Abstract

We present a combined theoretical and experimental investigation of the detection of pulsed terahertz waves via field-induced second-harmonic generation in gaseous media. The effects of the probe pulse energy, bias field strength, nonlinear susceptibility of the gases, phase matching, and focusing conditions of the terahertz and optical beams are discussed. The analytical calculation, which is based on a Gaussian-beam approximation, allows for the easy identification of the parameters important for the sensitivity of the terahertz gas sensor. A figure of merit is introduced to characterize the sensitivity of gases. The experimental results are found to be in good agreement with the calculation.

© 2009 Optical Society of America

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  1. H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725-2728 (1993).
    [CrossRef] [PubMed]
  2. D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. 25, 1210-1212 (2000).
    [CrossRef]
  3. M. Kress, T. Löffler, S. Eden, M. Thomson, and H. G. Rokos, “Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves,” Opt. Lett. 29, 1120-1122 (2004).
    [CrossRef] [PubMed]
  4. X. Xie, J. Dai, and X.-C. Zhang, “Coherent control of THz wave generation in ambient air,” Phys. Rev. Lett. 96, 075005 (2006).
    [CrossRef] [PubMed]
  5. T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, “Generation of single-cycle THz transients with high electric-field amplitudes,” Opt. Lett. 30, 2805-2807 (2005).
    [CrossRef] [PubMed]
  6. A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of THz radiation from laser filament in air by a static electric field,” Phys. Rev. Lett. 100, 255006 (2008).
    [CrossRef] [PubMed]
  7. K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2, 605-609 (2008).
    [CrossRef]
  8. N. Karpowicz and X.-C. Zhang, “Coherent terahertz echo of tunnel ionization in gases,” Phys. Rev. Lett. 102, 093001 (2009).
    [CrossRef] [PubMed]
  9. K. Kampfrath, J. Nötzold, and M. Wolf, “Sampling of broadband terahertz pulses with thick electro-optic crystals,” Appl. Phys. Lett. 90, 231113 (2007).
    [CrossRef]
  10. S. Kono, M. Tani, P. Gu, and K. Sakai, “Detection of up to 20 THz with a low-temperature grown GaAs photoconductive antenna gated with 15 fs light pulses,” Appl. Phys. Lett. 77, 4104-4106 (2000).
    [CrossRef]
  11. J. Dai, X. Xie, and X.-C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97, 103903 (2006).
    [CrossRef] [PubMed]
  12. N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
    [CrossRef]
  13. X. Lu, N. Karpowicz, Y. Chen, and X.-C. Zhang, “Systematic study of broadband terahertz gas sensor,” Appl. Phys. Lett. 93, 261106 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. R. S. Finn and J. F. Ward, “DC-induced optical second-harmonic generation in the inert gases,” Phys. Rev. Lett. 26, 285-289 (1971).
    [CrossRef]
  17. Q. Wu and X.-C. Zhang, “Free-space electro-optic sampling of terahertz beams,” Appl. Phys. Lett. 67, 3523-3525(1995).
    [CrossRef]
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  19. A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B: Lasers Opt. 73, 287-290 (2001).
    [CrossRef]
  20. D. P. Shelton, “Nonlinear-optical susceptibilities of gases measured at 1063 and 1319 nm,” Phys. Rev. A 42, 2578-2592 (1990).
    [CrossRef] [PubMed]
  21. R. W. Boyd, Nonlinear Optics (Academic, 1992).
  22. J. P. Hermann and J. Ducuing, “Third-order polarizabilities of long-chain molecules,” J. Appl. Phys. 45, 5100-5102 (1974).
    [CrossRef]
  23. K. C. Rustagi and J. Ducuing, “Third-order optical polarizability of conjugated organic molecules,” Opt. Commun. 10, 258-261 (1974).
    [CrossRef]
  24. D. A. Kleinman, A. Ashkin, and G. D. Boyd, “Second-harmonic generation of light by focused laser beams,” Phys. Rev. 145, 338-379 (1966).
    [CrossRef]
  25. J. A. Armstong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918-1939 (1962).
    [CrossRef]
  26. J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57-72 (1969).
    [CrossRef]
  27. L. G. Gouy, “Sur une propréité nouvelle des ondes lumineuses,” C. R. Hebd. Seances Acad. Sci. 110, 1251-1253 (1890).
  28. L. G. Gouy,“Sur la propagation anomale des ondes,” Ann. Chim. Phys. 24, 145-213 (1891).
  29. S. A. Korff and G. Breit, “Optical dispersion,” Rev. Mod. Phys. 4, 471-503 (1932).
    [CrossRef]

