Abstract

We report experiments on the generation of third and fifth harmonics of millijoule-level, tightly focused, femtosecond laser pulses at 2.2 μm wavelength in air. The measured ratio of yields of the third and fifth harmonics in our setup is found equal to 2 · 10−4. This result contradicts the recent suggestion that the Kerr effect in air saturates and changes sign in ultra-intense optical fields.

© 2012 OSA

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  1. V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components,” Opt. Express 17, 13429–13434 (2009).
    [CrossRef] [PubMed]
  2. V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components: erratum,” Opt. Express 18, 3011–3012 (2010).
    [CrossRef]
  3. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
    [CrossRef]
  4. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
    [CrossRef]
  5. S. L. Chin, Femtosecond Laser Filamentation (Springer, New York, 2010).
    [CrossRef]
  6. P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-Order Kerr Terms Allow Ionization-Free Filamentation in Gases,” Phys. Rev. Lett. 104, 103903 (2010).
    [CrossRef] [PubMed]
  7. N. Aközbek, M. Scalora, C. Bowden, and S. L. Chin, “White-light continuum generation and filamentation during the propagation of ultra-short laser pulses in air,” Opt. Commun. 191, 353–362 (2001).
    [CrossRef]
  8. A. Couairon, “Dynamics of femtosecond filamentation from saturation of self-focusing laser pulses,” Phys. Rev. A 68, 015801 (2003).
    [CrossRef]
  9. A. Vinco̧tte and L. Bergé, “χ(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,”Phys. Rev. A 70, 061802(R) (2004).
    [CrossRef]
  10. A. Talebpour, J. Yang, and S. L. Chin, “Semi-empirical model for the rate of tunneling ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29–32 (1999).
    [CrossRef]
  11. A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and refocusing of intense femtosecond laser pulses in nitrogen gas,” Appl. Phys. B 73, 287–290 (2001).
  12. P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, “Experimental tests of the new paradigm for laser filamentation in gases,” Phys. Rev. Lett. 106, 153902 (2011).
    [CrossRef] [PubMed]
  13. O. Kosareva, J.-F. Daigle, N. Panov, T. Wang, S. Hosseini, S. Yuan, G. Roy, V. Makarov, and S. L. Chin, “Arrest of self-focusing collapse in femtosecond air filaments: higher order Kerr or plasma defocusing?” Opt. Lett. 36, 1035–1037 (2011).
    [CrossRef] [PubMed]
  14. Y.-H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
    [CrossRef]
  15. P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J.-P. Wolf, and O. Faucher, “Transition from plasma-driven to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011).
    [CrossRef] [PubMed]
  16. A. Teleki, E. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
    [CrossRef]
  17. C. Bree, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).
  18. E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of a gaseous atomic medium in the field of an ultraintense femtosecond laser pulse,” J. Ex. Theor. Phys. Lett. 94, 559–564 (2011) (in Russian, English translation in press).
  19. J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, “Optical nonlinearity in Ar and N2 near the ionization threshold,” Phys. Rev. Lett. 107, 103901 (2011).
    [CrossRef] [PubMed]
  20. J. K. Wahlstrand and H. M. Milchberg, “Effect of a plasma grating on pump-probe experiments near the ionization threshold in gases,” Opt. Lett. 36, 3822–3824 (2011).
    [CrossRef] [PubMed]
  21. M. Kolesik, E. M. Wright, and J. V. Moloney, “Femtosecond filamentation in air and higher-order nonlinearities,” Opt. Lett. 35, 2550–2552 (2010).
    [CrossRef] [PubMed]
  22. W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, “Generalized Miller formulas,” Opt. Express 18, 6613–6620 (2010).
    [CrossRef] [PubMed]
  23. V. Mizrahi and D. P. Chelton, “Dispersion of nonlinear susceptibilities of Ar, N2, and O2 measured and compared,” Phys. Rev. Lett. 55, 696–699 (1985).
    [CrossRef] [PubMed]
  24. B. Shim, S. E. Schrauth, and A. L. Gaeta, “Filamentation in air with ultrashort mid-infrared pulses,” Opt. Express 19, 9118–9126 (2011).
    [CrossRef] [PubMed]
  25. W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, O. Faucher, B. Lavorel, J. Kasparian, and J.-P. Wolf, “Spectral dependence of purely-Kerr-driven filamentation in air and argon,” Phys. Rev. A 82, 033826 (2010).
    [CrossRef]
  26. K. Kosma, S. A. Trushin, W. E. Schmid, and W. Fus, “Vacuum ultraviolet pulses of 11 fs from fifth-harmonic generation of a Ti:Sapphire laser,” Opt. Lett. 33, 723–725 (2008).
    [CrossRef] [PubMed]
  27. P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “From higher-order Kerr nonlinearities to quantitative modeling of third and fifth harmonic generation in argon,” Opt. Lett. 36, 828–830 (2011).
    [CrossRef] [PubMed]
  28. P. Tzankov, M. Roth, Y. Kong, L. Xu, and Z. Sartania, “Spatio-Temporal Characterization of the Signal Pulse-Shortening in Type II Optical Parametric Amplifier Using BBO and BIBO crystals,” in Proceedings of the Conference on Lasers and Electro Optics (2008), paper CTuE3.
    [CrossRef]
  29. Data for refractive index of air, corrected for humidity and ambient temperature, is available at the NIST website at http://emtoolbox.nist.gov/Wavelength/Elden.asp , for the wavelength range between 300 nm and 1.7 μm. The value for the index at 2.2 μm wavelength that we used in the paper was evaluated by extrapolating the available data using an 8th-order rational function fit.
  30. J. H. Taylor and H. W. Yates, “Atmospheric transmission in the infrared,” J. Opt. Soc. Am. 47, 223–226 (1957).
    [CrossRef]

