Abstract

We report on the generation and detection of few-cycle THz pulses in the organic crystal DAST (4-N,N-dimethylamino-4’-N’-methyl stilbazolium tosylate) using the telecommunication wavelength 1.5 µm. A continuous spectrum from 1.3 to 4.8 THz was generated with a very high conversion efficiency (ETHz,max ~50 kV/cm at an optical pump pulse energy of 25 µJ in a 0.6 mm thick crystal) using the high nonlinear optical susceptibility of DAST (χ (2) 111=490 pm/V at λ=1535 nm) and velocity-matching observed in this material. Using a frequency-doubled probe beam at λ=750 nm, nearly velocity-matched detection can also be realized in ZnTe crystals, resulting in a continuous spectrum from 1.3 to 4 THz.

© 2006 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, "Electrooptic properties of the organic salt 4-N,N-dimethylamino-4’-N’-methyl-stilbazolium tosylate," Appl. Phys. Lett. 96,13-15 (1996)
    [CrossRef]
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    [CrossRef]
  12. Q. Wu, T. D. Hewitt, and X.-C. Zhang, "Two-dimensional electro-optic imaging of THz beams," Appl. Phys. Lett. 69,1026-1028 (1996)
    [CrossRef]
  13. J. Shan, A. S. Weling, E. Knoesel, L. Bartels, M. Bonn, A. Nahata, G. A. Reider, and T. F. Heinz, "Single-shot measurement of terahertz electromagnetic pulses by use of electro-optic sampling," Opt. Lett. 25,426-428 (2000)
    [CrossRef]
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    [CrossRef]
  15. A. Schneider, M. Neis, M. Stillhart, B. Ruiz, R. Khan, and P. Günter, "Generation of terahertz pulses through optical rectification in organic DAST crystals: Theory and experiment," J. Opt. Soc. Am. B, doc. ID 67685 (posted 24 April 2006, in press)
    [CrossRef]
  16. G. Gallot, J. Zhang, R. W. McGowan, T.-I. Jeon, and D. Grischkowsky, "Measurements of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of THz radiation," Appl. Phys. Lett. 74,3450-3452 (1999)
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    [CrossRef]
  21. T. Taniuchi, S. Okada, and H. Nakanishi,"Widely tunable terahertz-wave generation in an organic crystal and its spectroscopic application," J. Appl. Phys. 95,5984-5988 (2004)
    [CrossRef]

2006

A. Schneider, M. Neis, M. Stillhart, B. Ruiz, R. Khan, and P. Günter, "Generation of terahertz pulses through optical rectification in organic DAST crystals: Theory and experiment," J. Opt. Soc. Am. B, doc. ID 67685 (posted 24 April 2006, in press)
[CrossRef]

2004

M. Nagai, K. Tanaka, H. Ohtake, T. Bessho, T. Sugiura, T. Hirosumi, andM. Yoshida,"Generation and detection of terahertz radiation by electro-optical process in GaAs using 1.56 μm fiber laser pulses," Appl. Phys. Lett. 85,3974-3976 (2004).
[CrossRef]

A. Schneider, I. Biaggio, and P. Günter, "Terahertz-induced lensing and its use for the detection of terahertz pulses in a birefringent crystal," Appl. Phys. Lett. 84,2229-2231 (2004)
[CrossRef]

T. Taniuchi, S. Okada, and H. Nakanishi,"Widely tunable terahertz-wave generation in an organic crystal and its spectroscopic application," J. Appl. Phys. 95,5984-5988 (2004)
[CrossRef]

2003

L. M. Hayden, A.M. Sinyukov, M. R. Leahy, J. French, P. Lindahl, W. N. Herman, R. J. Twieg, and M. He, "New Materials for Optical Rectification and Electrooptic Sampling of Ultrashort Pulses in the Terahertz Regime," J. Polym. Sci. Part B Polym.Phys. 41,2492-2500 (2003)
[CrossRef]

