Abstract

Terahertz wave generation from air excited by tightly focused fundamental and second-harmonic pulses of a femtosecond Ti:sapphire laser is analyzed both theoretically and experimentally for various pump pulse energies. Numerical calculations, based on the microscopic polarization model, revealed that the experimentally obtained dependencies of terahertz yield can be well explained taking into account phase shifts of bichromatic pump waves, acquired during free propagation in air, and nonlinear second-harmonic crystal, as well as by considering the Gouy phases of focused laser beams.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  27. F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
    [CrossRef]

2013 (2)

Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
[CrossRef]

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[CrossRef]

2012 (2)

B. Clough, J. Dai, and X.-C. Zhang, “Laser air photonics: beyond the terahertz gap,” Mater. Today 15, 50–58 (2012).
[CrossRef]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “High-power broadband terahertz generation via two-color photoionization in gases,” IEEE J. Quantum Electron. 48, 797–805 (2012).
[CrossRef]

2011 (2)

H. Dai and J. Liu, “Phase dependence of the generation of terahertz waves from two-color laser-induced gas plasma,” J. Opt. 13, 055201 (2011).
[CrossRef]

V. Vaičaitis, V. Smilgevičius, and V. Jarutis, “Phase relations between focused bichromatic laser pulses in terahertz wave generation from gas plasma,” Opt. Commun. 284, 2206–2209 (2011).
[CrossRef]

2010 (2)

G. Rodriguez and G. L. Dakovski, “Scaling behavior of ultrafast two-color terahertz generation in plasma gas targets: energy and pressure dependence,” Opt. Express 18, 15130–15143 (2010).
[CrossRef]

I. Babushkin, W. Kuehn, C. Koehler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef]

2009 (6)

N. Karpowicz, X. Lu, and X.-C. Zhang, “Terahertz gas photonics,” J. Mod. Opt. 56, 1137–1150 (2009).
[CrossRef]

Y. Liu, A. Houard, M. Durand, B. Prade, and A. Mysyrowicz, “Maker fringes in the terahertz radiation produced by a 2-color laser field in air,” Opt. Express 17, 11480–11485 (2009).
[CrossRef]

H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett. 103, 023902 (2009).
[CrossRef]

Y. Chen, C. Marceau, S. Génier, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282, 4283–4287 (2009).
[CrossRef]

D. Dietze, J. Darmo, S. Roither, A. Pugzlys, J. N. Heyman, and K. Unterrainer, “Polarization of terahertz radiation from laser generated plasma filaments,” J. Opt. Soc. Am. B 26, 2016–2027 (2009).
[CrossRef]

L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Polarization sensitive terahertz time-domain spectroscopy for birefringent materials,” Appl. Phys. Lett. 94, 211106 (2009).
[CrossRef]

2008 (1)

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]

2007 (2)

M. D. Thomson, M. Kress, T. Loffler, and H. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: from fundamentals to applications,” Laser Photonics Rev. 1, 349–368 (2007).
[CrossRef]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (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]

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
[CrossRef]

2004 (1)

P. Sprangle, J. R. Penano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces,” Phys. Rev. E 69, 066415 (2004).
[CrossRef]

2001 (1)

2000 (1)

1996 (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]

1989 (1)

T. Trickl, E. F. Cromwell, Y. T. Lee, and A. H. Kung, “State–selective ionization of nitrogen in the X2Σ+gν+ = 0 and ν+ = 1 states by two–color (1 + 1) photon excitation near threshold,” J. Chem. Phys. 91, 6006–6012 (1989).
[CrossRef]

Babushkin, I.

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[CrossRef]

I. Babushkin, W. Kuehn, C. Koehler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef]

Bakker, H. J.

Bass, M.

M. Bass, Handbook of Optics, 3rd ed., Vol. 4 (McGraw Hill, 2009).

Becker, A.

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
[CrossRef]

Bergé, L.

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[CrossRef]

I. Babushkin, W. Kuehn, C. Koehler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef]

Boyd, R. W.

R. W. Boyd, “Second-harmonic generation,” in Nonlinear Optics, 3rd ed. (Academic, 2008), p. 97.

Châteauneuf, M.

Y. Chen, C. Marceau, S. Génier, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282, 4283–4287 (2009).
[CrossRef]

Chen, Y.

