Abstract

On the basis of the recently published generalized Miller formulas, we derive the spectral dependence of the contribution of arbitrary-order nonlinear indices to the group-velocity index. We show that in the context of laser filamentation in gases, all experimentally accessible orders (up to the ninth-order nonlinear susceptibility χ(9) in air and χ(11) in argon) have contributions of alternative signs and similar magnitudes. Moreover, we show both analytically and numerically that the dispersion term of the nonlinear indices must be considered when computing the intensity-dependent group velocity.

© 2010 Optical Society of America

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  1. R. W. Boyd, Nonlinear Optics (Academic, 2008).
  2. S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).
    [CrossRef]
  3. L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
    [CrossRef]
  4. A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
    [CrossRef]
  5. J. Kasparian and J.-P. Wolf, Opt. Express 16, 466 (2008).
    [CrossRef] [PubMed]
  6. J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
    [CrossRef]
  7. V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 17, 13429 (2009).
    [CrossRef] [PubMed]
  8. V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 18, 3011 (2010).
    [CrossRef]
  9. R. C. Miller, Appl. Phys. Lett. 5, 17 (1964).
    [CrossRef]
  10. W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, Opt. Express 18, 6613 (2010).
    [CrossRef] [PubMed]
  11. P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
    [CrossRef] [PubMed]
  12. B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
    [CrossRef]
  13. P. Béjot, B. E. Schmidt, J. Kasparian, J.-P. Wolf, and F. Legaré, Phys. Rev. A 81, 063828 (2010).
    [CrossRef]
  14. N. Aközbek, M. Scalora, C. M. Bowden, and S. L. Chin, Opt. Commun. 191, 353 (2001).
    [CrossRef]
  15. I. S. Golubtsov and O. G. Kosareva, J. Opt. Technol. 69, 462 (2002).
    [CrossRef]
  16. R. W. Boyd and D. J. Gauthier, Science 326, 1074 (2009).
    [CrossRef] [PubMed]
  17. J. Zhang, Z. H. Lu, and L. J. Wang, Appl. Opt. 47, 3143 (2008).
    [CrossRef] [PubMed]
  18. J. Kasparian, R. Sauerbrey, and S. L. Chin, Appl. Phys. B 71, 877 (2000).
  19. A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, Appl. Phys. B 73, 287(2001).

2010 (5)

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
[CrossRef]

P. Béjot, B. E. Schmidt, J. Kasparian, J.-P. Wolf, and F. Legaré, Phys. Rev. A 81, 063828 (2010).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 18, 3011 (2010).
[CrossRef]

W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, Opt. Express 18, 6613 (2010).
[CrossRef] [PubMed]

2009 (2)

2008 (2)

2007 (2)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

2006 (1)

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

2005 (1)

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).
[CrossRef]

2002 (1)

2001 (2)

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, Appl. Phys. B 73, 287(2001).

N. Aközbek, M. Scalora, C. M. Bowden, and S. L. Chin, Opt. Commun. 191, 353 (2001).
[CrossRef]

2000 (1)

J. Kasparian, R. Sauerbrey, and S. L. Chin, Appl. Phys. B 71, 877 (2000).

1964 (1)

R. C. Miller, Appl. Phys. Lett. 5, 17 (1964).
[CrossRef]

Aközbek, N.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).
[CrossRef]

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, Appl. Phys. B 73, 287(2001).

N. Aközbek, M. Scalora, C. M. Bowden, and S. L. Chin, Opt. Commun. 191, 353 (2001).
[CrossRef]

Becker, A.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).
[CrossRef]

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, Appl. Phys. B 73, 287(2001).

Béjot, P.

P. Béjot, B. E. Schmidt, J. Kasparian, J.-P. Wolf, and F. Legaré, Phys. Rev. A 81, 063828 (2010).
[CrossRef]

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

Bergé, L.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

Bisson, E.

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
[CrossRef]

Bowden, C. M.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, Appl. Phys. B 73, 287(2001).

N. Aközbek, M. Scalora, C. M. Bowden, and S. L. Chin, Opt. Commun. 191, 353 (2001).
[CrossRef]

Boyd, R. W.

R. W. Boyd and D. J. Gauthier, Science 326, 1074 (2009).
[CrossRef] [PubMed]

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

Chin, S. L.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).
[CrossRef]

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, Appl. Phys. B 73, 287(2001).

N. Aközbek, M. Scalora, C. M. Bowden, and S. L. Chin, Opt. Commun. 191, 353 (2001).
[CrossRef]

J. Kasparian, R. Sauerbrey, and S. L. Chin, Appl. Phys. B 71, 877 (2000).

Coen, S.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Corkum, P. B.

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
[CrossRef]

Couairon, A.

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

Dudley, J. M.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Ettoumi, W.

Faucher, O.

