Abstract

Forward and backward terahertz emission by ionizing two-color laser pulses in gas is investigated by means of a simple semianalytical model based on Jefimenko’s equations and rigorous Maxwell simulations in one and two dimensions. We find the emission in the backward direction has a much smaller spectral bandwidth than in the forward direction and explain this by interference effects. Forward terahertz radiation is generated predominantly at the ionization front and is thus almost not affected by the opacity of the plasma, in excellent agreement with results obtained from a unidirectional pulse propagation model.

© 2011 Optical Society of America

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  1. D. J. Cook and R. M. Hochstrasser, Opt. Lett. 25, 1210(2000).
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  2. K.-Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, Opt. Express 15, 4577 (2007).
    [CrossRef] [PubMed]
  3. T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, Opt. Lett. 30, 2805 (2005).
    [CrossRef] [PubMed]
  4. J. Dai, X. Xie, and X.-C. Zhang, Phys. Rev. Lett. 97, 103903(2006).
    [CrossRef] [PubMed]
  5. I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, Phys. Rev. Lett. 105, 053903 (2010).
    [CrossRef] [PubMed]
  6. J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, Phys. Rev. E 81, 026407 (2010).
    [CrossRef]
  7. O. D. Jefimenko, Electricity and Magnetism: An Introduction to the Theory of Electric and Magnetic Fields(Appleton-Century-Crofts, 1966).
  8. M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, Laser Photonics Rev. 1, 349 (2007).
    [CrossRef]
  9. I. Babushkin, S. Skupin, and J. Herrmann, Opt. Express 18, 9658 (2010).
    [CrossRef] [PubMed]
  10. R. M. Joseph and A. Taflove, IEEE Trans. Antennas Propag. 45, 364 (1997).
    [CrossRef]
  11. A. Dalgarno and A. E. Kingston, Proc. R. Soc. A 259, 424(1960).
    [CrossRef]
  12. M. Kolesik and J. V. Moloney, Phys. Rev. E 70, 036604(2004).
    [CrossRef]

2010 (3)

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef] [PubMed]

J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, Phys. Rev. E 81, 026407 (2010).
[CrossRef]

I. Babushkin, S. Skupin, and J. Herrmann, Opt. Express 18, 9658 (2010).
[CrossRef] [PubMed]

2007 (2)

K.-Y. Kim, J. H. Glownia, A. J. Taylor, and G. Rodriguez, Opt. Express 15, 4577 (2007).
[CrossRef] [PubMed]

M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, Laser Photonics Rev. 1, 349 (2007).
[CrossRef]

2006 (1)

J. Dai, X. Xie, and X.-C. Zhang, Phys. Rev. Lett. 97, 103903(2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

M. Kolesik and J. V. Moloney, Phys. Rev. E 70, 036604(2004).
[CrossRef]

2000 (1)

1997 (1)

R. M. Joseph and A. Taflove, IEEE Trans. Antennas Propag. 45, 364 (1997).
[CrossRef]

1966 (1)

O. D. Jefimenko, Electricity and Magnetism: An Introduction to the Theory of Electric and Magnetic Fields(Appleton-Century-Crofts, 1966).

1960 (1)

A. Dalgarno and A. E. Kingston, Proc. R. Soc. A 259, 424(1960).
[CrossRef]

Babushkin, I.

I. Babushkin, S. Skupin, and J. Herrmann, Opt. Express 18, 9658 (2010).
[CrossRef] [PubMed]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef] [PubMed]

Bartel, T.

Bergé, L.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef] [PubMed]

Cook, D. J.

Dai, J.

J. Dai, X. Xie, and X.-C. Zhang, Phys. Rev. Lett. 97, 103903(2006).
[CrossRef] [PubMed]

Dalgarno, A.

A. Dalgarno and A. E. Kingston, Proc. R. Soc. A 259, 424(1960).
[CrossRef]

Elsaesser, T.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef] [PubMed]

T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, Opt. Lett. 30, 2805 (2005).
[CrossRef] [PubMed]

Gaal, P.

Glownia, J. H.

Gordon, D.

J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, Phys. Rev. E 81, 026407 (2010).
[CrossRef]

Hafizi, B.

J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, Phys. Rev. E 81, 026407 (2010).
[CrossRef]

Herrmann, J.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef] [PubMed]

I. Babushkin, S. Skupin, and J. Herrmann, Opt. Express 18, 9658 (2010).
[CrossRef] [PubMed]

Hochstrasser, R. M.

Jefimenko, O. D.

O. D. Jefimenko, Electricity and Magnetism: An Introduction to the Theory of Electric and Magnetic Fields(Appleton-Century-Crofts, 1966).

Joseph, R. M.

R. M. Joseph and A. Taflove, IEEE Trans. Antennas Propag. 45, 364 (1997).
[CrossRef]

Kim, K.-Y.

Kingston, A. E.

A. Dalgarno and A. E. Kingston, Proc. R. Soc. A 259, 424(1960).
[CrossRef]

Köhler, C.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef] [PubMed]

Kolesik, M.

M. Kolesik and J. V. Moloney, Phys. Rev. E 70, 036604(2004).
[CrossRef]

Kress, M.

M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, Laser Photonics Rev. 1, 349 (2007).
[CrossRef]

Kuehn, W.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef] [PubMed]

Löffler, T.

M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, Laser Photonics Rev. 1, 349 (2007).
[CrossRef]

Moloney, J. V.

