Abstract

We have developed a scheme for determining the time origin by the maximum entropy method (MEM) in time-domain terahertz (THz) emission spectroscopy. By applying the MEM to trial damped sinusoidal waveforms, we confirmed that the MEM gives true phase shifts across the resonance features and that its inherent uncertainty in determining the time origin is ±15 fs for 100-fs-class excitation/sampling optical pulses. Furthermore, when the MEM was applied to a THz waveform recorded experimentally with a finite sampling interval for the Bloch oscillation in a semiconductor superlattice, a misplacement of the time origin was indeed detected with an accuracy limited by the worse of the MEM inherent uncertainty and the sampling interval.

© 2010 OSA

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  1. Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68(21), 2924 (1996).
    [CrossRef]
  2. A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Detectors and sources for ultrabroadband electro-optic sampling: Experiment and theory,” Appl. Phys. Lett. 74(11), 1516 (1999).
    [CrossRef]
  3. A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82 (25), 5140 (1999); “Femtosecond high-field transport in compound semiconductors,” Phys. Rev. B 61(24), 16642–16652 (2000).
  4. M. Abe, S. Madhavi, Y. Shimada, Y. Otsuka, K. Hirakawa, and K. Tomizawa, “Transient carrier velocities in bulk GaAs: Quantitative comparison between terahertz data and ensemble Monte Carlo calculations,” Appl. Phys. Lett. 81(4), 679 (2002).
    [CrossRef]
  5. E. Hendry, M. Koeberg, J. M. Schins, L. D. A. Siebbeles, and M. Bonn, “Ultrafast charge generation in a semiconducting polymer studied with THz emission spectroscopy,” Phys. Rev. B 70(3), 033202 (2004).
    [CrossRef]
  6. N. Sekine and K. Hirakawa, “Dispersive terahertz gain of a nonclassical oscillator: Bloch oscillation in semiconductor superlattices,” Phys. Rev. Lett. 94(5), 057408 (2005).
    [CrossRef] [PubMed]
  7. E. Beaurepaire, G. M. Turner, S. M. Harrel, M. C. Beard, J.-Y. Bigot, and C. A. Schmuttenmaer, “Coherent terahertz emission from ferromagnetic films excited by femtosecond laser pulses,” Appl. Phys. Lett. 84(18), 3465 (2004).
    [CrossRef]
  8. Y. Shimada, K. Hirakawa, M. Odnoblioudov, and K. A. Chao, “Terahertz conductivity and possible Bloch gain in semiconductor superlattices,” Phys. Rev. Lett. 90(4), 046806 (2003).
    [CrossRef] [PubMed]
  9. S. Haykin, Nonlinear Methods of Spectral Analysis (Springer, Berlin, 1983), Chap. 2.
  10. E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, “Phase retrieval in optical spectroscopy: Resolving optical constants from power spectra,” Appl. Spec. 50(10), 1283 (1996).
    [CrossRef]
  11. K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, Heidelberg, 1999), Chap. 5.
  12. E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, “Numerical phase correction method for terahertz time-domain reflection spectroscopy,” J. Appl. Phys. 96(8), 4171 (2004).
    [CrossRef]
  13. Y. Ino, B. Héroux, T. Mukaiyama, and M. Kuwata-Gonokami, “Reflection-type pulsed terahertz imaging with a phase retrieval algorithm,” Appl. Phys. Lett. 88(4), 041114 (2006).
    [CrossRef]
  14. We chose these frequency ranges by considering a tradeoff: the resonance feature is more accurately captured in wider frequency ranges, while the numerical error in solving the Toeplitz matrix equation becomes less in narrower frequency ranges.
  15. T. Unuma, N. Sekine, and K. Hirakawa, “Dephasing of Bloch oscillating electrons in GaAs-based superlattices due to interface roughness scattering,” Appl. Phys. Lett. 89(16), 161913 (2006).
    [CrossRef]
  16. V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, Berlin, 2005), Chap. 10.
  17. For example, seeA. Lisauskas, M. M. Dignam, N. V. Demarina, E. Mohler, and H. G. Roskos, “Examining the terahertz signal from a photoexcited biased semiconductor superlattice for evidence of gain,” Appl. Phys. Lett. 93(2), 021122 (2008).
    [CrossRef]
  18. T. Unuma, Y. Ino, M. Kuwata-Gonokami, G. Bastard, and K. Hirakawa, “Transient Bloch oscillation with the symmetry-governed phase in semiconductor superlattices,” Phys. Rev. B 81(12), 125329 (2010).
    [CrossRef]

