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Dynamics of elliptical beams in the anomalous group-velocity dispersion regimeBonggu Shim, Samuel E. Schrauth, Luat T. Vuong, Yoshitomo Okawachi, and Alexander L. Gaeta »View Author Affiliations
Bonggu Shim,1,3,*
Samuel E. Schrauth,1,3
Luat T. Vuong,1,2
Yoshitomo Okawachi,1
and Alexander L. Gaeta1
1School of Applied and Engineering Physics, Cornell University, Ithaca, NY 14853, USA 2Current address: Physics Department, CUNY, Queens College, Flushing, NY 11367, USA 3These authors contributed equally to this work *Corresponding author: bgs43@cornell.edu |
Optics Express, Vol. 19, Issue 10, pp. 9139-9146 (2011)
http://dx.doi.org/10.1364/OE.19.009139
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Abstract
We investigate 3D spatio-temporal focusing of elliptically-shaped beams in a bulk medium with Kerr nonlinearity and anomalous group-velocity dispersion (GVD). Strong space-time localization of the mode is observed through multi-filamentation with temporal compression by a factor of 3. This behavior is in contrast to the near-zero GVD regime in which minimal pulse temporal compression is observed. Our theoretical simulations qualitatively reproduce the experimental results showing the highly localized spatio-temporal profile in the anomalous-GVD regime, which contrasts to the weakly localized pulse in the normal-GVD regime.
© 2011 OSA
OCIS Codes
(190.5530) Nonlinear optics : Pulse propagation and temporal solitons
(190.7110) Nonlinear optics : Ultrafast nonlinear optics
ToC Category:
Nonlinear Optics
History
Original Manuscript: February 8, 2011
Revised Manuscript: March 31, 2011
Manuscript Accepted: April 19, 2011
Published: April 26, 2011
Citation
Bonggu Shim, Samuel E. Schrauth, Luat T. Vuong, Yoshitomo Okawachi, and Alexander L. Gaeta, "Dynamics of elliptical beams in the anomalous group-velocity dispersion regime," Opt. Express 19, 9139-9146 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-10-9139
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References
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- X. Liu, K. Beckwitt, and F. W. Wise, “Transverse instability of optical spatiotemporal solitons in quadratic media,” Phys. Rev. Lett. 85(9), 1871–1874 (2000). [CrossRef] [PubMed]
- L. BergéS. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007). [CrossRef]
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- V. Y. Fedorov, V. P. Kandidov, O. G. Kosareva, N. Akozbek, M. Scalora, and S. L. Chin, “Filamentation of a femtosecond laser pulse with the initial beam ellipticity,” Laser Phys. 16(8), 1227–1234 (2006). [CrossRef]
- A. Saliminia, S. L. Chin, and R. Vallée, “Ultra-broad and coherent white light generation in silica glass by focused femtosecond pulses at 1.5 um,” Opt. Express 13(15), 5731–5738 (2005). [CrossRef] [PubMed]
- 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, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications and new challenges,” Can. J. Phys. 83(9), 863–905 (2005). [CrossRef]
- A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007). [CrossRef]
- C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004). [CrossRef]
- L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002). [CrossRef] [PubMed]
- P. Audebert, Ph. Daguzan, A. Dos Santos, J. C. Gauthier, J. P. Geindre, S. Guizard, G. Hamoniaux, K. Krastev, P. Martin, G. Petite, and A. Antonetti, “Space-time observation of an electron gas in SiO2.,” Phys. Rev. Lett. 73(14), 1990–1993 (1994). [CrossRef] [PubMed]
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- P. Audebert, Ph. Daguzan, A. Dos Santos, J. C. Gauthier, J. P. Geindre, S. Guizard, G. Hamoniaux, K. Krastev, P. Martin, G. Petite, and A. Antonetti, “Space-time observation of an electron gas in SiO2.,” Phys. Rev. Lett. 73(14), 1990–1993 (1994). [CrossRef] [PubMed]
- D. Majus, V. Jukna, G. Tamošauskas, G. Valiulis, and A. Dubietis, “Three-dimensional mapping of multiple filament arrays,” Phys. Rev. A 81(4), 043811 (2010). [CrossRef]
- D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self-focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A 79(3), 033843 (2009). [CrossRef]
- M. A. Porras, A. Dubietis, A. Matijošius, R. Piskarskas, F. Bragheri, A. Averchi, and P. D. Trapani, “Characterization of conical emission of light filaments in media with anomalous dispersion,” J. Opt. Soc. Am. B 24(3), 581–584 (2007). [CrossRef]
- A. Dubietis, G. Tamosauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29(10), 1126–1128 (2004). [CrossRef] [PubMed]
- G. Tamošauskas, A. Dubietis, and G. Valiulis, “Soliton-effect optical pulse compression in bulk media with χ(3) nonlinerity,” Nonlinear Anal. Modelling Control 5, 99–105 (2000).