2009 (1)

N. Karpowicz and X.-C. Zhang, “Coherent terahertz echo of tunnel ionization in gases,” Phys. Rev. Lett. 102, 093001 (2009).
[CrossRef] [PubMed]

2008 (4)

A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of THz radiation from laser filament in air by a static electric field,” Phys. Rev. Lett. 100, 255006 (2008).
[CrossRef] [PubMed]

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2, 605-609 (2008).
[CrossRef]

N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

X. Lu, N. Karpowicz, Y. Chen, and X.-C. Zhang, “Systematic study of broadband terahertz gas sensor,” Appl. Phys. Lett. 93, 261106 (2008).
[CrossRef]

2007 (1)

K. Kampfrath, J. Nötzold, and M. Wolf, “Sampling of broadband terahertz pulses with thick electro-optic crystals,” Appl. Phys. Lett. 90, 231113 (2007).
[CrossRef]

2006 (2)

X. Xie, J. Dai, and X.-C. Zhang, “Coherent control of THz wave generation in ambient air,” Phys. Rev. Lett. 96, 075005 (2006).
[CrossRef] [PubMed]

J. Dai, X. Xie, and X.-C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97, 103903 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

2001 (1)

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B: Lasers Opt. 73, 287-290 (2001).
[CrossRef]

2000 (2)

D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. 25, 1210-1212 (2000).
[CrossRef]

S. Kono, M. Tani, P. Gu, and K. Sakai, “Detection of up to 20 THz with a low-temperature grown GaAs photoconductive antenna gated with 15 fs light pulses,” Appl. Phys. Lett. 77, 4104-4106 (2000).
[CrossRef]

1999 (1)

D. J. Cook, J. X. Chen, E. A. Morlino, and R. M. Hochstrasser, “THz-field-induced second-harmonic generation measurements of liquid dynamics,” Chem. Phys. Lett. 309, 221-228 (1999).
[CrossRef]

1998 (1)

1995 (1)

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

1993 (1)

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725-2728 (1993).
[CrossRef] [PubMed]

1990 (1)

D. P. Shelton, “Nonlinear-optical susceptibilities of gases measured at 1063 and 1319 nm,” Phys. Rev. A 42, 2578-2592 (1990).
[CrossRef] [PubMed]

1974 (2)

J. P. Hermann and J. Ducuing, “Third-order polarizabilities of long-chain molecules,” J. Appl. Phys. 45, 5100-5102 (1974).
[CrossRef]

K. C. Rustagi and J. Ducuing, “Third-order optical polarizability of conjugated organic molecules,” Opt. Commun. 10, 258-261 (1974).
[CrossRef]

1971 (1)

R. S. Finn and J. F. Ward, “DC-induced optical second-harmonic generation in the inert gases,” Phys. Rev. Lett. 26, 285-289 (1971).
[CrossRef]

1969 (1)

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57-72 (1969).
[CrossRef]

1966 (1)

D. A. Kleinman, A. Ashkin, and G. D. Boyd, “Second-harmonic generation of light by focused laser beams,” Phys. Rev. 145, 338-379 (1966).
[CrossRef]

1962 (1)

J. A. Armstong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

1932 (1)

S. A. Korff and G. Breit, “Optical dispersion,” Rev. Mod. Phys. 4, 471-503 (1932).
[CrossRef]

1891 (1)

L. G. Gouy,“Sur la propagation anomale des ondes,” Ann. Chim. Phys. 24, 145-213 (1891).

1890 (1)

L. G. Gouy, “Sur une propréité nouvelle des ondes lumineuses,” C. R. Hebd. Seances Acad. Sci. 110, 1251-1253 (1890).

Aközbek, N.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B: Lasers Opt. 73, 287-290 (2001).
[CrossRef]

Armstong, J. A.