2010 (1)

T. Unuma, Y. Ino, M. Kuwata-Gonokami, G. Bastard, and K. Hirakawa, “Transient Bloch oscillation with the symmetry-governed phase in semiconductor superlattices,” Phys. Rev. B 81(12), 125329 (2010).
[CrossRef]

2008 (1)

For example, seeA. Lisauskas, M. M. Dignam, N. V. Demarina, E. Mohler, and H. G. Roskos, “Examining the terahertz signal from a photoexcited biased semiconductor superlattice for evidence of gain,” Appl. Phys. Lett. 93(2), 021122 (2008).
[CrossRef]

2006 (2)

Y. Ino, B. Héroux, T. Mukaiyama, and M. Kuwata-Gonokami, “Reflection-type pulsed terahertz imaging with a phase retrieval algorithm,” Appl. Phys. Lett. 88(4), 041114 (2006).
[CrossRef]

T. Unuma, N. Sekine, and K. Hirakawa, “Dephasing of Bloch oscillating electrons in GaAs-based superlattices due to interface roughness scattering,” Appl. Phys. Lett. 89(16), 161913 (2006).
[CrossRef]

2005 (1)

N. Sekine and K. Hirakawa, “Dispersive terahertz gain of a nonclassical oscillator: Bloch oscillation in semiconductor superlattices,” Phys. Rev. Lett. 94(5), 057408 (2005).
[CrossRef] [PubMed]

2004 (3)

E. Beaurepaire, G. M. Turner, S. M. Harrel, M. C. Beard, J.-Y. Bigot, and C. A. Schmuttenmaer, “Coherent terahertz emission from ferromagnetic films excited by femtosecond laser pulses,” Appl. Phys. Lett. 84(18), 3465 (2004).
[CrossRef]

E. Hendry, M. Koeberg, J. M. Schins, L. D. A. Siebbeles, and M. Bonn, “Ultrafast charge generation in a semiconducting polymer studied with THz emission spectroscopy,” Phys. Rev. B 70(3), 033202 (2004).
[CrossRef]

E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, “Numerical phase correction method for terahertz time-domain reflection spectroscopy,” J. Appl. Phys. 96(8), 4171 (2004).
[CrossRef]

2003 (1)

Y. Shimada, K. Hirakawa, M. Odnoblioudov, and K. A. Chao, “Terahertz conductivity and possible Bloch gain in semiconductor superlattices,” Phys. Rev. Lett. 90(4), 046806 (2003).
[CrossRef] [PubMed]

2002 (1)

M. Abe, S. Madhavi, Y. Shimada, Y. Otsuka, K. Hirakawa, and K. Tomizawa, “Transient carrier velocities in bulk GaAs: Quantitative comparison between terahertz data and ensemble Monte Carlo calculations,” Appl. Phys. Lett. 81(4), 679 (2002).
[CrossRef]

1999 (2)

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Detectors and sources for ultrabroadband electro-optic sampling: Experiment and theory,” Appl. Phys. Lett. 74(11), 1516 (1999).
[CrossRef]

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82 (25), 5140 (1999); “Femtosecond high-field transport in compound semiconductors,” Phys. Rev. B 61(24), 16642–16652 (2000).