A. Schneider, I. Biaggio, and P. Günter, "Optimized generation of THz pulses via optical rectification in the organic salt DAST," Opt. Commun. 224,337-341 (2003)
[CrossRef]

2002

B. Ferguson and X.-C. Zhang, "Materials for terahertz science and technology," Nature Materials 1,26-33 (2002)
[CrossRef]

2001

M. Schall, M. Walther, and P. Uhd Jepsen, "Fundamental and second-order phonon processes in CdTe and ZnTe," Phys. Rev. B 64,094301 (2001)
[CrossRef]

2000

1999

G. Gallot, J. Zhang, R. W. McGowan, T.-I. Jeon, and D. Grischkowsky, "Measurements of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of THz radiation," Appl. Phys. Lett. 74,3450-3452 (1999)
[CrossRef]

1998

1996

Q. Wu, T. D. Hewitt, and X.-C. Zhang, "Two-dimensional electro-optic imaging of THz beams," Appl. Phys. Lett. 69,1026-1028 (1996)
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69,2321-2323 (1996)
[CrossRef]

Q. Wu and X.-C. Zhang, "Design and Characterization of Traveling-Wave Electrooptic Terahertz Sensors," IEEE J. Sel. Top. Quantum Electron. 2,693-700 (1996).
[CrossRef]

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, "Electrooptic properties of the organic salt 4-N,N-dimethylamino-4’-N’-methyl-stilbazolium tosylate," Appl. Phys. Lett. 96,13-15 (1996)
[CrossRef]

1995

Q. Wu and X.-C. Zhang, "Free-space electro-optic sampling of terahertz beams," Appl. Phys. Lett. 67,3523-3525 (1995)
[CrossRef]

1993

K. Sato and S. Adachi, "Optical properties of ZnTe," J. Appl. Phys. 73,926-931 (1993)
[CrossRef]

1966

Adachi, S.

K. Sato and S. Adachi, "Optical properties of ZnTe," J. Appl. Phys. 73,926-931 (1993)
[CrossRef]

Bakker, H. J.

Bartels, L.

Bessho, T.

M. Nagai, K. Tanaka, H. Ohtake, T. Bessho, T. Sugiura, T. Hirosumi, andM. Yoshida,"Generation and detection of terahertz radiation by electro-optical process in GaAs using 1.56 μm fiber laser pulses," Appl. Phys. Lett. 85,3974-3976 (2004).
[CrossRef]

Biaggio, I.

A. Schneider, I. Biaggio, and P. Günter, "Terahertz-induced lensing and its use for the detection of terahertz pulses in a birefringent crystal," Appl. Phys. Lett. 84,2229-2231 (2004)
[CrossRef]

A. Schneider, I. Biaggio, and P. Günter, "Optimized generation of THz pulses via optical rectification in the organic salt DAST," Opt. Commun. 224,337-341 (2003)
[CrossRef]

Bonn, M.

Bosshard, Ch.

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, "Electrooptic properties of the organic salt 4-N,N-dimethylamino-4’-N’-methyl-stilbazolium tosylate," Appl. Phys. Lett. 96,13-15 (1996)
[CrossRef]

Cho, G. C.

Ferguson, B.

B. Ferguson and X.-C. Zhang, "Materials for terahertz science and technology," Nature Materials 1,26-33 (2002)
[CrossRef]

Follonier, S.

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, "Electrooptic properties of the organic salt 4-N,N-dimethylamino-4’-N’-methyl-stilbazolium tosylate," Appl. Phys. Lett. 96,13-15 (1996)
[CrossRef]

French, J.

L. M. Hayden, A.M. Sinyukov, M. R. Leahy, J. French, P. Lindahl, W. N. Herman, R. J. Twieg, and M. He, "New Materials for Optical Rectification and Electrooptic Sampling of Ultrashort Pulses in the Terahertz Regime," J. Polym. Sci. Part B Polym.Phys. 41,2492-2500 (2003)
[CrossRef]

Gallot, G.