2011 (7)

2010 (7)

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components: erratum,” Opt. Express 18, 3011–3012 (2010).
[CrossRef]

W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, “Generalized Miller formulas,” Opt. Express 18, 6613–6620 (2010).
[CrossRef] [PubMed]

M. Kolesik, E. M. Wright, and J. V. Moloney, “Femtosecond filamentation in air and higher-order nonlinearities,” Opt. Lett. 35, 2550–2552 (2010).
[CrossRef] [PubMed]

W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, O. Faucher, B. Lavorel, J. Kasparian, and J.-P. Wolf, “Spectral dependence of purely-Kerr-driven filamentation in air and argon,” Phys. Rev. A 82, 033826 (2010).
[CrossRef]

A. Teleki, E. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
[CrossRef]

Y.-H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-Order Kerr Terms Allow Ionization-Free Filamentation in Gases,” Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

2009 (1)

2008 (2)

K. Kosma, S. A. Trushin, W. E. Schmid, and W. Fus, “Vacuum ultraviolet pulses of 11 fs from fifth-harmonic generation of a Ti:Sapphire laser,” Opt. Lett. 33, 723–725 (2008).
[CrossRef] [PubMed]

P. Tzankov, M. Roth, Y. Kong, L. Xu, and Z. Sartania, “Spatio-Temporal Characterization of the Signal Pulse-Shortening in Type II Optical Parametric Amplifier Using BBO and BIBO crystals,” in Proceedings of the Conference on Lasers and Electro Optics (2008), paper CTuE3.
[CrossRef]

2007 (2)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

2004 (1)

A. Vinco̧tte and L. Bergé, “χ(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,”Phys. Rev. A 70, 061802(R) (2004).
[CrossRef]

2003 (1)

A. Couairon, “Dynamics of femtosecond filamentation from saturation of self-focusing laser pulses,” Phys. Rev. A 68, 015801 (2003).
[CrossRef]

2001 (2)

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and refocusing of intense femtosecond laser pulses in nitrogen gas,” Appl. Phys. B 73, 287–290 (2001).