1996 (2)

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68(21), 2924 (1996).
[CrossRef]

E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, “Phase retrieval in optical spectroscopy: Resolving optical constants from power spectra,” Appl. Spec. 50(10), 1283 (1996).
[CrossRef]

Abe, M.

M. Abe, S. Madhavi, Y. Shimada, Y. Otsuka, K. Hirakawa, and K. Tomizawa, “Transient carrier velocities in bulk GaAs: Quantitative comparison between terahertz data and ensemble Monte Carlo calculations,” Appl. Phys. Lett. 81(4), 679 (2002).
[CrossRef]

Asakura, T.

E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, “Phase retrieval in optical spectroscopy: Resolving optical constants from power spectra,” Appl. Spec. 50(10), 1283 (1996).
[CrossRef]

Bastard, G.

T. Unuma, Y. Ino, M. Kuwata-Gonokami, G. Bastard, and K. Hirakawa, “Transient Bloch oscillation with the symmetry-governed phase in semiconductor superlattices,” Phys. Rev. B 81(12), 125329 (2010).
[CrossRef]

Beard, M. C.

E. Beaurepaire, G. M. Turner, S. M. Harrel, M. C. Beard, J.-Y. Bigot, and C. A. Schmuttenmaer, “Coherent terahertz emission from ferromagnetic films excited by femtosecond laser pulses,” Appl. Phys. Lett. 84(18), 3465 (2004).
[CrossRef]

Beaurepaire, E.

E. Beaurepaire, G. M. Turner, S. M. Harrel, M. C. Beard, J.-Y. Bigot, and C. A. Schmuttenmaer, “Coherent terahertz emission from ferromagnetic films excited by femtosecond laser pulses,” Appl. Phys. Lett. 84(18), 3465 (2004).
[CrossRef]

Bigot, J.-Y.

E. Beaurepaire, G. M. Turner, S. M. Harrel, M. C. Beard, J.-Y. Bigot, and C. A. Schmuttenmaer, “Coherent terahertz emission from ferromagnetic films excited by femtosecond laser pulses,” Appl. Phys. Lett. 84(18), 3465 (2004).
[CrossRef]

Bonn, M.

E. Hendry, M. Koeberg, J. M. Schins, L. D. A. Siebbeles, and M. Bonn, “Ultrafast charge generation in a semiconducting polymer studied with THz emission spectroscopy,” Phys. Rev. B 70(3), 033202 (2004).
[CrossRef]

Chao, K. A.

Y. Shimada, K. Hirakawa, M. Odnoblioudov, and K. A. Chao, “Terahertz conductivity and possible Bloch gain in semiconductor superlattices,” Phys. Rev. Lett. 90(4), 046806 (2003).
[CrossRef] [PubMed]

Demarina, N. V.

For example, seeA. Lisauskas, M. M. Dignam, N. V. Demarina, E. Mohler, and H. G. Roskos, “Examining the terahertz signal from a photoexcited biased semiconductor superlattice for evidence of gain,” Appl. Phys. Lett. 93(2), 021122 (2008).
[CrossRef]

Dignam, M. M.

For example, seeA. Lisauskas, M. M. Dignam, N. V. Demarina, E. Mohler, and H. G. Roskos, “Examining the terahertz signal from a photoexcited biased semiconductor superlattice for evidence of gain,” Appl. Phys. Lett. 93(2), 021122 (2008).
[CrossRef]

Harrel, S. M.

E. Beaurepaire, G. M. Turner, S. M. Harrel, M. C. Beard, J.-Y. Bigot, and C. A. Schmuttenmaer, “Coherent terahertz emission from ferromagnetic films excited by femtosecond laser pulses,” Appl. Phys. Lett. 84(18), 3465 (2004).
[CrossRef]

Hendry, E.

E. Hendry, M. Koeberg, J. M. Schins, L. D. A. Siebbeles, and M. Bonn, “Ultrafast charge generation in a semiconducting polymer studied with THz emission spectroscopy,” Phys. Rev. B 70(3), 033202 (2004).
[CrossRef]

Héroux, B.