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 18, 3011 (2010).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 17, 13429 (2009).
[CrossRef] [PubMed]

Gauthier, D. J.

R. W. Boyd and D. J. Gauthier, Science 326, 1074 (2009).
[CrossRef] [PubMed]

Genty, G.

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Giguère, M.

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
[CrossRef]

Golubtsov, I. S.

Henin, S.

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

Hertz, E.

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 18, 3011 (2010).
[CrossRef]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 17, 13429 (2009).
[CrossRef] [PubMed]

Hosseini, S. A.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).
[CrossRef]

Kandidov, V. P.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).
[CrossRef]

Kasparian, J.

P. Béjot, B. E. Schmidt, J. Kasparian, J.-P. Wolf, and F. Legaré, Phys. Rev. A 81, 063828 (2010).
[CrossRef]

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, Opt. Express 18, 6613 (2010).
[CrossRef] [PubMed]

J. Kasparian and J.-P. Wolf, Opt. Express 16, 466 (2008).
[CrossRef] [PubMed]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

J. Kasparian, R. Sauerbrey, and S. L. Chin, Appl. Phys. B 71, 877 (2000).

Kieffer, J.-C.

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
[CrossRef]

Kosareva, O. G.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).
[CrossRef]

I. S. Golubtsov and O. G. Kosareva, J. Opt. Technol. 69, 462 (2002).
[CrossRef]

Lavorel, B.

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 18, 3011 (2010).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 17, 13429 (2009).
[CrossRef] [PubMed]

Legaré, F.

P. Béjot, B. E. Schmidt, J. Kasparian, J.-P. Wolf, and F. Legaré, Phys. Rev. A 81, 063828 (2010).
[CrossRef]

Légaré, F.

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
[CrossRef]

Liu, W.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).
[CrossRef]

Loriot, V.

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 18, 3011 (2010).
[CrossRef]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

V. Loriot, E. Hertz, O. Faucher, and B. Lavorel, Opt. Express 17, 13429 (2009).
[CrossRef] [PubMed]

Lu, Z. H.

Luo, Q.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).
[CrossRef]

Miller, R. C.

R. C. Miller, Appl. Phys. Lett. 5, 17 (1964).
[CrossRef]

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

Nuter, R.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

Oral, E.

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, Appl. Phys. B 73, 287(2001).

Petit, Y.

Sauerbrey, R.

J. Kasparian, R. Sauerbrey, and S. L. Chin, Appl. Phys. B 71, 877 (2000).

Scalora, M.

N. Aközbek, M. Scalora, C. M. Bowden, and S. L. Chin, Opt. Commun. 191, 353 (2001).
[CrossRef]

Schmidt, B. E.

P. Béjot, B. E. Schmidt, J. Kasparian, J.-P. Wolf, and F. Legaré, Phys. Rev. A 81, 063828 (2010).
[CrossRef]

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
[CrossRef]

Schroeder, H.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).
[CrossRef]

Shiner, A. D.

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
[CrossRef]

Skupin, S.

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

Théberge, F.

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).
[CrossRef]

Trallero-Herrero, C.

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
[CrossRef]

Vieillard, T.

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, 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, Appl. Phys. B 73, 287(2001).

Villeneuve, D. M.

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
[CrossRef]

Wang, L. J.

Wolf, J.-P.

P. Béjot, B. E. Schmidt, J. Kasparian, J.-P. Wolf, and F. Legaré, Phys. Rev. A 81, 063828 (2010).
[CrossRef]

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
[CrossRef]

W. Ettoumi, Y. Petit, J. Kasparian, and J.-P. Wolf, Opt. Express 18, 6613 (2010).
[CrossRef] [PubMed]

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

J. Kasparian and J.-P. Wolf, Opt. Express 16, 466 (2008).
[CrossRef] [PubMed]

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

Zhang, J.

Appl. Opt. (1)

Appl. Phys. B (2)

J. Kasparian, R. Sauerbrey, and S. L. Chin, Appl. Phys. B 71, 877 (2000).

A. Becker, N. Aközbek, K. Vijayalakshmi, E. Oral, C. M. Bowden, and S. L. Chin, Appl. Phys. B 73, 287(2001).

Appl. Phys. Lett. (2)

R. C. Miller, Appl. Phys. Lett. 5, 17 (1964).
[CrossRef]

B. E. Schmidt, P. Béjot, M. Giguère, A. D. Shiner, C. Trallero-Herrero, E. Bisson, J. Kasparian, J.-P. Wolf, D. M. Villeneuve, J.-C. Kieffer, P. B. Corkum, and F. Légaré, Appl. Phys. Lett. 96, 121109 (2010).
[CrossRef]

Can. J. Phys. (1)

S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).
[CrossRef]

J. Opt. Technol. (1)

Opt. Commun. (1)