G. Gallot, J. Zhang, R. W. McGowan, T.-I. Jeon, and D. Grischkowsky, "Measurements of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of THz radiation," Appl. Phys. Lett. 74,3450-3452 (1999)
[CrossRef]

Grischkowsky, D.

G. Gallot, J. Zhang, R. W. McGowan, T.-I. Jeon, and D. Grischkowsky, "Measurements of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of THz radiation," Appl. Phys. Lett. 74,3450-3452 (1999)
[CrossRef]

Günter, P.

A. Schneider, M. Neis, M. Stillhart, B. Ruiz, R. Khan, and P. Günter, "Generation of terahertz pulses through optical rectification in organic DAST crystals: Theory and experiment," J. Opt. Soc. Am. B, doc. ID 67685 (posted 24 April 2006, in press)
[CrossRef]

A. Schneider, I. Biaggio, and P. Günter, "Terahertz-induced lensing and its use for the detection of terahertz pulses in a birefringent crystal," Appl. Phys. Lett. 84,2229-2231 (2004)
[CrossRef]

A. Schneider, I. Biaggio, and P. Günter, "Optimized generation of THz pulses via optical rectification in the organic salt DAST," Opt. Commun. 224,337-341 (2003)
[CrossRef]

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, "Electrooptic properties of the organic salt 4-N,N-dimethylamino-4’-N’-methyl-stilbazolium tosylate," Appl. Phys. Lett. 96,13-15 (1996)
[CrossRef]

Han, P. Y.

Hayden, L. M.

L. M. Hayden, A.M. Sinyukov, M. R. Leahy, J. French, P. Lindahl, W. N. Herman, R. J. Twieg, and M. He, "New Materials for Optical Rectification and Electrooptic Sampling of Ultrashort Pulses in the Terahertz Regime," J. Polym. Sci. Part B Polym.Phys. 41,2492-2500 (2003)
[CrossRef]

He, M.

L. M. Hayden, A.M. Sinyukov, M. R. Leahy, J. French, P. Lindahl, W. N. Herman, R. J. Twieg, and M. He, "New Materials for Optical Rectification and Electrooptic Sampling of Ultrashort Pulses in the Terahertz Regime," J. Polym. Sci. Part B Polym.Phys. 41,2492-2500 (2003)
[CrossRef]

Heinz, T. F.

J. Shan, A. S. Weling, E. Knoesel, L. Bartels, M. Bonn, A. Nahata, G. A. Reider, and T. F. Heinz, "Single-shot measurement of terahertz electromagnetic pulses by use of electro-optic sampling," Opt. Lett. 25,426-428 (2000)
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69,2321-2323 (1996)
[CrossRef]

Herman, W. N.

L. M. Hayden, A.M. Sinyukov, M. R. Leahy, J. French, P. Lindahl, W. N. Herman, R. J. Twieg, and M. He, "New Materials for Optical Rectification and Electrooptic Sampling of Ultrashort Pulses in the Terahertz Regime," J. Polym. Sci. Part B Polym.Phys. 41,2492-2500 (2003)
[CrossRef]

Hewitt, T. D.

Q. Wu, T. D. Hewitt, and X.-C. Zhang, "Two-dimensional electro-optic imaging of THz beams," Appl. Phys. Lett. 69,1026-1028 (1996)
[CrossRef]

Hirosumi, T.

M. Nagai, K. Tanaka, H. Ohtake, T. Bessho, T. Sugiura, T. Hirosumi, andM. Yoshida,"Generation and detection of terahertz radiation by electro-optical process in GaAs using 1.56 μm fiber laser pulses," Appl. Phys. Lett. 85,3974-3976 (2004).
[CrossRef]

Ito, H.

Jensby, K.

Jeon, T.-I.

G. Gallot, J. Zhang, R. W. McGowan, T.-I. Jeon, and D. Grischkowsky, "Measurements of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of THz radiation," Appl. Phys. Lett. 74,3450-3452 (1999)
[CrossRef]

Jost, J. M.

Keiding, S. R.

Khan, R.