Y. Ino, B. Héroux, T. Mukaiyama, and M. Kuwata-Gonokami, “Reflection-type pulsed terahertz imaging with a phase retrieval algorithm,” Appl. Phys. Lett. 88(4), 041114 (2006).
[CrossRef]

Hirakawa, K.

T. Unuma, Y. Ino, M. Kuwata-Gonokami, G. Bastard, and K. Hirakawa, “Transient Bloch oscillation with the symmetry-governed phase in semiconductor superlattices,” Phys. Rev. B 81(12), 125329 (2010).
[CrossRef]

T. Unuma, N. Sekine, and K. Hirakawa, “Dephasing of Bloch oscillating electrons in GaAs-based superlattices due to interface roughness scattering,” Appl. Phys. Lett. 89(16), 161913 (2006).
[CrossRef]

N. Sekine and K. Hirakawa, “Dispersive terahertz gain of a nonclassical oscillator: Bloch oscillation in semiconductor superlattices,” Phys. Rev. Lett. 94(5), 057408 (2005).
[CrossRef] [PubMed]

Y. Shimada, K. Hirakawa, M. Odnoblioudov, and K. A. Chao, “Terahertz conductivity and possible Bloch gain in semiconductor superlattices,” Phys. Rev. Lett. 90(4), 046806 (2003).
[CrossRef] [PubMed]

M. Abe, S. Madhavi, Y. Shimada, Y. Otsuka, K. Hirakawa, and K. Tomizawa, “Transient carrier velocities in bulk GaAs: Quantitative comparison between terahertz data and ensemble Monte Carlo calculations,” Appl. Phys. Lett. 81(4), 679 (2002).
[CrossRef]

Hunsche, S.

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Detectors and sources for ultrabroadband electro-optic sampling: Experiment and theory,” Appl. Phys. Lett. 74(11), 1516 (1999).
[CrossRef]

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82 (25), 5140 (1999); “Femtosecond high-field transport in compound semiconductors,” Phys. Rev. B 61(24), 16642–16652 (2000).

Ino, Y.

T. Unuma, Y. Ino, M. Kuwata-Gonokami, G. Bastard, and K. Hirakawa, “Transient Bloch oscillation with the symmetry-governed phase in semiconductor superlattices,” Phys. Rev. B 81(12), 125329 (2010).
[CrossRef]

Y. Ino, B. Héroux, T. Mukaiyama, and M. Kuwata-Gonokami, “Reflection-type pulsed terahertz imaging with a phase retrieval algorithm,” Appl. Phys. Lett. 88(4), 041114 (2006).
[CrossRef]

E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, “Numerical phase correction method for terahertz time-domain reflection spectroscopy,” J. Appl. Phys. 96(8), 4171 (2004).
[CrossRef]

Knox, W. H.

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Detectors and sources for ultrabroadband electro-optic sampling: Experiment and theory,” Appl. Phys. Lett. 74(11), 1516 (1999).
[CrossRef]

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82 (25), 5140 (1999); “Femtosecond high-field transport in compound semiconductors,” Phys. Rev. B 61(24), 16642–16652 (2000).

Koeberg, M.

E. Hendry, M. Koeberg, J. M. Schins, L. D. A. Siebbeles, and M. Bonn, “Ultrafast charge generation in a semiconducting polymer studied with THz emission spectroscopy,” Phys. Rev. B 70(3), 033202 (2004).
[CrossRef]

Kuwata-Gonokami, M.

T. Unuma, Y. Ino, M. Kuwata-Gonokami, G. Bastard, and K. Hirakawa, “Transient Bloch oscillation with the symmetry-governed phase in semiconductor superlattices,” Phys. Rev. B 81(12), 125329 (2010).
[CrossRef]

Y. Ino, B. Héroux, T. Mukaiyama, and M. Kuwata-Gonokami, “Reflection-type pulsed terahertz imaging with a phase retrieval algorithm,” Appl. Phys. Lett. 88(4), 041114 (2006).
[CrossRef]

E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, “Numerical phase correction method for terahertz time-domain reflection spectroscopy,” J. Appl. Phys. 96(8), 4171 (2004).
[CrossRef]

Leitenstorfer, A.