M. Kolesik and J. V. Moloney, Phys. Rev. E 70, 036604(2004).
[CrossRef]

Peñano, J.

J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, Phys. Rev. E 81, 026407 (2010).
[CrossRef]

Reimann, K.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef] [PubMed]

T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, Opt. Lett. 30, 2805 (2005).
[CrossRef] [PubMed]

Rodriguez, G.

Roskos, H. G.

M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, Laser Photonics Rev. 1, 349 (2007).
[CrossRef]

Serafim, P.

J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, Phys. Rev. E 81, 026407 (2010).
[CrossRef]

Skupin, S.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef] [PubMed]

I. Babushkin, S. Skupin, and J. Herrmann, Opt. Express 18, 9658 (2010).
[CrossRef] [PubMed]

Sprangle, P.

J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, Phys. Rev. E 81, 026407 (2010).
[CrossRef]

Taflove, A.

R. M. Joseph and A. Taflove, IEEE Trans. Antennas Propag. 45, 364 (1997).
[CrossRef]

Taylor, A. J.

Thomson, M. D.

M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, Laser Photonics Rev. 1, 349 (2007).
[CrossRef]

Woerner, M.

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef] [PubMed]

T. Bartel, P. Gaal, K. Reimann, M. Woerner, and T. Elsaesser, Opt. Lett. 30, 2805 (2005).
[CrossRef] [PubMed]

Xie, X.

J. Dai, X. Xie, and X.-C. Zhang, Phys. Rev. Lett. 97, 103903(2006).
[CrossRef] [PubMed]

Zhang, X.-C.

J. Dai, X. Xie, and X.-C. Zhang, Phys. Rev. Lett. 97, 103903(2006).
[CrossRef] [PubMed]

IEEE Trans. Antennas Propag. (1)

R. M. Joseph and A. Taflove, IEEE Trans. Antennas Propag. 45, 364 (1997).
[CrossRef]

Laser Photonics Rev. (1)

M. D. Thomson, M. Kress, T. Löffler, and H. G. Roskos, Laser Photonics Rev. 1, 349 (2007).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Phys. Rev. E (2)

M. Kolesik and J. V. Moloney, Phys. Rev. E 70, 036604(2004).
[CrossRef]

J. Peñano, P. Sprangle, B. Hafizi, D. Gordon, and P. Serafim, Phys. Rev. E 81, 026407 (2010).
[CrossRef]

Phys. Rev. Lett. (2)

J. Dai, X. Xie, and X.-C. Zhang, Phys. Rev. Lett. 97, 103903(2006).
[CrossRef] [PubMed]

I. Babushkin, W. Kuehn, C. Köhler, S. Skupin, L. Bergé, K. Reimann, M. Woerner, J. Herrmann, and T. Elsaesser, Phys. Rev. Lett. 105, 053903 (2010).
[CrossRef] [PubMed]

Proc. R. Soc. A (1)

A. Dalgarno and A. E. Kingston, Proc. R. Soc. A 259, 424(1960).
[CrossRef]

Other (1)

O. D. Jefimenko, Electricity and Magnetism: An Introduction to the Theory of Electric and Magnetic Fields(Appleton-Century-Crofts, 1966).

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic illustration of the interference being responsible for shaping FW and BW emission. A plasma line source of length L created by a propagating two-color pump pulse emits radiation. Blue circles centered around exemplary point sources represent planes of constant phase of elementary spherical waves. (c) In FW direction, spherical waves interfere constructively for all wavelengths and the resulting on-axis spectrum is proportional to the single-emitter spectrum. (b) In BW direction, the spectral form-factor Eq. (2) depletes wavelengths smaller than the source length (here L = 30 μm ).

Fig. 2
Fig. 2

2D FDTD simulations: terahertz spectra of (a) BW and (b) FW emission. The inset shows the on-axis BW spectrum obtained from a linearly propagated Gaussian pump pulse and Eq. (1). (c) On-axis BW spectral width versus plasma channel length L from Eq. (2) (solid line), 2D FDTD calculations (blue circles), and 3D Jefimenko approach (red crosses). (d) Snapshot of emitted terahertz fields ( < 100 THz ) and plasma channel, illustrating the strong (weak) emission in FW (BW) direction.

Fig. 3
Fig. 3

1D simulations: FW terahertz spectra for (a)  A = 31 GV / m ( 1 bar ) and (b)  A = 46 GV / m ( 5 bar ) from FDTD (solid black line) and UPPE simulations with (dashed red line) and without (dotted red line) Kerr effect included. The insets show the complete spectra. (c) UPPE results illustrate that tera-hertz emission (solid black line) takes place mainly at the ionization front (dashed red line). (d) BW tera hertz spectra for parameters used in (a) (solid line) and (b) (dashed line), both obtained from FDTD simulations. All spectra are normalized to E ^ in ( ν = 375 THz ) .

Equations (5)

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E J ( r , t ) = 1 4 π ϵ 0 ( 1 c 2 R J e ( r , t R / c ) t ) d 3 r
f ( λ 1 ) = Ei [ i 4 π λ ( z L / 2 ) ] Ei [ i 4 π λ ( z + L / 2 ) ] ,
E in ( r , t ) = [ 1 ξ cos ( ω 0 t ) + ξ cos ( 2 ω 0 t + φ ) ] × A exp ( r 2 w 2 t 2 σ t 2 )
t J e + 1 τ c J e = q 2 m e E ( t ) ρ e ( t ) .
μ 0 H x t = E y z , μ 0 H z t = E y x , D y t + J e = H x z H z x .

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