- S. Carrasco, S. Polyakov, H. Kim, L. Jankovic, G. I. Stegeman, J. P. Torres, L. Torner, M. Katz, and D. Eger, “Observation of multiple soliton generation mediated by amplification of asymmetries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046616 (2003). [CrossRef] [PubMed]
- H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87(4), 043902 (2001). [CrossRef] [PubMed]
- G. Fibich, S. Eisenmann, B. Ilan, Y. Erlich, M. Fraenkel, Z. Henis, A. L. Gaeta, and A. Zigler, “Self-focusing distance of very high power laser pulses,” Opt. Express 13(15), 5897–5903 (2005). [CrossRef] [PubMed]
- G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamentation in air,” Opt. Lett. 29(15), 1772–1774 (2004). [CrossRef] [PubMed]
- L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006). [CrossRef] [PubMed]
- V. Y. Fedorov, V. P. Kandidov, O. G. Kosareva, N. Akozbek, M. Scalora, and S. L. Chin, “Filamentation of a femtosecond laser pulse with the initial beam ellipticity,” Laser Phys. 16(8), 1227–1234 (2006). [CrossRef]
- V. P. Kandidov and V. Y. Fedorov, “Properties of self-focusing of elliptic beams,” Quantum Electron. 34, 1163–1168 (2004). [CrossRef]
- L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006). [CrossRef] [PubMed]
- G. Fibich, S. Eisenmann, B. Ilan, Y. Erlich, M. Fraenkel, Z. Henis, A. L. Gaeta, and A. Zigler, “Self-focusing distance of very high power laser pulses,” Opt. Express 13(15), 5897–5903 (2005). [CrossRef] [PubMed]
- G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamentation in air,” Opt. Lett. 29(15), 1772–1774 (2004). [CrossRef] [PubMed]
- A. Dubietis, G. Tamosauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29(10), 1126–1128 (2004). [CrossRef] [PubMed]
- G. Fibich and B. Ilan, “Self-focusing of circularly polarized beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(3), 036622 (2003). [CrossRef] [PubMed]
- K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the Townes profile,” Phys. Rev. Lett. 90(20), 203902 (2003). [CrossRef] [PubMed]
- G. Fibich and B. Ilan, “Self-focusing of elliptical beams:an example of the failure of the aberrationless approximation,” J. Opt. Soc. Am. B 17(10), 1749–1758 (2000). [CrossRef]
- G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25(5), 335–337 (2000). [CrossRef]
- L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002). [CrossRef] [PubMed]
- J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003). [CrossRef] [PubMed]
- L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006). [CrossRef] [PubMed]
- T. D. Grow and A. L. Gaeta, “Dependence of multiple filamentation on beam ellipticity,” Opt. Express 13(12), 4594–4599 (2005). [CrossRef] [PubMed]
- G. Fibich, S. Eisenmann, B. Ilan, Y. Erlich, M. Fraenkel, Z. Henis, A. L. Gaeta, and A. Zigler, “Self-focusing distance of very high power laser pulses,” Opt. Express 13(15), 5897–5903 (2005). [CrossRef] [PubMed]
- K. D. Moll and A. L. Gaeta, “Role of dispersion in multiple-collapse dynamics,” Opt. Lett. 29(9), 995–997 (2004). [CrossRef] [PubMed]
- K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the Townes profile,” Phys. Rev. Lett. 90(20), 203902 (2003). [CrossRef] [PubMed]
- A. L. Gaeta, “Optics. Collapsing light really shines,” Science 301(5629), 54–55 (2003). [CrossRef] [PubMed]
- G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25(5), 335–337 (2000). [CrossRef]
- J. K. Ranka, A. L. Gaeta, A. Baltuska, M. S. Pshenichnikov, and D. A. Wiersma, “Autocorrelation measurement of 6-fs pulses based on the two-photon-induced photocurrent in a GaAsP photodiode,” Opt. Lett. 22(17), 1344–1346 (1997). [CrossRef]
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Appl. Phys. B
- C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004). [CrossRef]
Can. J. Phys.