N. Aközbek, M. Scalora, C. M. Bowden, and S. L. Chin, Opt. Commun. 191, 353 (2001).
[CrossRef]

Opt. Express (4)

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, Phys. Rep. 441, 47 (2007).
[CrossRef]

Phys. Rev. A (1)

P. Béjot, B. E. Schmidt, J. Kasparian, J.-P. Wolf, and F. Legaré, Phys. Rev. A 81, 063828 (2010).
[CrossRef]

Phys. Rev. Lett. (1)

P. Béjot, J. Kasparian, S. Henin, V. Loriot, T. Vieillard, E. Hertz, O. Faucher, B. Lavorel, and J.-P. Wolf, Phys. Rev. Lett. 104, 103903 (2010).
[CrossRef] [PubMed]

Rep. Prog. Phys. (1)

L. Bergé, S. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, Rep. Prog. Phys. 70, 1633 (2007).
[CrossRef]

Rev. Mod. Phys. (1)

J. M. Dudley, G. Genty, and S. Coen, Rev. Mod. Phys. 78, 1135 (2006).
[CrossRef]

Science (1)

R. W. Boyd and D. J. Gauthier, Science 326, 1074 (2009).
[CrossRef] [PubMed]

Other (1)

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

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Figures (3)

Fig. 1
Fig. 1

Spectral dependence of the nonlinear group-velocity indices: (a) n g , 2 , (b) n g , 4 , (c) n g , 6 , and (d) n g , 8 of O 2 , N 2 , air, and Ar at 1 atm.

Fig. 2
Fig. 2

Relative error induced when neglecting the dispersion of the Kerr terms in the group velocity: (a) 1 n 2 / n g , 2 , (b) 1 n 4 / n g , 4 , (c) 1 n 6 / n g , 6 , and (d) 1 n 8 / n g , 8 of O 2 , N 2 , air, and Ar at 1 atm .

Fig. 3
Fig. 3

Influence of the higher-order indices contribution to the group-velocity index on the propagation of a 35 fs , pulse with fixed n 2 ( λ ) I in a 1-m-long hollow-core fiber filled with 1.4 bars argon: (a), (d) 250 nm , 286 μJ ; (b), (e) 400 nm , 360 μJ ; and (c), (f) 800 nm , 400 μJ .

Equations (16)

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n ( ω ) = n 0 ( ω ) + n 2 ( ω ) I + n 4 ( ω ) I 2 + = j = 0 n 2 j ( ω ) I j .
n 0 ( ω ) 1 + 1 2 χ ( 1 ) ( ω ) ,
n 2 j ( ω ) Z ( 2 j + 1 ) χ ( 2 j + 1 ) ( ω ) ,
n g ( ω ) = c v g = n ( ω ) + ω d n d ω ,
n g ( ω ) = j = 0 ( n 2 j ( ω ) + ω d n 2 j d ω ) I j j = 0 n g , 2 j I j ,
1 + j = 0 Z ( 2 j + 1 ) ( χ ( 2 j + 1 ) ( ω ) + ω d χ ( 2 j + 1 ) d ω ) I j .
n g , 0 ( ω ) 1 1 2 ( χ ( 1 ) + ω d χ ( 1 ) ( ω ) d ω ) ,
j 1 , n g , 2 j ( ω ) Z ( 2 j + 1 ) ( χ ( 2 j + 1 ) + ω d χ ( 2 j + 1 ) ( ω ) d ω ) .
χ ( 1 ) ( ω ) = N e 2 m ϵ 0 ( ω 0 2 ω 2 + i ω 0 γ ) ,
q 2 , χ ( q ) ( ω ) = N e ϵ 0 ( e m ) q Q ( q ) 1 Ω ( ω ) q + 1 ,
n g , 0 ( ω ) 1 ( n 0 ( ω ) 1 ) ω 0 2 + ω 2 + i ω 0 γ ω 0 2 ω 2 + i ω 0 γ ,
j 1 , n g , 2 j ( ω ) n 2 j ( ω ) ω 0 2 + ( 4 j + 3 ) ω 2 + i ω 0 γ Ω ( ω ) .
n g , 0 ( ω ) 1 ( n 0 ( ω ) 1 ) ω 0 2 + ω 2 ω 0 2 ω 2 ,
n g , 2 j ( ω ) n 2 j ω 0 2 + ( 4 j + 3 ) ω 2 ω 0 2 ω 2 .
n g , 2 I n g , 0 1 = n 2 I n 0 1 ω 0 2 + 7 ω 2 ω 0 2 + ω 2 ,
j 1 , n g , 2 j + 2 I j + 1 n g , 2 j I j = n 2 j + 2 I n 2 j ω 0 2 + ( 4 j + 7 ) ω 2 ω 0 2 + ( 4 j + 3 ) ω 2 .

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