J. A. Armstong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Ashkin, A.

D. A. Kleinman, A. Ashkin, and G. D. Boyd, “Second-harmonic generation of light by focused laser beams,” Phys. Rev. 145, 338-379 (1966).
[CrossRef]

Bartel, T.

Becker, A.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B: Lasers Opt. 73, 287-290 (2001).
[CrossRef]

Bloembergen, N.

J. A. Armstong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Bowden, C. M.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B: Lasers Opt. 73, 287-290 (2001).
[CrossRef]

Boyd, G. D.

D. A. Kleinman, A. Ashkin, and G. D. Boyd, “Second-harmonic generation of light by focused laser beams,” Phys. Rev. 145, 338-379 (1966).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic, 1992).

Breit, G.

S. A. Korff and G. Breit, “Optical dispersion,” Rev. Mod. Phys. 4, 471-503 (1932).
[CrossRef]

Chen, J. X.

D. J. Cook, J. X. Chen, E. A. Morlino, and R. M. Hochstrasser, “THz-field-induced second-harmonic generation measurements of liquid dynamics,” Chem. Phys. Lett. 309, 221-228 (1999).
[CrossRef]

Chen, Y.

X. Lu, N. Karpowicz, Y. Chen, and X.-C. Zhang, “Systematic study of broadband terahertz gas sensor,” Appl. Phys. Lett. 93, 261106 (2008).
[CrossRef]

N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

Chin, S. L.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B: Lasers Opt. 73, 287-290 (2001).
[CrossRef]

Cook, D. J.

D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. 25, 1210-1212 (2000).
[CrossRef]

D. J. Cook, J. X. Chen, E. A. Morlino, and R. M. Hochstrasser, “THz-field-induced second-harmonic generation measurements of liquid dynamics,” Chem. Phys. Lett. 309, 221-228 (1999).
[CrossRef]

Dai, J.

N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

J. Dai, X. Xie, and X.-C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97, 103903 (2006).
[CrossRef] [PubMed]

X. Xie, J. Dai, and X.-C. Zhang, “Coherent control of THz wave generation in ambient air,” Phys. Rev. Lett. 96, 075005 (2006).
[CrossRef] [PubMed]

Ducuing, J.

J. P. Hermann and J. Ducuing, “Third-order polarizabilities of long-chain molecules,” J. Appl. Phys. 45, 5100-5102 (1974).
[CrossRef]

K. C. Rustagi and J. Ducuing, “Third-order optical polarizability of conjugated organic molecules,” Opt. Commun. 10, 258-261 (1974).
[CrossRef]

J. A. Armstong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Eden, S.

Elsaesser, T.

Falcone, R. W.

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725-2728 (1993).
[CrossRef] [PubMed]

Finn, R. S.

R. S. Finn and J. F. Ward, “DC-induced optical second-harmonic generation in the inert gases,” Phys. Rev. Lett. 26, 285-289 (1971).
[CrossRef]

Fletcher, C.

N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

Gaal, P.

Glownia, J. H.

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2, 605-609 (2008).
[CrossRef]

Gordon, S.

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725-2728 (1993).
[CrossRef] [PubMed]

Gouy, L. G.

L. G. Gouy,“Sur la propagation anomale des ondes,” Ann. Chim. Phys. 24, 145-213 (1891).

L. G. Gouy, “Sur une propréité nouvelle des ondes lumineuses,” C. R. Hebd. Seances Acad. Sci. 110, 1251-1253 (1890).

Gu, P.

S. Kono, M. Tani, P. Gu, and K. Sakai, “Detection of up to 20 THz with a low-temperature grown GaAs photoconductive antenna gated with 15 fs light pulses,” Appl. Phys. Lett. 77, 4104-4106 (2000).
[CrossRef]

Hamster, H.

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725-2728 (1993).
[CrossRef] [PubMed]

Heinz, T. F.

Hermann, J. P.

J. P. Hermann and J. Ducuing, “Third-order polarizabilities of long-chain molecules,” J. Appl. Phys. 45, 5100-5102 (1974).
[CrossRef]

Hochstrasser, R. M.