A. Schneider, M. Neis, M. Stillhart, B. Ruiz, R. Khan, and P. Günter, "Generation of terahertz pulses through optical rectification in organic DAST crystals: Theory and experiment," J. Opt. Soc. Am. B, doc. ID 67685 (posted 24 April 2006, in press)
[CrossRef]

Knoesel, E.

Knöpfle, G.

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, "Electrooptic properties of the organic salt 4-N,N-dimethylamino-4’-N’-methyl-stilbazolium tosylate," Appl. Phys. Lett. 96,13-15 (1996)
[CrossRef]

Kurz, H.

Leahy, M. R.

L. M. Hayden, A.M. Sinyukov, M. R. Leahy, J. French, P. Lindahl, W. N. Herman, R. J. Twieg, and M. He, "New Materials for Optical Rectification and Electrooptic Sampling of Ultrashort Pulses in the Terahertz Regime," J. Polym. Sci. Part B Polym.Phys. 41,2492-2500 (2003)
[CrossRef]

Lindahl, P.

L. M. Hayden, A.M. Sinyukov, M. R. Leahy, J. French, P. Lindahl, W. N. Herman, R. J. Twieg, and M. He, "New Materials for Optical Rectification and Electrooptic Sampling of Ultrashort Pulses in the Terahertz Regime," J. Polym. Sci. Part B Polym.Phys. 41,2492-2500 (2003)
[CrossRef]

McGowan, R. W.

G. Gallot, J. Zhang, R. W. McGowan, T.-I. Jeon, and D. Grischkowsky, "Measurements of the THz absorption and dispersion of ZnTe and their relevance to the electro-optic detection of THz radiation," Appl. Phys. Lett. 74,3450-3452 (1999)
[CrossRef]

Nagai, M.

M. Nagai, K. Tanaka, H. Ohtake, T. Bessho, T. Sugiura, T. Hirosumi, andM. Yoshida,"Generation and detection of terahertz radiation by electro-optical process in GaAs using 1.56 μm fiber laser pulses," Appl. Phys. Lett. 85,3974-3976 (2004).
[CrossRef]

Nahata, A.

J. Shan, A. S. Weling, E. Knoesel, L. Bartels, M. Bonn, A. Nahata, G. A. Reider, and T. F. Heinz, "Single-shot measurement of terahertz electromagnetic pulses by use of electro-optic sampling," Opt. Lett. 25,426-428 (2000)
[CrossRef]

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69,2321-2323 (1996)
[CrossRef]

Nakanishi, H.

T. Taniuchi, S. Okada, and H. Nakanishi,"Widely tunable terahertz-wave generation in an organic crystal and its spectroscopic application," J. Appl. Phys. 95,5984-5988 (2004)
[CrossRef]

Neis, M.

A. Schneider, M. Neis, M. Stillhart, B. Ruiz, R. Khan, and P. Günter, "Generation of terahertz pulses through optical rectification in organic DAST crystals: Theory and experiment," J. Opt. Soc. Am. B, doc. ID 67685 (posted 24 April 2006, in press)
[CrossRef]

Ohtake, H.

M. Nagai, K. Tanaka, H. Ohtake, T. Bessho, T. Sugiura, T. Hirosumi, andM. Yoshida,"Generation and detection of terahertz radiation by electro-optical process in GaAs using 1.56 μm fiber laser pulses," Appl. Phys. Lett. 85,3974-3976 (2004).
[CrossRef]

Okada, S.

T. Taniuchi, S. Okada, and H. Nakanishi,"Widely tunable terahertz-wave generation in an organic crystal and its spectroscopic application," J. Appl. Phys. 95,5984-5988 (2004)
[CrossRef]

Pan, F.

P. Y. Han, M. Tani, F. Pan, and X.-C. Zhang, "Use of the organic crystal DAST for terahertz beam applications," Opt. Lett. 25,675-677 (2000)
[CrossRef]

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, "Electrooptic properties of the organic salt 4-N,N-dimethylamino-4’-N’-methyl-stilbazolium tosylate," Appl. Phys. Lett. 96,13-15 (1996)
[CrossRef]

Reider, G. A.