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Detectors and sources for ultrabroadband electro-optic sampling: Experiment and theory,” Appl. Phys. Lett. 74(11), 1516 (1999).
[CrossRef]

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82 (25), 5140 (1999); “Femtosecond high-field transport in compound semiconductors,” Phys. Rev. B 61(24), 16642–16652 (2000).

Lisauskas, A.

For example, seeA. Lisauskas, M. M. Dignam, N. V. Demarina, E. Mohler, and H. G. Roskos, “Examining the terahertz signal from a photoexcited biased semiconductor superlattice for evidence of gain,” Appl. Phys. Lett. 93(2), 021122 (2008).
[CrossRef]

Litz, M.

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68(21), 2924 (1996).
[CrossRef]

Madhavi, S.

M. Abe, S. Madhavi, Y. Shimada, Y. Otsuka, K. Hirakawa, and K. Tomizawa, “Transient carrier velocities in bulk GaAs: Quantitative comparison between terahertz data and ensemble Monte Carlo calculations,” Appl. Phys. Lett. 81(4), 679 (2002).
[CrossRef]

Mohler, E.

For example, seeA. Lisauskas, M. M. Dignam, N. V. Demarina, E. Mohler, and H. G. Roskos, “Examining the terahertz signal from a photoexcited biased semiconductor superlattice for evidence of gain,” Appl. Phys. Lett. 93(2), 021122 (2008).
[CrossRef]

Mukaiyama, T.

Y. Ino, B. Héroux, T. Mukaiyama, and M. Kuwata-Gonokami, “Reflection-type pulsed terahertz imaging with a phase retrieval algorithm,” Appl. Phys. Lett. 88(4), 041114 (2006).
[CrossRef]

Nuss, M. C.

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Detectors and sources for ultrabroadband electro-optic sampling: Experiment and theory,” Appl. Phys. Lett. 74(11), 1516 (1999).
[CrossRef]

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82 (25), 5140 (1999); “Femtosecond high-field transport in compound semiconductors,” Phys. Rev. B 61(24), 16642–16652 (2000).

Odnoblioudov, M.

Y. Shimada, K. Hirakawa, M. Odnoblioudov, and K. A. Chao, “Terahertz conductivity and possible Bloch gain in semiconductor superlattices,” Phys. Rev. Lett. 90(4), 046806 (2003).
[CrossRef] [PubMed]

Otsuka, Y.

M. Abe, S. Madhavi, Y. Shimada, Y. Otsuka, K. Hirakawa, and K. Tomizawa, “Transient carrier velocities in bulk GaAs: Quantitative comparison between terahertz data and ensemble Monte Carlo calculations,” Appl. Phys. Lett. 81(4), 679 (2002).
[CrossRef]

Peiponen, K.-E.

E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, “Numerical phase correction method for terahertz time-domain reflection spectroscopy,” J. Appl. Phys. 96(8), 4171 (2004).
[CrossRef]

E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, “Phase retrieval in optical spectroscopy: Resolving optical constants from power spectra,” Appl. Spec. 50(10), 1283 (1996).
[CrossRef]

Roskos, H. G.

For example, seeA. Lisauskas, M. M. Dignam, N. V. Demarina, E. Mohler, and H. G. Roskos, “Examining the terahertz signal from a photoexcited biased semiconductor superlattice for evidence of gain,” Appl. Phys. Lett. 93(2), 021122 (2008).
[CrossRef]

Schins, J. M.

E. Hendry, M. Koeberg, J. M. Schins, L. D. A. Siebbeles, and M. Bonn, “Ultrafast charge generation in a semiconducting polymer studied with THz emission spectroscopy,” Phys. Rev. B 70(3), 033202 (2004).
[CrossRef]

Schmuttenmaer, C. A.