D. J. Cook and R. M. Hochstrasser, “Intense terahertz pulses by four-wave rectification in air,” Opt. Lett. 25, 1210-1212 (2000).
[CrossRef]

D. J. Cook, J. X. Chen, E. A. Morlino, and R. M. Hochstrasser, “THz-field-induced second-harmonic generation measurements of liquid dynamics,” Chem. Phys. Lett. 309, 221-228 (1999).
[CrossRef]

Houard, A.

A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of THz radiation from laser filament in air by a static electric field,” Phys. Rev. Lett. 100, 255006 (2008).
[CrossRef] [PubMed]

Johnson, K.

N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

Kampfrath, K.

K. Kampfrath, J. Nötzold, and M. Wolf, “Sampling of broadband terahertz pulses with thick electro-optic crystals,” Appl. Phys. Lett. 90, 231113 (2007).
[CrossRef]

Karpowicz, N.

N. Karpowicz and X.-C. Zhang, “Coherent terahertz echo of tunnel ionization in gases,” Phys. Rev. Lett. 102, 093001 (2009).
[CrossRef] [PubMed]

X. Lu, N. Karpowicz, Y. Chen, and X.-C. Zhang, “Systematic study of broadband terahertz gas sensor,” Appl. Phys. Lett. 93, 261106 (2008).
[CrossRef]

N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

Kim, K. Y.

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2, 605-609 (2008).
[CrossRef]

Kleinman, D. A.

D. A. Kleinman, A. Ashkin, and G. D. Boyd, “Second-harmonic generation of light by focused laser beams,” Phys. Rev. 145, 338-379 (1966).
[CrossRef]

Kono, S.

S. Kono, M. Tani, P. Gu, and K. Sakai, “Detection of up to 20 THz with a low-temperature grown GaAs photoconductive antenna gated with 15 fs light pulses,” Appl. Phys. Lett. 77, 4104-4106 (2000).
[CrossRef]

Korff, S. A.

S. A. Korff and G. Breit, “Optical dispersion,” Rev. Mod. Phys. 4, 471-503 (1932).
[CrossRef]

Kress, M.

Lesimple, A.

N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

Liu, Y.

A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of THz radiation from laser filament in air by a static electric field,” Phys. Rev. Lett. 100, 255006 (2008).
[CrossRef] [PubMed]

Löffler, T.

Lu, X.

X. Lu, N. Karpowicz, Y. Chen, and X.-C. Zhang, “Systematic study of broadband terahertz gas sensor,” Appl. Phys. Lett. 93, 261106 (2008).
[CrossRef]

N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

Mamer, O.

N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

Morlino, E. A.

D. J. Cook, J. X. Chen, E. A. Morlino, and R. M. Hochstrasser, “THz-field-induced second-harmonic generation measurements of liquid dynamics,” Chem. Phys. Lett. 309, 221-228 (1999).
[CrossRef]

Mysyrowicz, A.

A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of THz radiation from laser filament in air by a static electric field,” Phys. Rev. Lett. 100, 255006 (2008).
[CrossRef] [PubMed]

Nahata, A.

New, G. H. C.

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57-72 (1969).
[CrossRef]

Nötzold, J.

K. Kampfrath, J. Nötzold, and M. Wolf, “Sampling of broadband terahertz pulses with thick electro-optic crystals,” Appl. Phys. Lett. 90, 231113 (2007).
[CrossRef]

Oral, E.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B: Lasers Opt. 73, 287-290 (2001).
[CrossRef]

Pershan, P. S.

J. A. Armstong, N. Bloembergen, J. Ducuing, and P. S. Pershan, “Interactions between light waves in a nonlinear dielectric,” Phys. Rev. 127, 1918-1939 (1962).
[CrossRef]

Prade, B.

A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of THz radiation from laser filament in air by a static electric field,” Phys. Rev. Lett. 100, 255006 (2008).
[CrossRef] [PubMed]

Price-Gallagher, M.

N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

Reimann, K.

Rodriguez, G.

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2, 605-609 (2008).
[CrossRef]

Rokos, H. G.

Rustagi, K. C.