N. Aközbek, M. Scalora, C. Bowden, and S. L. Chin, “White-light continuum generation and filamentation during the propagation of ultra-short laser pulses in air,” Opt. Commun. 191, 353–362 (2001).
[CrossRef]

1999 (1)

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

1985 (1)

V. Mizrahi and D. P. Chelton, “Dispersion of nonlinear susceptibilities of Ar, N2, and O2 measured and compared,” Phys. Rev. Lett. 55, 696–699 (1985).
[CrossRef] [PubMed]

1957 (1)

Aközbek, N.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and refocusing of intense femtosecond laser pulses in nitrogen gas,” Appl. Phys. B 73, 287–290 (2001).

N. Aközbek, M. Scalora, C. Bowden, and S. L. Chin, “White-light continuum generation and filamentation during the propagation of ultra-short laser pulses in air,” Opt. Commun. 191, 353–362 (2001).
[CrossRef]

Antonsen, T. M.

Y.-H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[CrossRef]

Becker, A.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and refocusing of intense femtosecond laser pulses in nitrogen gas,” Appl. Phys. B 73, 287–290 (2001).

Béjot, P.

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J.-P. Wolf, and O. Faucher, “Transition from plasma-driven to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011).
[CrossRef] [PubMed]

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “From higher-order Kerr nonlinearities to quantitative modeling of third and fifth harmonic generation in argon,” Opt. Lett. 36, 828–830 (2011).
[CrossRef] [PubMed]

W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, O. Faucher, B. Lavorel, J. Kasparian, and J.-P. Wolf, “Spectral dependence of purely-Kerr-driven filamentation in air and argon,” Phys. Rev. A 82, 033826 (2010).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-Order Kerr Terms Allow Ionization-Free Filamentation in Gases,” Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

Bergé, L.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

A. Vinco̧tte and L. Bergé, “χ(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,”Phys. Rev. A 70, 061802(R) (2004).
[CrossRef]

Bowden, C.

N. Aközbek, M. Scalora, C. Bowden, and S. L. Chin, “White-light continuum generation and filamentation during the propagation of ultra-short laser pulses in air,” Opt. Commun. 191, 353–362 (2001).
[CrossRef]

Bowden, C. M.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and refocusing of intense femtosecond laser pulses in nitrogen gas,” Appl. Phys. B 73, 287–290 (2001).

Bree, C.

C. Bree, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).

Chelton, D. P.

V. Mizrahi and D. P. Chelton, “Dispersion of nonlinear susceptibilities of Ar, N2, and O2 measured and compared,” Phys. Rev. Lett. 55, 696–699 (1985).
[CrossRef] [PubMed]

Chen, Y.-H.

J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, “Optical nonlinearity in Ar and N2 near the ionization threshold,” Phys. Rev. Lett. 107, 103901 (2011).
[CrossRef] [PubMed]

Y.-H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[CrossRef]

Cheng, Y.-H.

J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, “Optical nonlinearity in Ar and N2 near the ionization threshold,” Phys. Rev. Lett. 107, 103901 (2011).
[CrossRef] [PubMed]

Chin, S. L.

O. Kosareva, J.-F. Daigle, N. Panov, T. Wang, S. Hosseini, S. Yuan, G. Roy, V. Makarov, and S. L. Chin, “Arrest of self-focusing collapse in femtosecond air filaments: higher order Kerr or plasma defocusing?” Opt. Lett. 36, 1035–1037 (2011).
[CrossRef] [PubMed]

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and refocusing of intense femtosecond laser pulses in nitrogen gas,” Appl. Phys. B 73, 287–290 (2001).

N. Aközbek, M. Scalora, C. Bowden, and S. L. Chin, “White-light continuum generation and filamentation during the propagation of ultra-short laser pulses in air,” Opt. Commun. 191, 353–362 (2001).
[CrossRef]

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

S. L. Chin, Femtosecond Laser Filamentation (Springer, New York, 2010).
[CrossRef]

Couairon, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

A. Couairon, “Dynamics of femtosecond filamentation from saturation of self-focusing laser pulses,” Phys. Rev. A 68, 015801 (2003).
[CrossRef]

Daigle, J.-F.

