Abstract

A theoretical model has been proposed to describe the dependence of the THz wave generated in a laser-induced air plasma on the external electric field. Using this model we predict the following, (i) previously observed results show that the THz pulse enhances linearly with the increase of the external field; (ii) the THz pulse varies as a cosine function with the angle between the direction of the external electric field and the polarization of the incident exciting beam; (iii) and the amplitude is proportional to the square of the intensity of the incident pulse in a low energy region. These predictions are validated by our experiment.

© 2008 Optical Society of America

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References

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  1. H. Hamster and R. W. Falcone, Ultrafast Phenomena VII, edited by C. B. Harris et al (Springer, New York, 1990).
  2. H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Subpicosecond, Electrmagnetic Pulses from Intense Laser-Plasma Interaction," Phys. Rev. Lett. 71, 2725 (1993).
    [CrossRef] [PubMed]
  3. H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Short-pulse terahertz radiation from highintersity-laser-produced plasmas," Phys. Rev. E. 49, 671 (1994).
    [CrossRef]
  4. D. J. Cook and M. Hochstrasser, "Intense terahertz pulses by four-wave rectification in air," Opt. Lett. 25, 1210 (2000).
    [CrossRef]
  5. M. Kress, T. Loffer, S. Eden, M. Thomson, and H. G. Roskos, "Terahertz-pulse generation by photoionization of air with laser pulses composed of both fundamental and second-harmonic waves," Opt. Lett. 29, 1120 (2004).
    [CrossRef] [PubMed]
  6. T. Bartel, P. Reimann, M. Woerner, and T. Elsaesser, "Generation of single-cycle THz transients with high electric-field amplitudes," Opt. Lett. 30, 2805 (2005).
    [PubMed]
  7. 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]
  8. T. Loffler, F. Jacob, and H. G. Roskos, "Generation of terahertz pulses by photoionization of electrically biased air," Appl. Phys. Lett. 77, 453 (2000).
    [CrossRef]
  9. A. Houard, Y. Liu, B. Prade, V. T. Tikhonchuk, and A. Mysyrowicz, "Strong enhancement of terahertz radiation from laser filaments in air by a static electric field," Phys. Rev. Lett. 100, 255006 (2008).
    [PubMed]
  10. C. D. Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas,MFranco, B Prade, A Couairon, V. T. Tikhonchuk, and A. Mysyrowicz, "Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment," N. J. Phys. 10, 013015 (2008).
    [CrossRef]
  11. Y. R. Shen, The Principles of Nonlinear Optics (University of Cnlifirnia, Berkeley A Wiley-Interscience Publication, 1984).
  12. M. Melijiek, E. M. Wright, and J. V. Moloney, "Femtosecond pulse propagation in argon: A pressure dependence study," Phys. Rev. E 58, 4903 (1998).
    [CrossRef]

2008 (2)

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

C. D. Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas,MFranco, B Prade, A Couairon, V. T. Tikhonchuk, and A. Mysyrowicz, "Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment," N. J. Phys. 10, 013015 (2008).
[CrossRef]

2006 (1)

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]

2005 (1)

2004 (1)

2000 (2)

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

T. Loffler, F. Jacob, and H. G. Roskos, "Generation of terahertz pulses by photoionization of electrically biased air," Appl. Phys. Lett. 77, 453 (2000).
[CrossRef]

1998 (1)

M. Melijiek, E. M. Wright, and J. V. Moloney, "Femtosecond pulse propagation in argon: A pressure dependence study," Phys. Rev. E 58, 4903 (1998).
[CrossRef]

1994 (1)

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Short-pulse terahertz radiation from highintersity-laser-produced plasmas," Phys. Rev. E. 49, 671 (1994).
[CrossRef]

1993 (1)

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Subpicosecond, Electrmagnetic Pulses from Intense Laser-Plasma Interaction," Phys. Rev. Lett. 71, 2725 (1993).
[CrossRef] [PubMed]

Akturk, S.

C. D. Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas,MFranco, B Prade, A Couairon, V. T. Tikhonchuk, and A. Mysyrowicz, "Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment," N. J. Phys. 10, 013015 (2008).
[CrossRef]

Amico, C. D.

C. D. Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas,MFranco, B Prade, A Couairon, V. T. Tikhonchuk, and A. Mysyrowicz, "Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment," N. J. Phys. 10, 013015 (2008).
[CrossRef]

Bartel, T.

Cook, D. J.

Dai, J.

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]

Eden, S.

Elsaesser, T.