K. C. Rustagi and J. Ducuing, “Third-order optical polarizability of conjugated organic molecules,” Opt. Commun. 10, 258-261 (1974).
[CrossRef]

Sakai, K.

S. Kono, M. Tani, P. Gu, and K. Sakai, “Detection of up to 20 THz with a low-temperature grown GaAs photoconductive antenna gated with 15 fs light pulses,” Appl. Phys. Lett. 77, 4104-4106 (2000).
[CrossRef]

Shelton, D. P.

D. P. Shelton, “Nonlinear-optical susceptibilities of gases measured at 1063 and 1319 nm,” Phys. Rev. A 42, 2578-2592 (1990).
[CrossRef] [PubMed]

Sullivan, A.

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725-2728 (1993).
[CrossRef] [PubMed]

Tani, M.

S. Kono, M. Tani, P. Gu, and K. Sakai, “Detection of up to 20 THz with a low-temperature grown GaAs photoconductive antenna gated with 15 fs light pulses,” Appl. Phys. Lett. 77, 4104-4106 (2000).
[CrossRef]

Taylor, A. J.

K. Y. Kim, A. J. Taylor, J. H. Glownia, and G. Rodriguez, “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions,” Nat. Photonics 2, 605-609 (2008).
[CrossRef]

Thomson, M.

Tikhonchuk, V. T.

A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of THz radiation from laser filament in air by a static electric field,” Phys. Rev. Lett. 100, 255006 (2008).
[CrossRef] [PubMed]

Vijayalakshmi, K.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and re-focusing of intense femtosecond laser pulses in nitrogen molecular gas,” Appl. Phys. B: Lasers Opt. 73, 287-290 (2001).
[CrossRef]

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R. S. Finn and J. F. Ward, “DC-induced optical second-harmonic generation in the inert gases,” Phys. Rev. Lett. 26, 285-289 (1971).
[CrossRef]

J. F. Ward and G. H. C. New, “Optical third harmonic generation in gases by a focused laser beam,” Phys. Rev. 185, 57-72 (1969).
[CrossRef]

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H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725-2728 (1993).
[CrossRef] [PubMed]

Woerner, M.

Wolf, M.

K. Kampfrath, J. Nötzold, and M. Wolf, “Sampling of broadband terahertz pulses with thick electro-optic crystals,” Appl. Phys. Lett. 90, 231113 (2007).
[CrossRef]

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

Xie, X.

J. Dai, X. Xie, and X.-C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97, 103903 (2006).
[CrossRef] [PubMed]

X. Xie, J. Dai, and X.-C. Zhang, “Coherent control of THz wave generation in ambient air,” Phys. Rev. Lett. 96, 075005 (2006).
[CrossRef] [PubMed]

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N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

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N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

Zhang, L.

N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

Zhang, X.-C.

N. Karpowicz and X.-C. Zhang, “Coherent terahertz echo of tunnel ionization in gases,” Phys. Rev. Lett. 102, 093001 (2009).
[CrossRef] [PubMed]

N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

X. Lu, N. Karpowicz, Y. Chen, and X.-C. Zhang, “Systematic study of broadband terahertz gas sensor,” Appl. Phys. Lett. 93, 261106 (2008).
[CrossRef]

J. Dai, X. Xie, and X.-C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97, 103903 (2006).
[CrossRef] [PubMed]

X. Xie, J. Dai, and X.-C. Zhang, “Coherent control of THz wave generation in ambient air,” Phys. Rev. Lett. 96, 075005 (2006).
[CrossRef] [PubMed]

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[CrossRef]

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N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

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[CrossRef]

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

N. Karpowicz, J. Dai, X. Lu, Y. Chen, M. Yamaguchi, H. Zhao, X.-C. Zhang, L. Zhang, C. Zhang, M. Price-Gallagher, C. Fletcher, O. Mamer, A. Lesimple, and K. Johnson, “Coherent heterodyne time-domain spectrometry covering the entire 'terahertz gap',” Appl. Phys. Lett. 92, 011131 (2008).
[CrossRef]

X. Lu, N. Karpowicz, Y. Chen, and X.-C. Zhang, “Systematic study of broadband terahertz gas sensor,” Appl. Phys. Lett. 93, 261106 (2008).
[CrossRef]

