Abstract

Third harmonic generation by a weak femtosecond probe pulse intersecting a pump laser-induced plasma in air is investigated and a general model is developed to describe such signal, applicable to a wide range of focusing and plasma conditions. The effect of the surrounding air on the generated signal is discussed. The third-order nonlinear susceptibility of an air plasma with electron density Ne is determined to be χp(3)=χa(3)+γpNe with γp = 2 ± 1 × 10−49 m5 V−2 and χa(3) being the third-order susceptibility in air. Lateral scans of the probe through the plasma are used to determine electron density profiles and the effect of focusing and phase mismatch is discussed.

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    [CrossRef]
  3. S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Filamentation-induced third-harmonic generation in air via plasma-enhanced third-order susceptibility,” Phys. Rev. A 81, 033817 (2010).
    [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] [PubMed]
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    [CrossRef]
  15. L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

2011

Z. Sun, J. Chen, and W. Rudolph, “Determination of the transient electron temperature in a femtosecond-laser-induced air plasma,” Phys. Rev. E 83, 046408 (2011).
[CrossRef]

2010

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Filamentation-induced third-harmonic generation in air via plasma-enhanced third-order susceptibility,” Phys. Rev. A 81, 033817 (2010).
[CrossRef]

2009

2008

K. Hartinger and R. A. Bartels, “Enhancement of third harmonic generation by a laser-induced plasma,” Appl. Phys. Lett. 93, 151102 (2008).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

2004

A. A. Fridman and L. A. Kennedy, Plasma Physics and Engineering (Taylor & Francis, 2004).

2001

A. N. Naumov, D. A. Sidorov-Biryukov, A. B. Fedotov, and A. M. Zheltikov, “Third-harmonic generation in focused beams as a method of 3D microscopy of a laser-produced plasma,” Opt. Spectrosc. , 90, 778–783 (2001).
[CrossRef]

2000

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
[CrossRef]

1999

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29–32 (1999).
[CrossRef]

1997

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[CrossRef]

1996

1991

1969

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]

1965

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Abdollahpour, D.

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Filamentation-induced third-harmonic generation in air via plasma-enhanced third-order susceptibility,” Phys. Rev. A 81, 033817 (2010).
[CrossRef]

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Efficient third-harmonic generation through tailored IR femtosecond laser pulse filamentation in air,” Opt. Express 17, 3190–3195 (2009).
[CrossRef] [PubMed]

Backus, S.

Barad, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[CrossRef]

Bartels, R. A.

K. Hartinger and R. A. Bartels, “Enhancement of third harmonic generation by a laser-induced plasma,” Appl. Phys. Lett. 93, 151102 (2008).
[CrossRef]

Boyd, R. W.

R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

Chen, J.

Z. Sun, J. Chen, and W. Rudolph, “Determination of the transient electron temperature in a femtosecond-laser-induced air plasma,” Phys. Rev. E 83, 046408 (2011).
[CrossRef]

Chin, S. L.

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
[CrossRef]

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29–32 (1999).
[CrossRef]

Ciddor, P. E.

Eisenberg, H.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[CrossRef]

Fedotov, A. B.

A. N. Naumov, D. A. Sidorov-Biryukov, A. B. Fedotov, and A. M. Zheltikov, “Third-harmonic generation in focused beams as a method of 3D microscopy of a laser-produced plasma,” Opt. Spectrosc. , 90, 778–783 (2001).
[CrossRef]

A. B. Fedotov, S. M. Gladkov, N. I. Koroteev, and A. M. Zheltikov, “Highly efficient frequency tripling of laser radiation in a low-temperature laser-produced gaseous plasma,” J. Opt. Soc. Am. B 8, 363–366 (1991).
[CrossRef]

Fridman, A. A.

A. A. Fridman and L. A. Kennedy, Plasma Physics and Engineering (Taylor & Francis, 2004).

Gladkov, S. M.

Hartinger, K.

K. Hartinger and R. A. Bartels, “Enhancement of third harmonic generation by a laser-induced plasma,” Appl. Phys. Lett. 93, 151102 (2008).
[CrossRef]

Horowitz, M.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[CrossRef]

Kapteyn, H. C.

Kasparian, J.

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
[CrossRef]

Keldysh, L. V.

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Kennedy, L. A.

A. A. Fridman and L. A. Kennedy, Plasma Physics and Engineering (Taylor & Francis, 2004).

Koroteev, N. I.

Murnane, M. M.

Naumov, A. N.

A. N. Naumov, D. A. Sidorov-Biryukov, A. B. Fedotov, and A. M. Zheltikov, “Third-harmonic generation in focused beams as a method of 3D microscopy of a laser-produced plasma,” Opt. Spectrosc. , 90, 778–783 (2001).
[CrossRef]

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]

Papazoglou, D. G.