E. Beaurepaire, G. M. Turner, S. M. Harrel, M. C. Beard, J.-Y. Bigot, and C. A. Schmuttenmaer, “Coherent terahertz emission from ferromagnetic films excited by femtosecond laser pulses,” Appl. Phys. Lett. 84(18), 3465 (2004).
[CrossRef]

Sekine, N.

T. Unuma, N. Sekine, and K. Hirakawa, “Dephasing of Bloch oscillating electrons in GaAs-based superlattices due to interface roughness scattering,” Appl. Phys. Lett. 89(16), 161913 (2006).
[CrossRef]

N. Sekine and K. Hirakawa, “Dispersive terahertz gain of a nonclassical oscillator: Bloch oscillation in semiconductor superlattices,” Phys. Rev. Lett. 94(5), 057408 (2005).
[CrossRef] [PubMed]

Shah, J.

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82 (25), 5140 (1999); “Femtosecond high-field transport in compound semiconductors,” Phys. Rev. B 61(24), 16642–16652 (2000).

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Detectors and sources for ultrabroadband electro-optic sampling: Experiment and theory,” Appl. Phys. Lett. 74(11), 1516 (1999).
[CrossRef]

Shimada, Y.

Y. Shimada, K. Hirakawa, M. Odnoblioudov, and K. A. Chao, “Terahertz conductivity and possible Bloch gain in semiconductor superlattices,” Phys. Rev. Lett. 90(4), 046806 (2003).
[CrossRef] [PubMed]

M. Abe, S. Madhavi, Y. Shimada, Y. Otsuka, K. Hirakawa, and K. Tomizawa, “Transient carrier velocities in bulk GaAs: Quantitative comparison between terahertz data and ensemble Monte Carlo calculations,” Appl. Phys. Lett. 81(4), 679 (2002).
[CrossRef]

Shimano, R.

E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, “Numerical phase correction method for terahertz time-domain reflection spectroscopy,” J. Appl. Phys. 96(8), 4171 (2004).
[CrossRef]

Siebbeles, L. D. A.

E. Hendry, M. Koeberg, J. M. Schins, L. D. A. Siebbeles, and M. Bonn, “Ultrafast charge generation in a semiconducting polymer studied with THz emission spectroscopy,” Phys. Rev. B 70(3), 033202 (2004).
[CrossRef]

Svirko, Y. P.

E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, “Numerical phase correction method for terahertz time-domain reflection spectroscopy,” J. Appl. Phys. 96(8), 4171 (2004).
[CrossRef]

Tomizawa, K.

M. Abe, S. Madhavi, Y. Shimada, Y. Otsuka, K. Hirakawa, and K. Tomizawa, “Transient carrier velocities in bulk GaAs: Quantitative comparison between terahertz data and ensemble Monte Carlo calculations,” Appl. Phys. Lett. 81(4), 679 (2002).
[CrossRef]

Turner, G. M.

E. Beaurepaire, G. M. Turner, S. M. Harrel, M. C. Beard, J.-Y. Bigot, and C. A. Schmuttenmaer, “Coherent terahertz emission from ferromagnetic films excited by femtosecond laser pulses,” Appl. Phys. Lett. 84(18), 3465 (2004).
[CrossRef]

Unuma, T.

T. Unuma, Y. Ino, M. Kuwata-Gonokami, G. Bastard, and K. Hirakawa, “Transient Bloch oscillation with the symmetry-governed phase in semiconductor superlattices,” Phys. Rev. B 81(12), 125329 (2010).
[CrossRef]

T. Unuma, N. Sekine, and K. Hirakawa, “Dephasing of Bloch oscillating electrons in GaAs-based superlattices due to interface roughness scattering,” Appl. Phys. Lett. 89(16), 161913 (2006).
[CrossRef]

Vartiainen, E. M.