K. Kampfrath, J. Nötzold, and M. Wolf, “Sampling of broadband terahertz pulses with thick electro-optic crystals,” Appl. Phys. Lett. 90, 231113 (2007).
[CrossRef]

S. Kono, M. Tani, P. Gu, and K. Sakai, “Detection of up to 20 THz with a low-temperature grown GaAs photoconductive antenna gated with 15 fs light pulses,” Appl. Phys. Lett. 77, 4104-4106 (2000).
[CrossRef]

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[CrossRef]

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R. S. Finn and J. F. Ward, “DC-induced optical second-harmonic generation in the inert gases,” Phys. Rev. Lett. 26, 285-289 (1971).
[CrossRef]

A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, “Strong enhancement of THz radiation from laser filament in air by a static electric field,” Phys. Rev. Lett. 100, 255006 (2008).
[CrossRef] [PubMed]

X. Xie, J. Dai, and X.-C. Zhang, “Coherent control of THz wave generation in ambient air,” Phys. Rev. Lett. 96, 075005 (2006).
[CrossRef] [PubMed]

N. Karpowicz and X.-C. Zhang, “Coherent terahertz echo of tunnel ionization in gases,” Phys. Rev. Lett. 102, 093001 (2009).
[CrossRef] [PubMed]

J. Dai, X. Xie, and X.-C. Zhang, “Detection of broadband terahertz waves with a laser-induced plasma in gases,” Phys. Rev. Lett. 97, 103903 (2006).
[CrossRef] [PubMed]

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, “Subpicosecond, electromagnetic pulses from intense laser-plasma interaction,” Phys. Rev. Lett. 71, 2725-2728 (1993).
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Edited by D.R.Lide, CRC Handbook of Chemistry and Physics , 80th ed. (CRC, 1999).

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Figures (8)

Fig. 1
Fig. 1

Schematic of the experimental setup. BS, beam splitter. BBO, type I beta barium borate. PM, parabolic mirror. PMT, photomultiplier tube. HV, high voltage modulator. The THz wave is generated through laser-induced plasma in air. An iris with a diameter of 10 mm is placed at a distance about 50 mm after the plasma. A high-resistivity silicon wafer blocks the residual pump beam. The THz beam and probe beam focus collinearly in the presence of a modulated bias, resulting in a second-harmonic signal detected by PMT.

Fig. 2
Fig. 2

Measured second-harmonic intensity ( I 2 ω ) versus the probe pulse energy ( I ω ) at a bias field of 7.5 kV cm , and gas pressure of 756 T orr from xenon and S F 6 gases. The dots are from measurements and the dashed lines are the quadratic fits. The divergences of the probe energy dependence above 50 μ J for xenon and 70 μ J for S F 6 are consistent with the onset of intensity clamping due to plasma formation.

Fig. 3
Fig. 3

Measured second-harmonic intensity ( I 2 ω ) versus the DC bias field ( E DC ) at gas pressure (a) 100 T orr and (b) 756 T orr , probe pulse energy of 50 μ J . The dots are from measurements and the dashed lines are the linear fits.

Fig. 4
Fig. 4

Detected second-harmonic intensity ( I 2 ω ) versus third-order nonlinear susceptibility ( χ ( 3 ) ) . The dots are from experimental data and the dashed curve is the quadratic fit. The y axis is normalized with the reference signal taken with 100 T orr nitrogen gas at the same experimental condition. Also, all the χ ( 3 ) are normalized with that of nitrogen.

Fig. 5
Fig. 5

Pressure dependence of detected second-harmonic intensity from (a) xenon, (b) propane, and (c) n-butane gas at various Rayleigh lengths of THz beam. The probe beam power is set to be 20 mW and bias field strength is about 8 kV cm . The dots are from measurements without iris (with iris) condition and dashed curves are fit from analytical expression. The fitted Rayleigh lengths are z T = 0.8 mm and z T = 1.5 mm .

Fig. 6
Fig. 6

2D plot of detected THz spectra versus pressure with or without iris. The F numbers without and with the iris are estimated to be 1.8 and 2.4, respectively, using fitted THz Rayleigh length. The different phase match of each frequency component results in a spectral shift towards high frequency.

