement using interferometric autocorrelator based on two-photon-absorption detector at 1.55-μm wavelength region," in Proc. of SPIE 5633, 424-429 (2005).
[CrossRef]

Zhang, H.

M. Yan, M. Yao, H. Zhang, and Q. Wu, "Ultrashort pulse measurement using interferometric autocorrelator based on two-photon-absorption detector at 1.55-μm wavelength region," in Proc. of SPIE 5633, 424-429 (2005).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

U. Höfer, "Time-resolved coherent spectroscopy of surface states," Appl. Phys. B 68, 383-392 (1999).
[CrossRef]

Appl. Phys. Lett. (3)

A. M. Streltsov, K. D. Moll, A. L. Gaeta, P. Kung, D. Walker and M. Razeghi, "Pulse autocorrelation measurements based on two- and three-photon conductivity in a GaN photodiode," Appl. Phys. Lett. 75, 3778-3780 (1999).
[CrossRef]

M. Schall and P. Uhd Jepsena, "Above-band gap two-photon absorption and its influence on ultrafast carrier dynamics in ZnTe and CdTe," Appl. Phys. Lett. 80, 4771-4773 (2002).
[CrossRef]

J. Liu, H. Schroeder, S. Leang Chin, R. Li, and Z. Xu, "Ultrafast control of multiple filamentation by ultrafast laser pulses," Appl. Phys. Lett. 87, 161105 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

J. P. Callan, A. M.-T. Kim, C. A. D. Roeser, and E. Mazur, "Ultrafast laser-induced phase transitions in amorphous GeSb films," Phys. Rev. Lett. 86, 3650-3653 (2001).
[CrossRef] [PubMed]

J. M. Bao, L. N. Pfeiffer, K. W. West, and R. Merlin, "Ultrafast dynamic control of spin and charge density oscillations in a GaAs quantum well," Phys. Rev. Lett. 92, 236601 (2004).
[CrossRef] [PubMed]

Proc. of SPIE (1)

M. Yan, M. Yao, H. Zhang, and Q. Wu, "Ultrashort pulse measurement using interferometric autocorrelator based on two-photon-absorption detector at 1.55-μm wavelength region," in Proc. of SPIE 5633, 424-429 (2005).
[CrossRef]

Rep. Prog. Phys. (1)

T. Fujisawa, T. Hayashi, and S. Sasaki, "Time-dependent single-electron transport through quantum dots," Rep. Prog. Phys. 69, 759-796 (2006).
[CrossRef]

Other (4)

S. M. Sze, Physics of Semiconductor Device, 2nd ed. (Wiley, 1981).

J. I. Pankove, Optical Processes in Semiconductors (Princeton U. Press, 1973).

Spectra-Physics, User's Manual of Tsunami (Spectra-Physics, 1999).

J. C. Diels, Ultrashort Laser Pulse Phenomena (Academic, 1996).

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Figures (5)

Fig. 1
Fig. 1

Setup for the measurement, that is well known as the autocorrelation measurement. BS, beam splitter; MS, metal–semiconductor junction; Delay, time-delay line; lock-in, lock-in amplifier.

Fig. 2
Fig. 2

Sketch of the Al-(p-Si) Schottky junction. In the open circuit state, due to the internal electric field, the electron–hole pairs generated by the laser drift in opposite directions. The electrons and holes separately stay in piles at the left and right boundaries of the space-charge region of the MS junction in the figure, resulting in the fact that the measured voltage of the MS junction is not zero.

Fig. 3
Fig. 3

Experimental and calculated results in the low-power scheme ( 10   mW ) . The upper and lower parts of the envelope are horizontally symmetric. From the measurement and fitting, we get that the FWHM of the pulse is 102.6 fs. The inset is the enlargement of the results in which the oscillation can be seen distinctly. From the oscillation, we can get the central frequency of the pulse, and the central wavelength of the pulse is calculated to be 800 n m , which fits the result measured by a spectrometer very well, as shown in Fig. 5.

Fig. 4
Fig. 4

Experimental and calculated results in the high-power scheme ( 400   mW ) . The upper and lower parts of the envelope are not horizontally symmetric now. From the measurement and fitting, we can get that the FWHM of the pulse is also 102 fs.

Fig. 5
Fig. 5

Spectrum of the pulse simulated from the Gaussian distribution with the FWHM = 9.6 nm is well fitted to the one measured by the spectrum meter. The inset is the intensity envelope of the pulse with the FWHM = 102.6 fs, which is obtained by the simulation in Fig. 3.

Equations (12)

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E 1 ( ω , t ) = ε ( t ) exp ( i [ ω t + ψ ( t ) ] ) ,
E 2 ( ω , t τ ) = α ε ( t τ ) exp ( i [ ω ( t τ ) + ψ ( t τ ) ] ) ,
E ( ω , t ) = E 1 ( ω , t ) + E 2 ( ω , t τ ) = ε ( t ) exp ( i [ ω t + ψ ( t ) ] ) + α ε ( t τ ) exp ( i [ ω ( t τ ) + ψ ( t τ ) ] ) .
S ( τ ) = K + E E * d t ,
S ( τ ) = A [ 1 + G ( τ ) cos ( ω τ ) ] ,
A = ( α 2 + 1 ) K + ε 2 ( t ) d t ,
G = 2 α α 2 + 1 + ε ( t ) ε ( t τ ) d t + ε 2 ( t ) d t .
ε ( t ) = E 0 exp ( ( 4 ln 2 ) t 2 σ 2 ) ,
S ( τ ) = B [ 1 + C exp ( ( 2 ln 2 ) τ 2 σ 2 ) cos ( ω τ ) ] ,
B = ( α 2 + 1 ) K I 0 2 σ π 8 ln 2 , C = 2 α 2 α 2 + 1 .
S ( τ ) = S ω ( τ ) + S 2 ω ( τ ) = K + E E * d t + p k K + E 2 E * 2 d t ,
S ( τ ) = A + B exp ( 4 ln ( 2 ) τ 2 σ 2 ) + C exp ( 3 ln ( 2 ) τ 2 σ 2 ) cos ( ω τ ) + D exp ( 2 ln ( 2 ) τ 2 σ 2 ) cos ( ω τ ) + E exp ( 4 ln ( 2 ) τ 2 σ 2 ) cos ( 2 ω τ ) ,

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