E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, “Numerical phase correction method for terahertz time-domain reflection spectroscopy,” J. Appl. Phys. 96(8), 4171 (2004).
[CrossRef]

E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, “Phase retrieval in optical spectroscopy: Resolving optical constants from power spectra,” Appl. Spec. 50(10), 1283 (1996).
[CrossRef]

Wu, Q.

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68(21), 2924 (1996).
[CrossRef]

Zhang, X.-C.

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68(21), 2924 (1996).
[CrossRef]

Appl. Phys. Lett. (7)

Q. Wu, M. Litz, and X.-C. Zhang, “Broadband detection capability of ZnTe electro-optic field detectors,” Appl. Phys. Lett. 68(21), 2924 (1996).
[CrossRef]

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Detectors and sources for ultrabroadband electro-optic sampling: Experiment and theory,” Appl. Phys. Lett. 74(11), 1516 (1999).
[CrossRef]

M. Abe, S. Madhavi, Y. Shimada, Y. Otsuka, K. Hirakawa, and K. Tomizawa, “Transient carrier velocities in bulk GaAs: Quantitative comparison between terahertz data and ensemble Monte Carlo calculations,” Appl. Phys. Lett. 81(4), 679 (2002).
[CrossRef]

E. Beaurepaire, G. M. Turner, S. M. Harrel, M. C. Beard, J.-Y. Bigot, and C. A. Schmuttenmaer, “Coherent terahertz emission from ferromagnetic films excited by femtosecond laser pulses,” Appl. Phys. Lett. 84(18), 3465 (2004).
[CrossRef]

Y. Ino, B. Héroux, T. Mukaiyama, and M. Kuwata-Gonokami, “Reflection-type pulsed terahertz imaging with a phase retrieval algorithm,” Appl. Phys. Lett. 88(4), 041114 (2006).
[CrossRef]

T. Unuma, N. Sekine, and K. Hirakawa, “Dephasing of Bloch oscillating electrons in GaAs-based superlattices due to interface roughness scattering,” Appl. Phys. Lett. 89(16), 161913 (2006).
[CrossRef]

For example, seeA. Lisauskas, M. M. Dignam, N. V. Demarina, E. Mohler, and H. G. Roskos, “Examining the terahertz signal from a photoexcited biased semiconductor superlattice for evidence of gain,” Appl. Phys. Lett. 93(2), 021122 (2008).
[CrossRef]

Appl. Spec. (1)

E. M. Vartiainen, K.-E. Peiponen, and T. Asakura, “Phase retrieval in optical spectroscopy: Resolving optical constants from power spectra,” Appl. Spec. 50(10), 1283 (1996).
[CrossRef]

J. Appl. Phys. (1)

E. M. Vartiainen, Y. Ino, R. Shimano, M. Kuwata-Gonokami, Y. P. Svirko, and K.-E. Peiponen, “Numerical phase correction method for terahertz time-domain reflection spectroscopy,” J. Appl. Phys. 96(8), 4171 (2004).
[CrossRef]

Phys. Rev. B (2)

T. Unuma, Y. Ino, M. Kuwata-Gonokami, G. Bastard, and K. Hirakawa, “Transient Bloch oscillation with the symmetry-governed phase in semiconductor superlattices,” Phys. Rev. B 81(12), 125329 (2010).
[CrossRef]

E. Hendry, M. Koeberg, J. M. Schins, L. D. A. Siebbeles, and M. Bonn, “Ultrafast charge generation in a semiconducting polymer studied with THz emission spectroscopy,” Phys. Rev. B 70(3), 033202 (2004).
[CrossRef]

Phys. Rev. Lett. (2)

N. Sekine and K. Hirakawa, “Dispersive terahertz gain of a nonclassical oscillator: Bloch oscillation in semiconductor superlattices,” Phys. Rev. Lett. 94(5), 057408 (2005).
[CrossRef] [PubMed]