Y. Chen, C. Marceau, S. Génier, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282, 4283–4287 (2009).
[CrossRef]

Chin, S. L.

Y. Chen, C. Marceau, S. Génier, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282, 4283–4287 (2009).
[CrossRef]

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
[CrossRef]

Ciddor, P. E.

Clough, B.

B. Clough, J. Dai, and X.-C. Zhang, “Laser air photonics: beyond the terahertz gap,” Mater. Today 15, 50–58 (2012).
[CrossRef]

Cook, D. J.

Cromwell, E. F.

T. Trickl, E. F. Cromwell, Y. T. Lee, and A. H. Kung, “State–selective ionization of nitrogen in the X2Σ+gν+ = 0 and ν+ = 1 states by two–color (1 + 1) photon excitation near threshold,” J. Chem. Phys. 91, 6006–6012 (1989).
[CrossRef]

Dai, H.

H. Dai and J. Liu, “Phase dependence of the generation of terahertz waves from two-color laser-induced gas plasma,” J. Opt. 13, 055201 (2011).
[CrossRef]

Dai, J.

B. Clough, J. Dai, and X.-C. Zhang, “Laser air photonics: beyond the terahertz gap,” Mater. Today 15, 50–58 (2012).
[CrossRef]

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

Dakovski, G. L.

Darmo, J.

Deng, C.

L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Polarization sensitive terahertz time-domain spectroscopy for birefringent materials,” Appl. Phys. Lett. 94, 211106 (2009).
[CrossRef]

Dietze, D.

Dubois, J.

Y. Chen, C. Marceau, S. Génier, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282, 4283–4287 (2009).
[CrossRef]

Durand, M.

Elsaesser, T.

I. Babushkin, W. Kuehn, C. Koehler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef]

Génier, S.

Y. Chen, C. Marceau, S. Génier, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282, 4283–4287 (2009).
[CrossRef]

Glownia, J. H.

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “High-power broadband terahertz generation via two-color photoionization in gases,” IEEE J. Quantum Electron. 48, 797–805 (2012).
[CrossRef]

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]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
[CrossRef]

Hafizi, B.

P. Sprangle, J. R. Penano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces,” Phys. Rev. E 69, 066415 (2004).
[CrossRef]

Herrmann, J.

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[CrossRef]

I. Babushkin, W. Kuehn, C. Koehler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef]

Heyman, J. N.

Hochstrasser, R. M.

Houard, A.

Jarutis, V.

V. Vaičaitis, V. Smilgevičius, and V. Jarutis, “Phase relations between focused bichromatic laser pulses in terahertz wave generation from gas plasma,” Opt. Commun. 284, 2206–2209 (2011).
[CrossRef]

Kapetanakos, C. A.

P. Sprangle, J. R. Penano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces,” Phys. Rev. E 69, 066415 (2004).
[CrossRef]

Karpowicz, N.

N. Karpowicz, X. Lu, and X.-C. Zhang, “Terahertz gas photonics,” J. Mod. Opt. 56, 1137–1150 (2009).
[CrossRef]

Kim, K. Y.

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “High-power broadband terahertz generation via two-color photoionization in gases,” IEEE J. Quantum Electron. 48, 797–805 (2012).
[CrossRef]

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]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
[CrossRef]

Koehler, C.

I. Babushkin, W. Kuehn, C. Koehler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef]

Köhler, C.

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[CrossRef]

Kress, M.

M. D. Thomson, M. Kress, T. Loffler, and H. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: from fundamentals to applications,” Laser Photonics Rev. 1, 349–368 (2007).
[CrossRef]

Kuehn, W.

I. Babushkin, W. Kuehn, C. Koehler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef]

Kung, A. H.

T. Trickl, E. F. Cromwell, Y. T. Lee, and A. H. Kung, “State–selective ionization of nitrogen in the X2Σ+gν+ = 0 and ν+ = 1 states by two–color (1 + 1) photon excitation near threshold,” J. Chem. Phys. 91, 6006–6012 (1989).
[CrossRef]

Kurihara, T.

Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
[CrossRef]

Lee, Y. T.