Demircan, A.

C. Bree, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).

Ettoumi, W.

W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, O. Faucher, B. Lavorel, J. Kasparian, and J.-P. Wolf, “Spectral dependence of purely-Kerr-driven filamentation in air and argon,” Phys. Rev. A 82, 033826 (2010).
[CrossRef]

W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, “Generalized Miller formulas,” Opt. Express 18, 6613–6620 (2010).
[CrossRef] [PubMed]

Faucher, O.

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J.-P. Wolf, and O. Faucher, “Transition from plasma-driven to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011).
[CrossRef] [PubMed]

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “From higher-order Kerr nonlinearities to quantitative modeling of third and fifth harmonic generation in argon,” Opt. Lett. 36, 828–830 (2011).
[CrossRef] [PubMed]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components: erratum,” Opt. Express 18, 3011–3012 (2010).
[CrossRef]

W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, O. Faucher, B. Lavorel, J. Kasparian, and J.-P. Wolf, “Spectral dependence of purely-Kerr-driven filamentation in air and argon,” Phys. Rev. A 82, 033826 (2010).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-Order Kerr Terms Allow Ionization-Free Filamentation in Gases,” Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components,” Opt. Express 17, 13429–13434 (2009).
[CrossRef] [PubMed]

Fus, W.

Gaeta, A. L.

Henin, S.

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-Order Kerr Terms Allow Ionization-Free Filamentation in Gases,” Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

Hertz, E.

Hosseini, S.

Kasparian, J.

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “From higher-order Kerr nonlinearities to quantitative modeling of third and fifth harmonic generation in argon,” Opt. Lett. 36, 828–830 (2011).
[CrossRef] [PubMed]

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J.-P. Wolf, and O. Faucher, “Transition from plasma-driven to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011).
[CrossRef] [PubMed]

W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, “Generalized Miller formulas,” Opt. Express 18, 6613–6620 (2010).
[CrossRef] [PubMed]

W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, O. Faucher, B. Lavorel, J. Kasparian, and J.-P. Wolf, “Spectral dependence of purely-Kerr-driven filamentation in air and argon,” Phys. Rev. A 82, 033826 (2010).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-Order Kerr Terms Allow Ionization-Free Filamentation in Gases,” Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Kolesik, M.

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, “Experimental tests of the new paradigm for laser filamentation in gases,” Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef] [PubMed]

A. Teleki, E. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
[CrossRef]

M. Kolesik, E. M. Wright, and J. V. Moloney, “Femtosecond filamentation in air and higher-order nonlinearities,” Opt. Lett. 35, 2550–2552 (2010).
[CrossRef] [PubMed]

Kong, Y.

P. Tzankov, M. Roth, Y. Kong, L. Xu, and Z. Sartania, “Spatio-Temporal Characterization of the Signal Pulse-Shortening in Type II Optical Parametric Amplifier Using BBO and BIBO crystals,” in Proceedings of the Conference on Lasers and Electro Optics (2008), paper CTuE3.
[CrossRef]

Kosareva, O.

Kosma, K.

Lavorel, B.

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J.-P. Wolf, and O. Faucher, “Transition from plasma-driven to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011).
[CrossRef] [PubMed]

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “From higher-order Kerr nonlinearities to quantitative modeling of third and fifth harmonic generation in argon,” Opt. Lett. 36, 828–830 (2011).
[CrossRef] [PubMed]

W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, O. Faucher, B. Lavorel, J. Kasparian, and J.-P. Wolf, “Spectral dependence of purely-Kerr-driven filamentation in air and argon,” Phys. Rev. A 82, 033826 (2010).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components: erratum,” Opt. Express 18, 3011–3012 (2010).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-Order Kerr Terms Allow Ionization-Free Filamentation in Gases,” Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components,” Opt. Express 17, 13429–13434 (2009).
[CrossRef] [PubMed]

Loriot, V.