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Filamentation-induced third-harmonic generation in air via plasma-enhanced third-order susceptibility,” Phys. Rev. A 81, 033817 (2010).
[CrossRef]

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Efficient third-harmonic generation through tailored IR femtosecond laser pulse filamentation in air,” Opt. Express 17, 3190–3195 (2009).
[CrossRef] [PubMed]

Peatross, J.

Rudolph, W.

Z. Sun, J. Chen, and W. Rudolph, “Determination of the transient electron temperature in a femtosecond-laser-induced air plasma,” Phys. Rev. E 83, 046408 (2011).
[CrossRef]

Rundquist, A.

Sauerbrey, R.

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
[CrossRef]

Sidorov-Biryukov, D. A.

A. N. Naumov, D. A. Sidorov-Biryukov, A. B. Fedotov, and A. M. Zheltikov, “Third-harmonic generation in focused beams as a method of 3D microscopy of a laser-produced plasma,” Opt. Spectrosc. , 90, 778–783 (2001).
[CrossRef]

Silberberg, Y.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[CrossRef]

Sun, Z.

Z. Sun, J. Chen, and W. Rudolph, “Determination of the transient electron temperature in a femtosecond-laser-induced air plasma,” Phys. Rev. E 83, 046408 (2011).
[CrossRef]

Suntsov, S.

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Filamentation-induced third-harmonic generation in air via plasma-enhanced third-order susceptibility,” Phys. Rev. A 81, 033817 (2010).
[CrossRef]

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Efficient third-harmonic generation through tailored IR femtosecond laser pulse filamentation in air,” Opt. Express 17, 3190–3195 (2009).
[CrossRef] [PubMed]

Taft, G.

Talebpour, A.

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29–32 (1999).
[CrossRef]

Tzortzakis, S.

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Filamentation-induced third-harmonic generation in air via plasma-enhanced third-order susceptibility,” Phys. Rev. A 81, 033817 (2010).
[CrossRef]

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Efficient third-harmonic generation through tailored IR femtosecond laser pulse filamentation in air,” Opt. Express 17, 3190–3195 (2009).
[CrossRef] [PubMed]

Ward, J. F.

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]

Yang, J.

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29–32 (1999).
[CrossRef]

Zeek, Z.

Zheltikov, A. M.

A. N. Naumov, D. A. Sidorov-Biryukov, A. B. Fedotov, and A. M. Zheltikov, “Third-harmonic generation in focused beams as a method of 3D microscopy of a laser-produced plasma,” Opt. Spectrosc. , 90, 778–783 (2001).
[CrossRef]

A. B. Fedotov, S. M. Gladkov, N. I. Koroteev, and A. M. Zheltikov, “Highly efficient frequency tripling of laser radiation in a low-temperature laser-produced gaseous plasma,” J. Opt. Soc. Am. B 8, 363–366 (1991).
[CrossRef]

Appl. Opt.

Appl. Phys. B

J. Kasparian, R. Sauerbrey, and S. L. Chin, “The critical laser intensity of self-guided light filaments in air,” Appl. Phys. B 71, 877–879 (2000).
[CrossRef]

Appl. Phys. Lett.

Y. Barad, H. Eisenberg, M. Horowitz, and Y. Silberberg, “Nonlinear scanning laser microscopy by third harmonic generation,” Appl. Phys. Lett. 70, 922–924 (1997).
[CrossRef]

K. Hartinger and R. A. Bartels, “Enhancement of third harmonic generation by a laser-induced plasma,” Appl. Phys. Lett. 93, 151102 (2008).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29–32 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Spectrosc.

A. N. Naumov, D. A. Sidorov-Biryukov, A. B. Fedotov, and A. M. Zheltikov, “Third-harmonic generation in focused beams as a method of 3D microscopy of a laser-produced plasma,” Opt. Spectrosc. , 90, 778–783 (2001).
[CrossRef]

Phys. Rev.

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]

Phys. Rev. A

S. Suntsov, D. Abdollahpour, D. G. Papazoglou, and S. Tzortzakis, “Filamentation-induced third-harmonic generation in air via plasma-enhanced third-order susceptibility,” Phys. Rev. A 81, 033817 (2010).
[CrossRef]

Phys. Rev. E

Z. Sun, J. Chen, and W. Rudolph, “Determination of the transient electron temperature in a femtosecond-laser-induced air plasma,” Phys. Rev. E 83, 046408 (2011).
[CrossRef]

Sov. Phys. JETP

L. V. Keldysh, “Ionization in the field of a strong electromagnetic wave,” Sov. Phys. JETP 20, 1307–1314 (1965).

Other

R. W. Boyd, Nonlinear Optics (Academic Press, 2008).

A. A. Fridman and L. A. Kennedy, Plasma Physics and Engineering (Taylor & Francis, 2004).

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Figures (8)

Fig. 1
Fig. 1

Generated TH field as a function of position z. (a) For an infinite medium the integration over the entire space yields no net TH. (b) If a slab of a material of thickness D is introduced in the focus, the TH field no longer vanishes.