Falcone, R. W.

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Short-pulse terahertz radiation from highintersity-laser-produced plasmas," Phys. Rev. E. 49, 671 (1994).
[CrossRef]

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Subpicosecond, Electrmagnetic Pulses from Intense Laser-Plasma Interaction," Phys. Rev. Lett. 71, 2725 (1993).
[CrossRef] [PubMed]

Gordon, S.

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Short-pulse terahertz radiation from highintersity-laser-produced plasmas," Phys. Rev. E. 49, 671 (1994).
[CrossRef]

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Subpicosecond, Electrmagnetic Pulses from Intense Laser-Plasma Interaction," Phys. Rev. Lett. 71, 2725 (1993).
[CrossRef] [PubMed]

Hamster, H.

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Short-pulse terahertz radiation from highintersity-laser-produced plasmas," Phys. Rev. E. 49, 671 (1994).
[CrossRef]

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Subpicosecond, Electrmagnetic Pulses from Intense Laser-Plasma Interaction," Phys. Rev. Lett. 71, 2725 (1993).
[CrossRef] [PubMed]

Hochstrasser, M.

Houard, A.

C. D. Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas,MFranco, B Prade, A Couairon, V. T. Tikhonchuk, and A. Mysyrowicz, "Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment," N. J. Phys. 10, 013015 (2008).
[CrossRef]

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

Jacob, F.

T. Loffler, F. Jacob, and H. G. Roskos, "Generation of terahertz pulses by photoionization of electrically biased air," Appl. Phys. Lett. 77, 453 (2000).
[CrossRef]

Kress, M.

Le Bloas, J.

C. D. Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas,MFranco, B Prade, A Couairon, V. T. Tikhonchuk, and A. Mysyrowicz, "Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment," N. J. Phys. 10, 013015 (2008).
[CrossRef]

Liu, Y.

C. D. Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas,MFranco, B Prade, A Couairon, V. T. Tikhonchuk, and A. Mysyrowicz, "Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment," N. J. Phys. 10, 013015 (2008).
[CrossRef]

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

Loffer, T.

Loffler, T.

T. Loffler, F. Jacob, and H. G. Roskos, "Generation of terahertz pulses by photoionization of electrically biased air," Appl. Phys. Lett. 77, 453 (2000).
[CrossRef]

Melijiek, M.

M. Melijiek, E. M. Wright, and J. V. Moloney, "Femtosecond pulse propagation in argon: A pressure dependence study," Phys. Rev. E 58, 4903 (1998).
[CrossRef]

Moloney, J. V.

M. Melijiek, E. M. Wright, and J. V. Moloney, "Femtosecond pulse propagation in argon: A pressure dependence study," Phys. Rev. E 58, 4903 (1998).
[CrossRef]

Mysyrowicz, A.

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

Prade, B.

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

Reimann, P.

Roskos, H. G.

Sullivan, A.

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Short-pulse terahertz radiation from highintersity-laser-produced plasmas," Phys. Rev. E. 49, 671 (1994).
[CrossRef]

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Subpicosecond, Electrmagnetic Pulses from Intense Laser-Plasma Interaction," Phys. Rev. Lett. 71, 2725 (1993).
[CrossRef] [PubMed]

Thomson, M.

Tikhonchuk, V. T.

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

White, W.

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Short-pulse terahertz radiation from highintersity-laser-produced plasmas," Phys. Rev. E. 49, 671 (1994).
[CrossRef]

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Subpicosecond, Electrmagnetic Pulses from Intense Laser-Plasma Interaction," Phys. Rev. Lett. 71, 2725 (1993).
[CrossRef] [PubMed]

Woerner, M.

Wright, E. M.

M. Melijiek, E. M. Wright, and J. V. Moloney, "Femtosecond pulse propagation in argon: A pressure dependence study," Phys. Rev. E 58, 4903 (1998).
[CrossRef]

Xie, X.

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]

Zhang, X. C.