T. Trickl, E. F. Cromwell, Y. T. Lee, and A. H. Kung, “State–selective ionization of nitrogen in the X2Σ+gν+ = 0 and ν+ = 1 states by two–color (1 + 1) photon excitation near threshold,” J. Chem. Phys. 91, 6006–6012 (1989).
[CrossRef]

Lindenberg, A. M.

H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett. 103, 023902 (2009).
[CrossRef]

Liu, J.

H. Dai and J. Liu, “Phase dependence of the generation of terahertz waves from two-color laser-induced gas plasma,” J. Opt. 13, 055201 (2011).
[CrossRef]

Liu, W.

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
[CrossRef]

Liu, Y.

Loffler, T.

M. D. Thomson, M. Kress, T. Loffler, and H. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: from fundamentals to applications,” Laser Photonics Rev. 1, 349–368 (2007).
[CrossRef]

Lu, X.

N. Karpowicz, X. Lu, and X.-C. Zhang, “Terahertz gas photonics,” J. Mod. Opt. 56, 1137–1150 (2009).
[CrossRef]

Marceau, C.

Y. Chen, C. Marceau, S. Génier, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282, 4283–4287 (2009).
[CrossRef]

Minami, Y.

Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
[CrossRef]

Mysyrowicz, A.

Nakajima, M.

Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
[CrossRef]

Nienhuys, H.-K.

Penano, J. R.

P. Sprangle, J. R. Penano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces,” Phys. Rev. E 69, 066415 (2004).
[CrossRef]

Planken, P. C. M.

Prade, B.

Pugzlys, A.

Reimann, K.

I. Babushkin, W. Kuehn, C. Koehler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef]

Rodriguez, G.

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “High-power broadband terahertz generation via two-color photoionization in gases,” IEEE J. Quantum Electron. 48, 797–805 (2012).
[CrossRef]

G. Rodriguez and G. L. Dakovski, “Scaling behavior of ultrafast two-color terahertz generation in plasma gas targets: energy and pressure dependence,” Opt. Express 18, 15130–15143 (2010).
[CrossRef]

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]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
[CrossRef]

Roither, S.

Roskos, H.

M. D. Thomson, M. Kress, T. Loffler, and H. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: from fundamentals to applications,” Laser Photonics Rev. 1, 349–368 (2007).
[CrossRef]

Simard, P. T.

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
[CrossRef]

Skupin, S.

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[CrossRef]

I. Babushkin, W. Kuehn, C. Koehler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef]

Smilgevicius, V.

V. Vaičaitis, V. Smilgevičius, and V. Jarutis, “Phase relations between focused bichromatic laser pulses in terahertz wave generation from gas plasma,” Opt. Commun. 284, 2206–2209 (2011).
[CrossRef]

Sprangle, P.

P. Sprangle, J. R. Penano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces,” Phys. Rev. E 69, 066415 (2004).
[CrossRef]

Suemoto, T.

Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
[CrossRef]

Taylor, A. J.

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “High-power broadband terahertz generation via two-color photoionization in gases,” IEEE J. Quantum Electron. 48, 797–805 (2012).
[CrossRef]

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]

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “Terahertz emission from ultrafast ionizing air in symmetry-broken laser fields,” Opt. Express 15, 4577–4584 (2007).
[CrossRef]

Théberge, F.

Y. Chen, C. Marceau, S. Génier, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282, 4283–4287 (2009).
[CrossRef]

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
[CrossRef]

Thomson, M. D.

M. D. Thomson, M. Kress, T. Loffler, and H. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: from fundamentals to applications,” Laser Photonics Rev. 1, 349–368 (2007).
[CrossRef]

Trickl, T.

T. Trickl, E. F. Cromwell, Y. T. Lee, and A. H. Kung, “State–selective ionization of nitrogen in the X2Σ+gν+ = 0 and ν+ = 1 states by two–color (1 + 1) photon excitation near threshold,” J. Chem. Phys. 91, 6006–6012 (1989).
[CrossRef]

Unterrainer, K.

Vaicaitis, V.

V. Vaičaitis, V. Smilgevičius, and V. Jarutis, “Phase relations between focused bichromatic laser pulses in terahertz wave generation from gas plasma,” Opt. Commun. 284, 2206–2209 (2011).
[CrossRef]

Wen, H.

H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett. 103, 023902 (2009).
[CrossRef]

Wenckebach, T.

Woerner, M.

I. Babushkin, W. Kuehn, C. Koehler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef]

Wu, Q.