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-Order Kerr Terms Allow Ionization-Free Filamentation in Gases,” Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components: erratum,” Opt. Express 18, 3011–3012 (2010).
[CrossRef]

W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, O. Faucher, B. Lavorel, J. Kasparian, and J.-P. Wolf, “Spectral dependence of purely-Kerr-driven filamentation in air and argon,” Phys. Rev. A 82, 033826 (2010).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, “Measurement of high order Kerr refractive index of major air components,” Opt. Express 17, 13429–13434 (2009).
[CrossRef] [PubMed]

Makarov, V.

Milchberg, H. M.

J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, “Optical nonlinearity in Ar and N2 near the ionization threshold,” Phys. Rev. Lett. 107, 103901 (2011).
[CrossRef] [PubMed]

J. K. Wahlstrand and H. M. Milchberg, “Effect of a plasma grating on pump-probe experiments near the ionization threshold in gases,” Opt. Lett. 36, 3822–3824 (2011).
[CrossRef] [PubMed]

Y.-H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[CrossRef]

Mizrahi, V.

V. Mizrahi and D. P. Chelton, “Dispersion of nonlinear susceptibilities of Ar, N2, and O2 measured and compared,” Phys. Rev. Lett. 55, 696–699 (1985).
[CrossRef] [PubMed]

Moloney, J. V.

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, “Experimental tests of the new paradigm for laser filamentation in gases,” Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef] [PubMed]

M. Kolesik, E. M. Wright, and J. V. Moloney, “Femtosecond filamentation in air and higher-order nonlinearities,” Opt. Lett. 35, 2550–2552 (2010).
[CrossRef] [PubMed]

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

Nuter, R.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Oral, E.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and refocusing of intense femtosecond laser pulses in nitrogen gas,” Appl. Phys. B 73, 287–290 (2001).

Panov, N.

Petit, Y.

W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, O. Faucher, B. Lavorel, J. Kasparian, and J.-P. Wolf, “Spectral dependence of purely-Kerr-driven filamentation in air and argon,” Phys. Rev. A 82, 033826 (2010).
[CrossRef]

W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, “Generalized Miller formulas,” Opt. Express 18, 6613–6620 (2010).
[CrossRef] [PubMed]

Polynkin, P.

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, “Experimental tests of the new paradigm for laser filamentation in gases,” Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef] [PubMed]

Popov, A. M.

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of a gaseous atomic medium in the field of an ultraintense femtosecond laser pulse,” J. Ex. Theor. Phys. Lett. 94, 559–564 (2011) (in Russian, English translation in press).

Roth, M.

P. Tzankov, M. Roth, Y. Kong, L. Xu, and Z. Sartania, “Spatio-Temporal Characterization of the Signal Pulse-Shortening in Type II Optical Parametric Amplifier Using BBO and BIBO crystals,” in Proceedings of the Conference on Lasers and Electro Optics (2008), paper CTuE3.
[CrossRef]

Roy, G.

Sartania, Z.

P. Tzankov, M. Roth, Y. Kong, L. Xu, and Z. Sartania, “Spatio-Temporal Characterization of the Signal Pulse-Shortening in Type II Optical Parametric Amplifier Using BBO and BIBO crystals,” in Proceedings of the Conference on Lasers and Electro Optics (2008), paper CTuE3.
[CrossRef]

Scalora, M.

N. Aközbek, M. Scalora, C. Bowden, and S. L. Chin, “White-light continuum generation and filamentation during the propagation of ultra-short laser pulses in air,” Opt. Commun. 191, 353–362 (2001).
[CrossRef]

Schmid, W. E.

Schrauth, S. E.

Shim, B.

Skupin, S.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Steinmeyer, G.

C. Bree, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).

Talebpour, A.

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

Taylor, J. H.

Teleki, A.

A. Teleki, E. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
[CrossRef]

Tikhonova, O. V.

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of a gaseous atomic medium in the field of an ultraintense femtosecond laser pulse,” J. Ex. Theor. Phys. Lett. 94, 559–564 (2011) (in Russian, English translation in press).