Y. Shimada, K. Hirakawa, M. Odnoblioudov, and K. A. Chao, “Terahertz conductivity and possible Bloch gain in semiconductor superlattices,” Phys. Rev. Lett. 90(4), 046806 (2003).
[CrossRef] [PubMed]

Phys. Rev. Lett. 82 (1)

A. Leitenstorfer, S. Hunsche, J. Shah, M. C. Nuss, and W. H. Knox, “Femtosecond charge transport in polar semiconductors,” Phys. Rev. Lett. 82 (25), 5140 (1999); “Femtosecond high-field transport in compound semiconductors,” Phys. Rev. B 61(24), 16642–16652 (2000).

Other (4)

S. Haykin, Nonlinear Methods of Spectral Analysis (Springer, Berlin, 1983), Chap. 2.

K.-E. Peiponen, E. M. Vartiainen, and T. Asakura, Dispersion, Complex Analysis and Optical Spectroscopy (Springer, Heidelberg, 1999), Chap. 5.

V. Lucarini, J. J. Saarinen, K.-E. Peiponen, and E. M. Vartiainen, Kramers-Kronig Relations in Optical Materials Research (Springer, Berlin, 2005), Chap. 10.

We chose these frequency ranges by considering a tradeoff: the resonance feature is more accurately captured in wider frequency ranges, while the numerical error in solving the Toeplitz matrix equation becomes less in narrower frequency ranges.

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Figures (3)

Fig. 1
Fig. 1

MEM analysis of a trial THz waveform simulated for a damped sine current J(t) = J 0Θ(t)exp(−γt)sinω 0 t. (a) THz waveform E THz(t) simulated with ω 0/2π = 1.5 THz, γ = 1.1 THz, and a temporal resolution of τ res = 300 fs. (b) Spectra of amplitude | THz(ω)| (solid curve) and phase arg THz(ω) (dash-dotted curve). (c) MEM phase spectra ψM (ω) computed in three different frequency ranges. (d) Error phase spectra φ err(ω) (solid curves). Dashed lines are the linear fits to φ err(ω).

Fig. 2
Fig. 2

MEM analysis of a trial THz waveform simulated for a damped cosine current J(t) = J 0Θ(t)exp(−γt)cosω 0 t. (a) THz waveform E THz(t) simulated with ω 0/2π = 1.5 THz, γ = 1.1 THz, and a temporal resolution of τ res = 300 fs. (b) Spectra of amplitude | THz(ω)| (solid curve) and phase arg THz(ω) (dash-dotted curve). (c) MEM phase spectra ψM (ω) computed in three different frequency ranges. (d) Error phase spectra φ err(ω) (solid curves). Dashed lines are the linear fits to φ err(ω).

Fig. 3
Fig. 3

MEM analysis of a THz waveform recorded experimentally for the Bloch oscillation in a GaAs/AlAs superlattice at 10 K. (a) THz waveform E THz(t) recorded with a tentative time origin (t = 0). (b) Spectra of amplitude | THz(ω)| (solid curve) and phase arg THz(ω) (dash-dotted curve). (c) MEM phase spectra ψM (ω) computed in three different frequency ranges. (d) Error phase spectra φ err(ω) (solid curves). Dashed lines are the linear fits to φ err(ω), the slopes of which show that the time origin should be shifted to the position indicated by a red vertical line in (a).

Equations (5)

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E ˜ THz ( ω ) = E THz ( t ) exp ( i ω t ) d t ,
| E ˜ T H z ( ω ) | 2 = b | 1 + m = 1 M a m exp ( i ω m Δ t ) | 2 .
E ˜ T H z ( ω ) = b exp [ i φ e r r ( ω ) ] 1 + m = 1 M a m exp ( i ω m Δ t )
arg E ˜ T H z ( ω ) = ψ M ( ω ) + φ e r r ( ω )
ψ M ( ω ) = arg [ 1 + m = 1 M a m exp ( i ω m Δ t ) ] .

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