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

Yamaguchi, K.

Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
[CrossRef]

Zhang, C. L.

L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Polarization sensitive terahertz time-domain spectroscopy for birefringent materials,” Appl. Phys. Lett. 94, 211106 (2009).
[CrossRef]

Zhang, L. L.

L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Polarization sensitive terahertz time-domain spectroscopy for birefringent materials,” Appl. Phys. Lett. 94, 211106 (2009).
[CrossRef]

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]

Zhang, X.-C.

B. Clough, J. Dai, and X.-C. Zhang, “Laser air photonics: beyond the terahertz gap,” Mater. Today 15, 50–58 (2012).
[CrossRef]

N. Karpowicz, X. Lu, and X.-C. Zhang, “Terahertz gas photonics,” J. Mod. Opt. 56, 1137–1150 (2009).
[CrossRef]

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

Zhao, Y. J.

L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Polarization sensitive terahertz time-domain spectroscopy for birefringent materials,” Appl. Phys. Lett. 94, 211106 (2009).
[CrossRef]

Zhong, H.

L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Polarization sensitive terahertz time-domain spectroscopy for birefringent materials,” Appl. Phys. Lett. 94, 211106 (2009).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

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

L. L. Zhang, H. Zhong, C. Deng, C. L. Zhang, and Y. J. Zhao, “Polarization sensitive terahertz time-domain spectroscopy for birefringent materials,” Appl. Phys. Lett. 94, 211106 (2009).
[CrossRef]

Y. Minami, T. Kurihara, K. Yamaguchi, M. Nakajima, and T. Suemoto, “High-power THz wave generation in plasma induced by polarization adjusted two-color laser pulses,” Appl. Phys. Lett. 102, 041105 (2013).
[CrossRef]

IEEE J. Quantum Electron. (1)

K. Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, “High-power broadband terahertz generation via two-color photoionization in gases,” IEEE J. Quantum Electron. 48, 797–805 (2012).
[CrossRef]

J. Chem. Phys. (1)

T. Trickl, E. F. Cromwell, Y. T. Lee, and A. H. Kung, “State–selective ionization of nitrogen in the X2Σ+gν+ = 0 and ν+ = 1 states by two–color (1 + 1) photon excitation near threshold,” J. Chem. Phys. 91, 6006–6012 (1989).
[CrossRef]

J. Mod. Opt. (1)

N. Karpowicz, X. Lu, and X.-C. Zhang, “Terahertz gas photonics,” J. Mod. Opt. 56, 1137–1150 (2009).
[CrossRef]

J. Opt. (1)

H. Dai and J. Liu, “Phase dependence of the generation of terahertz waves from two-color laser-induced gas plasma,” J. Opt. 13, 055201 (2011).
[CrossRef]

J. Opt. Soc. Am. B (2)

Laser Photonics Rev. (1)

M. D. Thomson, M. Kress, T. Loffler, and H. Roskos, “Broadband THz emission from gas plasmas induced by femtosecond optical pulses: from fundamentals to applications,” Laser Photonics Rev. 1, 349–368 (2007).
[CrossRef]

Mater. Today (1)

B. Clough, J. Dai, and X.-C. Zhang, “Laser air photonics: beyond the terahertz gap,” Mater. Today 15, 50–58 (2012).
[CrossRef]

Nat. Photonics (1)

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]

Opt. Commun. (2)

Y. Chen, C. Marceau, S. Génier, F. Théberge, M. Châteauneuf, J. Dubois, and S. L. Chin, “Elliptically polarized terahertz emission through four-wave mixing in a two-color filament in air,” Opt. Commun. 282, 4283–4287 (2009).
[CrossRef]

V. Vaičaitis, V. Smilgevičius, and V. Jarutis, “Phase relations between focused bichromatic laser pulses in terahertz wave generation from gas plasma,” Opt. Commun. 284, 2206–2209 (2011).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. E (2)

P. Sprangle, J. R. Penano, B. Hafizi, and C. A. Kapetanakos, “Ultrashort laser pulses and electromagnetic pulse generation in air and on dielectric surfaces,” Phys. Rev. E 69, 066415 (2004).
[CrossRef]

