Abstract

Experimentally measured conical emission rings on the blue side of the filament supercontinuum of a 800nm 50fs pulse in air are reproduced in simulations with plasma and the third-order Kerr as the nonlinear terms. This agreement indicates plasma as the dominant mechanism arresting the self-focusing collapse. The higher order Kerr terms with the recently measured coefficients stop the collapse at a lower intensity than the plasma does and lead to the spherical angle-wavelength spectrum without blueshifted rings.

© 2011 Optical Society of America

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M. Kolesik, D. Mirell, J.-C. Diels, and J. V. Moloney, Opt. Lett. 35, 3685 (2010).
[CrossRef] [PubMed]

P. Bejot, 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]

2009 (3)

2008 (2)

2007 (1)

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

2006 (2)

2005 (1)

2001 (1)

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

1999 (1)

A. Talebpour, J. Yang, and S. L. Chin, Opt. Commun. 163, 29 (1999).
[CrossRef]

1994 (1)

1966 (1)

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, Sov. Phys. JETP 23, 924 (1966).

Akozbek, N.

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

Altucci, C.

Amoruso, S.

Bai, X.

H. Cai, J. Wu, P. Lu, X. Bai, L. Ding, and H. Zeng, Phys. Rev. A 80, 051802 (2009).
[CrossRef]

Bejot, P.

P. Bejot, 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.

Binhammer, T.

Bowden, C. M.

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

Bragheri, F.

Bruzzese, R.

Cai, H.

H. Cai, J. Wu, Y. Peng, and H. Zeng, Opt. Express 17, 5822 (2009).
[PubMed]

H. Cai, J. Wu, P. Lu, X. Bai, L. Ding, and H. Zeng, Phys. Rev. A 80, 051802 (2009).
[CrossRef]

Châteauneuf, M.

Chin, S. L.

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

A. Talebpour, J. Yang, and S. L. Chin, Opt. Commun. 163, 29 (1999).
[CrossRef]

Couairon, A.

Degiorgio, V.

Di Trapani, P.

Diels, J.-C.

Ding, L.

H. Cai, J. Wu, P. Lu, X. Bai, L. Ding, and H. Zeng, Phys. Rev. A 80, 051802 (2009).
[CrossRef]

Dubietis, A.

Dubois, J.

Faccio, D.

Faucher, O.

P. Bejot, 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]

Henin, S.

P. Bejot, 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. Bejot, 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]

Kasparian, J.

P. Bejot, 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]

Kolesik, M.

Kovacev, M.

Kuchinskas, E.

Lavorel, B.

P. Bejot, 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]

Loriot, V.

P. Bejot, 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]

Lu, P.

H. Cai, J. Wu, P. Lu, X. Bai, L. Ding, and H. Zeng, Phys. Rev. A 80, 051802 (2009).
[CrossRef]

Luther, G. G.

Mathieu, P.

Mirell, D.

Moloney, J. V.

Morgner, U.

Mysyrowicz, A.

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

Newell, A. C.

Nuter, R.

Peng, Y.

Perelomov, A. M.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, Sov. Phys. JETP 23, 924 (1966).

Popov, V. S.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, Sov. Phys. JETP 23, 924 (1966).

Porras, M. A.

Ross, V.

Schulz, E.

Steingrube, D.

Steinmeyer, G.

Stibenz, G.

Talebpour, A.

A. Talebpour, J. Yang, and S. L. Chin, Opt. Commun. 163, 29 (1999).
[CrossRef]

Terent’ev, M. V.

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, Sov. Phys. JETP 23, 924 (1966).

Théberge, F.

Velotta, R.

Vieillard, T.

P. Bejot, 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]

Vockerodt, T.

Wang, X.

Wolf, J.-P.

P. Bejot, 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]

Wright, E. M.

Wu, J.

H. Cai, J. Wu, P. Lu, X. Bai, L. Ding, and H. Zeng, Phys. Rev. A 80, 051802 (2009).
[CrossRef]

H. Cai, J. Wu, Y. Peng, and H. Zeng, Opt. Express 17, 5822 (2009).
[PubMed]

Xia, J.

Yang, J.

A. Talebpour, J. Yang, and S. L. Chin, Opt. Commun. 163, 29 (1999).
[CrossRef]

Zeng, H.

H. Cai, J. Wu, Y. Peng, and H. Zeng, Opt. Express 17, 5822 (2009).
[PubMed]

H. Cai, J. Wu, P. Lu, X. Bai, L. Ding, and H. Zeng, Phys. Rev. A 80, 051802 (2009).
[CrossRef]

Zhavoronkov, N.

J. Opt. Soc. Am. B (1)

Opt. Commun. (2)

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

A. Talebpour, J. Yang, and S. L. Chin, Opt. Commun. 163, 29 (1999).
[CrossRef]

Opt. Express (3)

Opt. Lett. (5)

Phys. Rep. (1)

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

Phys. Rev. A (1)

H. Cai, J. Wu, P. Lu, X. Bai, L. Ding, and H. Zeng, Phys. Rev. A 80, 051802 (2009).
[CrossRef]

Phys. Rev. Lett. (1)

P. Bejot, 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]

Sov. Phys. JETP (1)

A. M. Perelomov, V. S. Popov, and M. V. Terent’ev, Sov. Phys. JETP 23, 924 (1966).

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Figures (3)

Fig. 1
Fig. 1

(a), (b)  N 2 fluorescence signal in the experiment (each square is a 50-shot average with an error bar within the symbol size and less than 6% of the signal); the peak intensity from the standard [(a), triangles] and the higher order Kerr [(b), circles] model. (c)–(h) Transverse distributions of the spectral intensity and the corresponding y = 0 profiles at (c)–(e)  800 nm or (f)–(h)  700 nm for the experiment [left column (c), (f)], the standard [middle column (d), (g)], and the higher order Kerr [right column (e), (h)] models, z = 9.1 m . The beam is collimated for all plots except for the triangles in the profile beneath (g), simulated with a 6 m focal length lens.

Fig. 2
Fig. 2

Simulated transverse distributions of spectral intensity at 700 nm (a)–(c) temporal intensity (filled or circles) and (d)–(f) refractive index (rhombs) profiles; z = 9.1 m . In all plots, the filled profiles bordered by a solid line are calculated with the Kerr coefficients [7], independent of the number of Kerr terms considered. Profiles marked by open circles show the robustness analysis. Left column (a), (d) the standard model Δ n k = n 2 I (filled); Δ n k = n 2 I + ( n 4 / 5 ) I 2 (circles). Inset in (a) magnified conical rings. Middle column (b), (e) reduced higher order model Δ n k = n 2 I + n 4 I 2 (filled); Δ n k = n 2 I + ( n 4 / 1.5 ) I 2 (circles). Right column (c), (f) higher order model Δ n k = n 2 I + n 4 I 2 + n 6 I 3 + n 8 I 4 (filled); Δ n k = n 2 I + n 4 I 2 + ( n 6 / 8 ) I 3 + ( n 8 / 8 ) I 4 (circles).

Fig. 3
Fig. 3

Angle-wavelength spectra simulated based on (a) the standard, (b) the reduced, and (c) the full higher order Kerr models. The equal-intensity contours are numbered according to log ( S / S max ) , where S max is the maximum at 800 nm for each spectrum. Distance z = 9.1 m .

Equations (1)

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2 i k 0 z E = T ^ Δ E k 0 ( k τ τ E + i k τ τ τ E / 3 ) + 2 k 0 2 / n 0 ( T ^ + Δ n k + T ^ Δ n p ) E i k 0 α E ,

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