Ruiz, B.

A. Schneider, M. Neis, M. Stillhart, B. Ruiz, R. Khan, and P. Günter, "Generation of terahertz pulses through optical rectification in organic DAST crystals: Theory and experiment," J. Opt. Soc. Am. B, doc. ID 67685 (posted 24 April 2006, in press)
[CrossRef]

Sato, K.

K. Sato and S. Adachi, "Optical properties of ZnTe," J. Appl. Phys. 73,926-931 (1993)
[CrossRef]

Schall, M.

M. Schall, M. Walther, and P. Uhd Jepsen, "Fundamental and second-order phonon processes in CdTe and ZnTe," Phys. Rev. B 64,094301 (2001)
[CrossRef]

Schneider, A.

A. Schneider, M. Neis, M. Stillhart, B. Ruiz, R. Khan, and P. Günter, "Generation of terahertz pulses through optical rectification in organic DAST crystals: Theory and experiment," J. Opt. Soc. Am. B, doc. ID 67685 (posted 24 April 2006, in press)
[CrossRef]

A. Schneider, I. Biaggio, and P. Günter, "Terahertz-induced lensing and its use for the detection of terahertz pulses in a birefringent crystal," Appl. Phys. Lett. 84,2229-2231 (2004)
[CrossRef]

A. Schneider, I. Biaggio, and P. Günter, "Optimized generation of THz pulses via optical rectification in the organic salt DAST," Opt. Commun. 224,337-341 (2003)
[CrossRef]

Shan, J.

Sinyukov, A.M.

L. M. Hayden, A.M. Sinyukov, M. R. Leahy, J. French, P. Lindahl, W. N. Herman, R. J. Twieg, and M. He, "New Materials for Optical Rectification and Electrooptic Sampling of Ultrashort Pulses in the Terahertz Regime," J. Polym. Sci. Part B Polym.Phys. 41,2492-2500 (2003)
[CrossRef]

Sliker, T. R.

Spreiter, R.

F. Pan, G. Knöpfle, Ch. Bosshard, S. Follonier, R. Spreiter, M. S. Wong, and P. Günter, "Electrooptic properties of the organic salt 4-N,N-dimethylamino-4’-N’-methyl-stilbazolium tosylate," Appl. Phys. Lett. 96,13-15 (1996)
[CrossRef]

Stillhart, M.

A. Schneider, M. Neis, M. Stillhart, B. Ruiz, R. Khan, and P. Günter, "Generation of terahertz pulses through optical rectification in organic DAST crystals: Theory and experiment," J. Opt. Soc. Am. B, doc. ID 67685 (posted 24 April 2006, in press)
[CrossRef]

Sugiura, T.

M. Nagai, K. Tanaka, H. Ohtake, T. Bessho, T. Sugiura, T. Hirosumi, andM. Yoshida,"Generation and detection of terahertz radiation by electro-optical process in GaAs using 1.56 μm fiber laser pulses," Appl. Phys. Lett. 85,3974-3976 (2004).
[CrossRef]

Takahashi, H.

Tanaka, K.

M. Nagai, K. Tanaka, H. Ohtake, T. Bessho, T. Sugiura, T. Hirosumi, andM. Yoshida,"Generation and detection of terahertz radiation by electro-optical process in GaAs using 1.56 μm fiber laser pulses," Appl. Phys. Lett. 85,3974-3976 (2004).
[CrossRef]

Tani, M.

Taniuchi, T.

T. Taniuchi, S. Okada, and H. Nakanishi,"Widely tunable terahertz-wave generation in an organic crystal and its spectroscopic application," J. Appl. Phys. 95,5984-5988 (2004)
[CrossRef]

Twieg, R. J.