Fig. 2
Fig. 2

Schematic diagram of a Gaussian beam propagating through a sample consisting of a host material in which a medium of thickness D is embedded.

Fig. 3
Fig. 3

TH signal as a function of Ne for (a) weak focusing conditions, Dz 0, and (b) tight focusing conditions, Dz 0, using Eq. (2), solid blue line, and Eq. (2) neglecting the contribution from air, solid red line. The dashed line in (a) shows a parabolic fit. (c) TH signal as a function of 2z 0 for Ne = 1.5 × 1023 m−3 and D = 100 μm.

Fig. 4
Fig. 4

Schematic diagram of the experimental setup to measure THG by a probe pulse intersecting transversely a pump pulse produced plasma. L1, L2, L3, lenses; BS, beam splitter; DM, dichroic mirror; A, variable attenuator; P, prism; PMT, photomultiplier tube.

Fig. 5
Fig. 5

TH signal as a function of the probe energy with a pump induced plasma present. The solid line shows a power law with κ ≈ 3 as expected for THG.

Fig. 6
Fig. 6

TH signal as a function of the electron density in the plasma. The solid line shows simulation results based on Eq. (8). Because the profiles changed with delay, the TH signal does not scale quadratically with the electron density.

Fig. 7
Fig. 7

TH signal obtained by scanning the probe laterally (y direction) through the plasma (τ = 20 ps). The solid line shows simulation results based on Eq. (8).

Fig. 8
Fig. 8

TH signal obtained by scanning the probe laterally through the plasma for different pump energies (left column) and a pump-probe delay of 1.5 ps. The solid line (right column) shows simulation results based on Eq. (8). The dashed line shows the spatial electron density distribution obtained from a multi-photon ionization model in air.

Equations (8)

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E 3 ω ( z ) = 3 i ω E ω 3 2 n 3 ω , a c χ a ( 3 ) z exp ( i Δ k a z ) ( 1 + i z / z 0 , a ) 2 d z z 0 ,
E 3 ω = 3 i ω E ω 3 2 c [ t a p 3 ω t p a 3 ω χ a ( 3 ) n 3 ω , a D 2 exp ( i Δ k a Z ) ( 1 + i Z / z 0 , a ) 2 d z + ( t a p ω ) 3 t p a 3 ω χ p ( 3 ) n 3 ω , p exp ( i D 2 [ Δ k p Δ k a ] ) D 2 + D 2 exp ( i Δ k p Z ) ( 1 + i Z / z 0 , p ) 2 d z + ( t a p ω ) 3 ( t p a ω ) 3 χ a ( 3 ) n 3 ω , a exp ( i D [ Δ k p Δ k a ] ) + D 2 + exp ( i Δ k a Z ) ( 1 + i Z / z 0 , a ) 2 d z ] .
n ω , p = n ω , a N e 2 N c ,
Δ k p = Δ k a + q N e ,
χ p ( 3 ) = χ a ( 3 ) + γ p N e ,
E 3 ω = 3 i ω E ω 3 c n 3 ω exp ( i D 2 [ Δ k p Δ k a ] ) { χ a ( 3 ) [ i sin ( D 2 [ Δ k p Δ k a ] ) 0 + exp ( i Δ k a z ) ( 1 + i z / z 0 ) 2 d z D 2 cos ( D 2 [ Δ k p Δ k a ] ) ] + χ p ( 3 ) sin [ D 2 Δ k p ] Δ k p } ,
E 3 ω = 3 i ω E ω 3 2 c n 3 ω D N e [ i q χ a ( 3 ) 0 + exp ( i Δ k a z ) ( 1 + i z / z 0 ) 2 d z + γ p ] .
E 3 ω = 3 i ω E ω 3 2 c n 3 ω { χ a ( 3 ) D 2 exp ( i Δ k a z ) ( 1 + i z / z 0 ) 2 d z + exp [ i D 2 Δ k a ] Δ z m = 1 M exp [ i Δ k p ( z m ) Δ z ] ( 1 + i z m / z 0 ) 2 χ p ( 3 ) ( z m ) + χ a ( 3 ) exp [ i D Δ k a ] exp [ i m = 1 M Δ k p ( z m ) Δ z ] + D 2 + exp ( i Δ k a z ) ( 1 + i z / z 0 ) 2 d z } ,

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