Trushin, S. A.

Tzankov, P.

P. Tzankov, M. Roth, Y. Kong, L. Xu, and Z. Sartania, “Spatio-Temporal Characterization of the Signal Pulse-Shortening in Type II Optical Parametric Amplifier Using BBO and BIBO crystals,” in Proceedings of the Conference on Lasers and Electro Optics (2008), paper CTuE3.
[CrossRef]

Varma, S.

Y.-H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[CrossRef]

Vieillard, T.

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-Order Kerr Terms Allow Ionization-Free Filamentation in Gases,” Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

Vijayalakshmi, K.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and refocusing of intense femtosecond laser pulses in nitrogen gas,” Appl. Phys. B 73, 287–290 (2001).

Vinco¸tte, A.

A. Vinco̧tte and L. Bergé, “χ(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,”Phys. Rev. A 70, 061802(R) (2004).
[CrossRef]

Volkova, E. A.

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of a gaseous atomic medium in the field of an ultraintense femtosecond laser pulse,” J. Ex. Theor. Phys. Lett. 94, 559–564 (2011) (in Russian, English translation in press).

Wahlstrand, J. K.

J. K. Wahlstrand and H. M. Milchberg, “Effect of a plasma grating on pump-probe experiments near the ionization threshold in gases,” Opt. Lett. 36, 3822–3824 (2011).
[CrossRef] [PubMed]

J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, “Optical nonlinearity in Ar and N2 near the ionization threshold,” Phys. Rev. Lett. 107, 103901 (2011).
[CrossRef] [PubMed]

Wang, T.

Wolf, J.-P.

P. Béjot, E. Hertz, B. Lavorel, J. Kasparian, J.-P. Wolf, and O. Faucher, “From higher-order Kerr nonlinearities to quantitative modeling of third and fifth harmonic generation in argon,” Opt. Lett. 36, 828–830 (2011).
[CrossRef] [PubMed]

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J.-P. Wolf, and O. Faucher, “Transition from plasma-driven to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011).
[CrossRef] [PubMed]

W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, “Generalized Miller formulas,” Opt. Express 18, 6613–6620 (2010).
[CrossRef] [PubMed]

W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, O. Faucher, B. Lavorel, J. Kasparian, and J.-P. Wolf, “Spectral dependence of purely-Kerr-driven filamentation in air and argon,” Phys. Rev. A 82, 033826 (2010).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-Order Kerr Terms Allow Ionization-Free Filamentation in Gases,” Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Wright, E.

A. Teleki, E. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
[CrossRef]

Wright, E. M.

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, “Experimental tests of the new paradigm for laser filamentation in gases,” Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef] [PubMed]

M. Kolesik, E. M. Wright, and J. V. Moloney, “Femtosecond filamentation in air and higher-order nonlinearities,” Opt. Lett. 35, 2550–2552 (2010).
[CrossRef] [PubMed]

Xu, L.

P. Tzankov, M. Roth, Y. Kong, L. Xu, and Z. Sartania, “Spatio-Temporal Characterization of the Signal Pulse-Shortening in Type II Optical Parametric Amplifier Using BBO and BIBO crystals,” in Proceedings of the Conference on Lasers and Electro Optics (2008), paper CTuE3.
[CrossRef]

Yang, J.

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

Yates, H. W.

Yuan, S.

Appl. Phys. B (1)

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, “Intensity clamping and refocusing of intense femtosecond laser pulses in nitrogen gas,” Appl. Phys. B 73, 287–290 (2001).

J. Ex. Theor. Phys. Lett. (1)

E. A. Volkova, A. M. Popov, and O. V. Tikhonova, “Nonlinear polarization response of a gaseous atomic medium in the field of an ultraintense femtosecond laser pulse,” J. Ex. Theor. Phys. Lett. 94, 559–564 (2011) (in Russian, English translation in press).