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]

Appl. Phys. Lett. (1)

T. Loffler, F. Jacob, and H. G. Roskos, "Generation of terahertz pulses by photoionization of electrically biased air," Appl. Phys. Lett. 77, 453 (2000).
[CrossRef]

N. J. Phys. (1)

C. D. Amico, A. Houard, S. Akturk, Y. Liu, J. Le Bloas,MFranco, B Prade, A Couairon, V. T. Tikhonchuk, and A. Mysyrowicz, "Forward THz radiation emission by femtosecond filamentation in gases: theory and experiment," N. J. Phys. 10, 013015 (2008).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. E (1)

M. Melijiek, E. M. Wright, and J. V. Moloney, "Femtosecond pulse propagation in argon: A pressure dependence study," Phys. Rev. E 58, 4903 (1998).
[CrossRef]

Phys. Rev. E. (1)

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Short-pulse terahertz radiation from highintersity-laser-produced plasmas," Phys. Rev. E. 49, 671 (1994).
[CrossRef]

Phys. Rev. Lett. (3)

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]

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

H. Hamster, A. Sullivan, S. Gordon, W. White, and R. W. Falcone, "Subpicosecond, Electrmagnetic Pulses from Intense Laser-Plasma Interaction," Phys. Rev. Lett. 71, 2725 (1993).
[CrossRef] [PubMed]

Other (2)

H. Hamster and R. W. Falcone, Ultrafast Phenomena VII, edited by C. B. Harris et al (Springer, New York, 1990).

Y. R. Shen, The Principles of Nonlinear Optics (University of Cnlifirnia, Berkeley A Wiley-Interscience Publication, 1984).

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Figures (5)

Fig. 1.
Fig. 1.

Schematic plan of the setup used for THz generation controlled by an external electric field.

Fig. 2.
Fig. 2.

The THz pulses generated in air plasma (a) and fourier transformed spectrums (b). The solid curve corresponds to a case without an external field and the dashed curve to the case of external field Eex =1.2kV/cm with θ=0°.

Fig. 3.
Fig. 3.

Observed THz amplitudes (circles) generated in air plasma corresponding to different external fields Eex when θ=0°. The straight line is a curve of best fit for the amplitudes.

Fig. 4.
Fig. 4.

Observed THz amplitudes corresponding to different rotation angles. The solid curve is a cosine form fitted to the observed amplitudes.

Fig. 5.
Fig. 5.

Observed THz amplitudes corresponding to different laser pulse energies. The solid quadratic curve is fitted to the amplitudes in the low energy region.

Equations (17)

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J ( 2 ) = i ρ ( 0 ) e 2 2 ω 2 m 2 [ 1 ω ( E ( 1 ) · ) E ( 1 ) + 1 c E ( 1 ) · B ( 1 ) ] + i e 2 ( ρ ( 0 ) · E ( 1 ) ) m 2 ω 2 ( 1 + ω p 2 ω 2 ) E ( 1 ) .
ρ ( 0 ) ( E ex t 2 , z ) = ρ ( 0 ) ( 0 , 0 ) + z ρ ( 0 ) ( 0 , z ) z = 0 z + E ex t 2 ρ ( 0 ) ( E ex t 2 , 0 ) E ex t 2 = 0 E ex t 2
1 2 2 z 2 ρ ( 0 ) ( 0 , z ) z = 0 z 2 + 1 2 2 ( E ex t 2 ) 2 ρ ( 0 ) ( E ex t 2 , 0 ) E ex t 2 = 0 ( E ex t 2 ) 2
+ 1 2 2 ( E ex t 2 ) z × ρ ( 0 ) ( E ex t 2 , z ) E ex t 2 = 0 , z ' = 0 ( E ex t 2 ) z .
ρ ( 0 ) = z ̂ a E ex .
a = 1 2 2 z E ex t 2 ρ ( 0 ) ( E ex t 2 , z ) E ex t 2 = 0 , z = 0 t 2 .
J ( 2 ) = b cos θ E ex exp ( 2 i k y y 2 i ω t ) z ̂ .
b = i e 2 a m 2 ω 2 ( 1 + ω p 2 ω 2 ) E ( 1 ) 2 .
φ ( 2 ) ( r , t ) = v 0 t · J ( 2 ) ( r , t ) r r dt d r .
A ( 2 ) ( r , t ) = 1 c J ( 2 ) ( r , t r r c ) r r d r .
A ( 2 ) ( r , t ) = b E ex cos θ c I ( r ) exp ( i 2 ω ) z ̂ .
I ( r ) = exp [ i 2 k y ( y ' + r r ' ) ] r r ' d r ' .
E ( 2 ) ( r , t ) = φ ( 2 ) 1 c t A ( 2 ) = i 2 ω b E ex cos θ c 2 I ( r ) exp ( i 2 ω ) z ̂ .
E T Hz E ( 1 ) 2 E ( 2 ) .
E T Hz E ( 1 ) 4 E ex cos θ .
E T Hz I ω 2 .
E T Hz I ω .

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