Fig. 7
Fig. 7

Pressure dependence of various frequency components from xenon sensor at (a) F number = 1.8 and (b) F number = 2.4 . The probe beam power is 20 mW and bias field strength is about 8 kV cm . The data are normalized with peak value for clarity.

Fig. 8
Fig. 8

Calculated dependence of the detected second-harmonic intensity on the THz Rayleigh length for various probe focusing conditions.

Tables (1)

Tables Icon

Table 1 Properties of a Few Gases Suitable for THz Detection

Equations (25)

Equations on this page are rendered with MathJax. Learn more.

E 2 ω THz χ ( 3 ) E ω E ω E THz ,
I 2 ω THz [ χ ( 3 ) I ω ] 2 I THz .
I 2 ω ( E 2 ω THz + E 2 ω LO ) 2 ( E 2 ω THz ) 2 + ( E 2 ω LO ) 2 + 2 χ ( 3 ) I ω E 2 ω LO E THz .
E 2 ω DC χ ( 3 ) E ω E ω E DC ,
I 2 ω ( E 2 ω THz + E 2 ω DC ) 2 ( E 2 ω THz ) 2 + ( E 2 ω DC ) 2 + 2 ( χ ( 3 ) I ω ) 2 E DC E THz .
I 2 ω [ χ ( 3 ) I ω ] 2 E DC E THz ,
E ω ( r , z ) = E ω 1 + iz z R e r 2 w 0 2 ( 1 + iz z R ) ,
E THz ( r , z ) = E THz 1 + iz z T ,
E 2 ω ( r , z ) = E 2 ω ( z ) 1 + iz z R e 2 r 2 w 0 2 ( 1 + iz z R ) .
2 ik 2 ω E 2 ω z + T 2 E 2 ω = 16 π ω 2 c 2 χ ( 2 ) E ω 2 e i Δ kz .
χ eff ( 2 ) = χ ( 3 ) E THz * + c.c.
E 2 ω ( z ) = i 4 π ω nc χ ( 3 ) E ω 2 E THz * J ( Δ k , z 0 , z ) ,
E 2 ω THz = i 8 π 2 ω nc χ ( 3 ) E ω 2 E THz z R z T z R + z T e z T Δ k ,
E DC ( z ) = 2 V d cosh 1 ( l 2 a ) 1 1 + [ 2 z d ] 2 ,
E 2 ω DC = i 8 π 2 ω nc cosh 1 ( l 2 a ) χ ( 3 ) E ω 2 V z R 2 z R + d e d Δ k 2 .
I 2 ω E 2 ω DC E 2 ω THz ( χ ( 3 ) I ω ) 2 E THz V z R 2 z T ( z R + z T ) ( 2 z R + d ) e ( z T + d 2 ) Δ k ,
Δ k = p dk = 2 π p Δ n 0 λ 400 ,
I 2 ω = A z R 2 z T ( z R + z T ) ( 2 z R + d ) ( χ 0 ( 3 ) p ) 2 e ( z T + d 2 ) dkp ,
p opt = 2 ( z T + d 2 ) dk .
I 2 ω = A e 2 4 z R 2 z T ( z R + z T ) ( 2 z R + d ) ( z T + d 2 ) 2 ( χ 0 ( 3 ) dk ) 2 .
FOM = χ 0 ( 3 ) dk .
I ω I ω E THz = [ 32 2 π c 5 2 λ THz 1 2 λ ω 1 P ω 2 P THz 1 2 ] 1 z R z T ,
A = ( i 8 π 2 ω c 1 ) 2 [ 32 2 π c 5 2 λ THz 1 2 λ ω 1 P ω 2 P THz 1 2 V ] ,
I 2 ω = A z T ( z R + z T ) ( 2 z R + d ) ( χ 0 ( 3 ) p ) 2 e ( z T + d 2 ) dkp ,
I 2 ω = A e 2 4 z T ( z R + z T ) ( 2 z R + d ) ( z T + d 2 ) 2 ( χ 0 ( 3 ) dk ) 2 .

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