J. Opt. Soc. Am. (1)

Opt. Commun. (2)

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

N. Aközbek, M. Scalora, C. Bowden, and S. L. Chin, “White-light continuum generation and filamentation during the propagation of ultra-short laser pulses in air,” Opt. Commun. 191, 353–362 (2001).
[CrossRef]

Opt. Express (4)

Opt. Lett. (5)

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
[CrossRef]

Phys. Rev. A (4)

A. Couairon, “Dynamics of femtosecond filamentation from saturation of self-focusing laser pulses,” Phys. Rev. A 68, 015801 (2003).
[CrossRef]

A. Vinco̧tte and L. Bergé, “χ(5) susceptibility stabilizes the propagation of ultrashort laser pulses in air,”Phys. Rev. A 70, 061802(R) (2004).
[CrossRef]

A. Teleki, E. Wright, and M. Kolesik, “Microscopic model for the higher-order nonlinearity in optical filaments,” Phys. Rev. A 82, 065801 (2010).
[CrossRef]

W. Ettoumi, P. Béjot, Y. Petit, V. Loriot, O. Faucher, B. Lavorel, J. Kasparian, and J.-P. Wolf, “Spectral dependence of purely-Kerr-driven filamentation in air and argon,” Phys. Rev. A 82, 033826 (2010).
[CrossRef]

Phys. Rev. Lett. (7)

J. K. Wahlstrand, Y.-H. Cheng, Y.-H. Chen, and H. M. Milchberg, “Optical nonlinearity in Ar and N2 near the ionization threshold,” Phys. Rev. Lett. 107, 103901 (2011).
[CrossRef] [PubMed]

V. Mizrahi and D. P. Chelton, “Dispersion of nonlinear susceptibilities of Ar, N2, and O2 measured and compared,” Phys. Rev. Lett. 55, 696–699 (1985).
[CrossRef] [PubMed]

C. Bree, A. Demircan, and G. Steinmeyer, “Saturation of the all-optical Kerr effect,” Phys. Rev. Lett. 106, 183902 (2011).

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, “Higher-Order Kerr Terms Allow Ionization-Free Filamentation in Gases,” Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

P. Polynkin, M. Kolesik, E. M. Wright, and J. V. Moloney, “Experimental tests of the new paradigm for laser filamentation in gases,” Phys. Rev. Lett. 106, 153902 (2011).
[CrossRef] [PubMed]

Y.-H. Chen, S. Varma, T. M. Antonsen, and H. M. Milchberg, “Direct measurement of the electron density of extended femtosecond laser pulse-induced filaments,” Phys. Rev. Lett. 105, 215005 (2010).
[CrossRef]

P. Béjot, E. Hertz, J. Kasparian, B. Lavorel, J.-P. Wolf, and O. Faucher, “Transition from plasma-driven to Kerr-driven laser filamentation,” Phys. Rev. Lett. 106, 243902 (2011).
[CrossRef] [PubMed]

Proceedings of the Conference on Lasers and Electro Optics (1)

P. Tzankov, M. Roth, Y. Kong, L. Xu, and Z. Sartania, “Spatio-Temporal Characterization of the Signal Pulse-Shortening in Type II Optical Parametric Amplifier Using BBO and BIBO crystals,” in Proceedings of the Conference on Lasers and Electro Optics (2008), paper CTuE3.
[CrossRef]

Rep. Prog. Phys. (1)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized, optically transparent media,” Rep. Prog. Phys. 70, 1633–1713 (2007).
[CrossRef]

Other (2)

S. L. Chin, Femtosecond Laser Filamentation (Springer, New York, 2010).
[CrossRef]

Data for refractive index of air, corrected for humidity and ambient temperature, is available at the NIST website at http://emtoolbox.nist.gov/Wavelength/Elden.asp , for the wavelength range between 300 nm and 1.7 μm. The value for the index at 2.2 μm wavelength that we used in the paper was evaluated by extrapolating the available data using an 8th-order rational function fit.

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Figures (2)

Fig. 1
Fig. 1

Experimental setup.

Fig. 2
Fig. 2

Normalized spectra of the generated third and fifth harmonics on linear scale.

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