Abstract

It is demonstrated numerically that the supercontinuum generation and third-harmonic generation that accompany optical filamentation in nonlinear dispersive bulk media can be described as first-order scattering processes akin to the first Born approximation. In particular, for an incident ultrashort pulse the angularly resolved spectrum of the transmitted pulse is shown to be accurately determined using first-order scattering of the incident field from the nonlinearly modified refractive index due to the optical filament. Thus, although an optical filament is a highly nonlinear object, the accompanying supercontinuum generation and third-harmonic generation are driven parametrically by the filament and have negligible back action upon it.

© 2007 Optical Society of America

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References

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2007 (2)

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

S. L. Chin, F. Theberge, and W. Liu, Appl. Phys. B 86, 477 (2007).
[CrossRef]

2006 (5)

M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, Appl. Phys. B 85, 531 (2006).
[CrossRef]

D. Faccio, A. Averchi, A. Couairon, A. Dubietis, R. Piskarskas, A. Matijosius, F. Bragheri, M. A. Porras, A. Piskarskas, and P. D. Trapani, Phys. Rev. E 74, 047603 (2006).
[CrossRef]

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. D. Trapani, Opt. Commun. 265, 672 (2006).
[CrossRef]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. D. Trapani, Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

A. Couairon, E. Gaizauskas, D. Faccio, A. Dubietis, and P. D. Trapani, Phys. Rev. E 73, 016608 (2006).
[CrossRef]

2005 (7)

M. A. Porras, A. Parola, and P. D. Trapani, J. Opt. Soc. Am. B 22, 1406 (2005).
[CrossRef]

M. Kolesik, E. M. Wright, and J. V. Moloney, Opt. Express 13, 10729 (2005).
[CrossRef] [PubMed]

F. Theberge, N. Akozbek, W. Liu, J. F. Gravel, and S. L. Chin, Opt. Commun. 245, 399 (2005).
[CrossRef]

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarskas, A. Varanavicius, E. Gaizauskas, A. Piskarskas, A. Couairon, and P. D. Trapani, Phys. Rev. E 72, 037601 (2005).
[CrossRef]

D. Faccio, P. D. Trapani, S. Minardi, A. Bramati, F. Bragheri, C. Liberale, V. Degiorgio, A. Dubietis, and A. Matijosius, J. Opt. Soc. Am. B 22, 862 (2005).
[CrossRef]

F. Theberge, W. Liu, Q. Luo, and S. L. Chin, Appl. Phys. B 80, 221 (2005).
[CrossRef]

L. Berge, S. Skupin, G. Mejean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, Phys. Rev. E 71, 016602 (2005).
[CrossRef]

2004 (2)

M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

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

2003 (3)

N. Akozbek, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, Appl. Phys. B 77, 177 (2003).
[CrossRef]

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. Andre, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef] [PubMed]

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
[CrossRef] [PubMed]

2002 (2)

N. Akozbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, Phys. Rev. Lett. 89, 143901 (2002).
[CrossRef] [PubMed]

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

2001 (1)

I. S. Golubtsov, V. P. Kandidov, and O. G. Kosareva, Atmos. Oceanic Opt. 14, 303 (2001).

2000 (1)

A. L. Gaeta, Phys. Rev. Lett. 84, 3582 (2000).
[CrossRef] [PubMed]

1997 (1)

1993 (1)

Appl. Opt. (1)

Appl. Phys. B (4)

M. Kolesik, E. M. Wright, A. Becker, and J. V. Moloney, Appl. Phys. B 85, 531 (2006).
[CrossRef]

F. Theberge, W. Liu, Q. Luo, and S. L. Chin, Appl. Phys. B 80, 221 (2005).
[CrossRef]

S. L. Chin, F. Theberge, and W. Liu, Appl. Phys. B 86, 477 (2007).
[CrossRef]

N. Akozbek, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, Appl. Phys. B 77, 177 (2003).
[CrossRef]

Atmos. Oceanic Opt. (1)

I. S. Golubtsov, V. P. Kandidov, and O. G. Kosareva, Atmos. Oceanic Opt. 14, 303 (2001).

J. Opt. Soc. Am. B (2)

J. Opt. Technol. (1)

Opt. Commun. (2)

D. Faccio, M. A. Porras, A. Dubietis, G. Tamosauskas, E. Kucinskas, A. Couairon, and P. D. Trapani, Opt. Commun. 265, 672 (2006).
[CrossRef]

F. Theberge, N. Akozbek, W. Liu, J. F. Gravel, and S. L. Chin, Opt. Commun. 245, 399 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rep. (1)

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

Phys. Rev. E (5)

D. Faccio, A. Averchi, A. Couairon, A. Dubietis, R. Piskarskas, A. Matijosius, F. Bragheri, M. A. Porras, A. Piskarskas, and P. D. Trapani, Phys. Rev. E 74, 047603 (2006).
[CrossRef]

L. Berge, S. Skupin, G. Mejean, J. Kasparian, J. Yu, S. Frey, E. Salmon, and J. P. Wolf, Phys. Rev. E 71, 016602 (2005).
[CrossRef]

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarskas, A. Varanavicius, E. Gaizauskas, A. Piskarskas, A. Couairon, and P. D. Trapani, Phys. Rev. E 72, 037601 (2005).
[CrossRef]

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

A. Couairon, E. Gaizauskas, D. Faccio, A. Dubietis, and P. D. Trapani, Phys. Rev. E 73, 016608 (2006).
[CrossRef]

Phys. Rev. Lett. (5)

M. Kolesik, E. M. Wright, and J. V. Moloney, Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

D. Faccio, M. A. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. D. Trapani, Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

M. Kolesik, G. Katona, J. V. Moloney, and E. M. Wright, Phys. Rev. Lett. 91, 043905 (2003).
[CrossRef] [PubMed]

N. Akozbek, A. Iwasaki, A. Becker, M. Scalora, S. L. Chin, and C. M. Bowden, Phys. Rev. Lett. 89, 143901 (2002).
[CrossRef] [PubMed]

A. L. Gaeta, Phys. Rev. Lett. 84, 3582 (2000).
[CrossRef] [PubMed]

Science (1)

J. Kasparian, M. Rodriguez, G. Mejean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y.-B. Andre, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, Science 301, 61 (2003).
[CrossRef] [PubMed]

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Figures (2)

Fig. 1
Fig. 1

Log plot of the angularly resolved power spectrum A ( k , ω ) 2 for SC generation in the anomalous GVD regime in water. Left, full simulation; right, first Born approximation.

Fig. 2
Fig. 2

SC and TH generation in air. Full simulation results (left) versus the first Born K-Ω spectrum (right).

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

E ( z , r , t ) = k , ω A ( z , k , ω ) e i ω t + i k r + i K ( ω , k ) z ,
z A ( z , k , ω ) = i ω 2 μ 0 2 K ( ω , k ) e i [ ω t k r K ( ω , k ) z ] P ( r , z , t ) d 2 r d t .
A ( k , ω ) ω c d 2 r d t d z × exp { i [ ( ω ω 0 ) t k r ( K ( ω , k ) K ( ω 0 , 0 ) ) z ] } Δ n ( z , r , t ) .

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