- 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, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications and new challenges,” Can. J. Phys. 83(9), 863–905 (2005). [CrossRef]
IEEE J. Quantum Electron.
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J. Opt. Soc. Am. B
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JETP Lett.
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Laser Phys.
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Nonlinear Anal. Modelling Control
- G. Tamošauskas, A. Dubietis, and G. Valiulis, “Soliton-effect optical pulse compression in bulk media with χ(3) nonlinerity,” Nonlinear Anal. Modelling Control 5, 99–105 (2000).
Opt. Express
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- A. Saliminia, S. L. Chin, and R. Vallée, “Ultra-broad and coherent white light generation in silica glass by focused femtosecond pulses at 1.5 um,” Opt. Express 13(15), 5731–5738 (2005). [CrossRef] [PubMed]
- J.-P. Bérubé, R. Vallée, M. Bernier, O. Kosareva, N. Panov, V. Kandidov, and S. L. Chin, “Self and forced periodic arrangement of multiple filaments in glass,” Opt. Express 18(3), 1801–1819 (2010). [CrossRef] [PubMed]
Opt. Lett.
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- G. Fibich, S. Eisenmann, B. Ilan, and A. Zigler, “Control of multiple filamentation in air,” Opt. Lett. 29(15), 1772–1774 (2004). [CrossRef] [PubMed]
Phys. Rep.
- A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007). [CrossRef]
Phys. Rev. A
- D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self-focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A 79(3), 033843 (2009). [CrossRef]
- D. Majus, V. Jukna, G. Tamošauskas, G. Valiulis, and A. Dubietis, “Three-dimensional mapping of multiple filament arrays,” Phys. Rev. A 81(4), 043811 (2010). [CrossRef]
- J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74(4), 043801 (2006). [CrossRef]
Phys. Rev. E
- L. Bergé andS. Skupin, “Self-channeling of ultrashort laser pulses in materials with anomalous dispersion,” Phys. Rev. E 71(6), 065601(R) (2005).
Phys. Rev. E Stat. Nonlin. Soft Matter Phys.
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Phys. Rev. Lett.
- J. W. Grantham, H. M. Gibbs, G. Khitrova, J. F. Valley, and X. Jiajin, “Kaleidoscopic spatial instability: Bifurcations of optical transverse solitary waves,” Phys. Rev. Lett. 66(11), 1422–1425 (1991). [CrossRef] [PubMed]
- L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006). [CrossRef] [PubMed]
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- H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87(4), 043902 (2001). [CrossRef] [PubMed]
- K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the Townes profile,” Phys. Rev. Lett. 90(20), 203902 (2003). [CrossRef] [PubMed]
- R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964). [CrossRef]
- P. Audebert, Ph. Daguzan, A. Dos Santos, J. C. Gauthier, J. P. Geindre, S. Guizard, G. Hamoniaux, K. Krastev, P. Martin, G. Petite, and A. Antonetti, “Space-time observation of an electron gas in SiO2.,” Phys. Rev. Lett. 73(14), 1990–1993 (1994). [CrossRef] [PubMed]
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Physica D
- S. Skupin and L. Berge, “Self-guiding of femtosecond light pulses in condensed media: Plasma generation versus chromatic dispersion,” Physica D 220(1), 14–30 (2006). [CrossRef]
Pramana J. Phys.