F. Théberge, W. Liu, P. T. Simard, A. Becker, and S. L. Chin, “Plasma density inside a femtosecond laser filament in air: strong dependence on external focusing,” Phys. Rev. E 74, 036406 (2006).
[CrossRef]

Phys. Rev. Lett. (4)

L. Bergé, S. Skupin, C. Köhler, I. Babushkin, and J. Herrmann, “3D numerical simulations of THz generation by two-color laser filaments,” Phys. Rev. Lett. 110, 073901 (2013).
[CrossRef]

H. Wen and A. M. Lindenberg, “Coherent terahertz polarization control through manipulation of electron trajectories,” Phys. Rev. Lett. 103, 023902 (2009).
[CrossRef]

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

I. Babushkin, W. Kuehn, C. Koehler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, “Ultrafast spatiotemporal dynamics of terahertz generation by ionizing two-color femtosecond pulses in gases,” Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef]

Other (2)

R. W. Boyd, “Second-harmonic generation,” in Nonlinear Optics, 3rd ed. (Academic, 2008), p. 97.

M. Bass, Handbook of Optics, 3rd ed., Vol. 4 (McGraw Hill, 2009).

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Figures (6)

Fig. 1.
Fig. 1.

Experimental setup (above) and configuration of electric wave vectors of the pump and THz fields (below).

Fig. 2.
Fig. 2.

Typical THz pulse time waveform (inset) detected by a 0.5-mm-thick ZnTe crystal and corresponding power spectrum, calculated by Fourier transform of the time domain pulse. The spectral dips between 0.5 and 4 THz result from the absorption of atmospheric water vapor.

Fig. 3.
Fig. 3.

(a), (b) Dependence of THz radiation energy on the distance from the lens focus at pump energy of 0.8 mJ (1, 2) and 0.4 mJ (3, 4) for the x (1, 3) and y (2, 4) polarizations. (c), (d) Dependence of the plasma electron density (1, 2) as well as phase φ12 (3) on the distance from the lens focus. Pump energy [mJ]: 0.8 (1), 0.4 (2). Phase difference (c) Δφ12=0.13π and (d) Δφ12=0.09π. α=40°. Focal length f [cm]: (a), (c) 15 and (b), (d) 10.

Fig. 4.
Fig. 4.

(a), (b) Dependence of the fundamental wave intensity and nonlinear phase on the distance from the lens at pump energy of 0.8 mJ (1, 3) and 0.4 mJ (2, 4). (c), (d) Dependence of maximal THz generation position zf0 and phase φ12 at this point on pump pulse energy. Focus length f [cm]: (a), (c) 15 and (b), (d) 10.

Fig. 5.
Fig. 5.

Dependence of the THz radiation energy on the distance between the crystal and the lens focus Lf at α=40°. Pump energy [mJ]: (a), (c) 0.8 and (b), (d) 0.4. (a), (b) Experimental and (c), (d) theoretical data. x and y polarizations. Focus length f=15cm.

Fig. 6.
Fig. 6.

Dependence of the x-polarized THz pulse energy on the polarization angle of the pump wave. Pump energy: 0.8 mJ. (a) Experimental and (b) theoretical data. Lf [cm]: 7.8 (1), 6.6 (2). Focal length f=15cm.

Equations (7)

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

A1(r,z,t)=ia0Ldz[1+i(Ld/zLd/f)]×exp(r2ρ12Ld2z2[1+(Ld/zLd/f)2])×exp(ir2ρ12Ldz[1Ldz(Ld/zLd/f)1+(Ld/zLd/f)2])×exp(t2τ12),
A2x(r,z=fLf,t)=LcLna0A1y2(r,z=fLf,t)exp(iπ/2),
ρ2=ρ112[Ld2(fLf)211+(Ld/(fLf)Ld/f)2]1/2,f2=ρ12ρ22(1(fLf)Ld(fLf)2Ld/(fLf)Ld/f(1+(Ld/(fLf)Ld/f)2))1,Ld2=2Ldρ22ρ12.
E1x(z=fzf)=R(A1(z=fzf)sinαexp(iω0t)),E1y(z=fzf)=R(A1(z=fzf)cosαexp(iω0t+iΔφc)),
E2x(z=fzf)=R(A2x(z=fzf)exp(2iω0t+iΔφ)).
ρet=W(|E|)(ρatρe),
Jet+Jeτe=q2meEρe,

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