L. M. Hayden, A.M. Sinyukov, M. R. Leahy, J. French, P. Lindahl, W. N. Herman, R. J. Twieg, and M. He, "New Materials for Optical Rectification and Electrooptic Sampling of Ultrashort Pulses in the Terahertz Regime," J. Polym. Sci. Part B Polym.Phys. 41,2492-2500 (2003)
[CrossRef]

Uhd Jepsen, P.

M. Schall, M. Walther, and P. Uhd Jepsen, "Fundamental and second-order phonon processes in CdTe and ZnTe," Phys. Rev. B 64,094301 (2001)
[CrossRef]

Walther, M.

M. Schall, M. Walther, and P. Uhd Jepsen, "Fundamental and second-order phonon processes in CdTe and ZnTe," Phys. Rev. B 64,094301 (2001)
[CrossRef]

M. Walther, K. Jensby, S. R. Keiding, H. Takahashi, and H. Ito,"Far-infrared properties of DAST," Opt. Lett. 25,911-913 (2000)
[CrossRef]

Weling, A. S.

J. Shan, A. S. Weling, E. Knoesel, L. Bartels, M. Bonn, A. Nahata, G. A. Reider, and T. F. Heinz, "Single-shot measurement of terahertz electromagnetic pulses by use of electro-optic sampling," Opt. Lett. 25,426-428 (2000)
[CrossRef]

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Appl. Phys. Lett.

A. Nahata, A. S. Weling, and T. F. Heinz, "A wideband coherent terahertz spectroscopy system using optical rectification and electro-optic sampling," Appl. Phys. Lett. 69,2321-2323 (1996)
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M. Nagai, K. Tanaka, H. Ohtake, T. Bessho, T. Sugiura, T. Hirosumi, andM. Yoshida,"Generation and detection of terahertz radiation by electro-optical process in GaAs using 1.56 μm fiber laser pulses," Appl. Phys. Lett. 85,3974-3976 (2004).
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Figures (6)

Fig. 1.
Fig. 1.

Contour plot of the coherence length lc for THz generation and/or detection in DAST. The numbers indicate the value of the contour in millimeters.

Fig. 2.
Fig. 2.

Contour plot of the coherence length lc for THz generation and/or detection in ZnTe. The numbers indicate the value of the contour in millimeters.

Fig. 3.
Fig. 3.

Color plot of the coherence length lc for THz generation and detection; a darker shade corresponds to a lower lc . Red: DAST at fundamental wavelength (lower x-scale), no coloring for lc >1.5 mm. Green: ZnTe at SHG wavelength (upper x-scale), no coloring for lc >0.75 mm.

Fig. 4.
Fig. 4.

Experimental setup using a pump beam at ω and a frequency-doubled probe beam at 2ω. EM: Ellipsoidal mirror; PBS: Polarizing Beam Splitter.

Fig. 5.
Fig. 5.

THz pulse generated through optical rectification in a 0.60 mm thick DAST crystal and detected using THz-induced lensing [20] in a 0.69 mm thick DAST crystal, at an optical wavelength of 1.50 µm. Left panel: Signal in time-domain. The indicated modulation is in first order proportional to the THz electric field, limited by nonlinear effects (see text for details). Right panel: Fourier transform of the same THz pulse. Absorption by the residual ambient water vapor leads in time-domain to the oscillation that persists for t>1 ps, in frequency-domain to the numerous dips; thus the effectively emitted THz spectrum is given by the envelope.

Fig. 6.
Fig. 6.

THz pulse generated through optical rectification of 1.5 µm pulses in a 0.60 mm thick DAST crystal and detected by electro-optic sampling in a 0.5 mm thick ZnTe crystal using a frequency-doubled probe beam (λ=0.75µm). Left panel: Time-domain. Right panel: Frequency-domain. The effect of water vapor absorption is the same as in Fig. 5.

Equations (3)

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f ( l , ν , λ ) = l sin c [ π 2 l l c ( ν , λ ) ]
l c ( ν , λ ) = c 2 ν n g ( λ ) n ( ν )
n g ( λ ) = n ( λ ) λ n λ λ

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