- R. Gopal, V. Deepak, and S. Sivaramakrishnan, ““Sytematic study of spatiotemporal dynamics of intense femtosecond laser pulses in BK-7 glass,” Pramana J. Phys. 68(4), 547–569 (2007). [CrossRef]
Quantum Electron.
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Rep. Prog. Phys.
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Science
- J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003). [CrossRef] [PubMed]
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Other
- G. P. Agrawal, Nonlinear Fiber Optics, 4th ed. (Academic, San Diego, 2007).
2010, Bérubé, Opt. Express
- D. Majus, V. Jukna, G. Tamošauskas, G. Valiulis, and A. Dubietis, “Three-dimensional mapping of multiple filament arrays,” Phys. Rev. A 81(4), 043811 (2010). [CrossRef]
- D. Majus, V. Jukna, G. Valiulis, and A. Dubietis, “Generation of periodic filament arrays by self-focusing of highly elliptical ultrashort pulsed laser beams,” Phys. Rev. A 79(3), 033843 (2009). [CrossRef]
- A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441(2-4), 47–189 (2007). [CrossRef]
- L. BergéS. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007). [CrossRef]
- L. BergéS. Skupin, R. Nuter, J. Kasparian, and J.-P. Wolf, “Ultrashort filaments of light in weakly ionized optically transparent media,” Rep. Prog. Phys. 70(10), 1633–1713 (2007). [CrossRef]
- R. Gopal, V. Deepak, and S. Sivaramakrishnan, ““Sytematic study of spatiotemporal dynamics of intense femtosecond laser pulses in BK-7 glass,” Pramana J. Phys. 68(4), 547–569 (2007). [CrossRef]
- S. Skupin and L. Berge, “Self-guiding of femtosecond light pulses in condensed media: Plasma generation versus chromatic dispersion,” Physica D 220(1), 14–30 (2006). [CrossRef]
- J. Liu, R. Li, and Z. Xu, “Few-cycle spatiotemporal soliton wave excited by filamentation of a femtosecond laser pulse in materials with anomalous dispersion,” Phys. Rev. A 74(4), 043801 (2006). [CrossRef]
- V. Y. Fedorov, V. P. Kandidov, O. G. Kosareva, N. Akozbek, M. Scalora, and S. L. Chin, “Filamentation of a femtosecond laser pulse with the initial beam ellipticity,” Laser Phys. 16(8), 1227–1234 (2006). [CrossRef]
- L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006). [CrossRef] [PubMed]
- 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, “The propagation of powerful femtosecond laser pulses in optical media: physics, applications and new challenges,” Can. J. Phys. 83(9), 863–905 (2005). [CrossRef]
- L. Bergé andS. Skupin, “Self-channeling of ultrashort laser pulses in materials with anomalous dispersion,” Phys. Rev. E 71(6), 065601(R) (2005).
- L. Bergé andS. Skupin, “Self-channeling of ultrashort laser pulses in materials with anomalous dispersion,” Phys. Rev. E 71(6), 065601(R) (2005).
- C. P. Hauri, W. Kornelis, F. W. Helbing, A. Heinrich, A. Couairon, A. Mysyrowicz, J. Biegert, and U. Keller, “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Appl. Phys. B 79(6), 673–677 (2004). [CrossRef]
- V. P. Kandidov and V. Y. Fedorov, “Properties of self-focusing of elliptic beams,” Quantum Electron. 34, 1163–1168 (2004). [CrossRef]
- K. D. Moll, A. L. Gaeta, and G. Fibich, “Self-similar optical wave collapse: observation of the Townes profile,” Phys. Rev. Lett. 90(20), 203902 (2003). [CrossRef] [PubMed]
- G. Fibich and B. Ilan, “Self-focusing of circularly polarized beams,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(3), 036622 (2003). [CrossRef] [PubMed]
- S. Carrasco, S. Polyakov, H. Kim, L. Jankovic, G. I. Stegeman, J. P. Torres, L. Torner, M. Katz, and D. Eger, “Observation of multiple soliton generation mediated by amplification of asymmetries,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 67(4), 046616 (2003). [CrossRef] [PubMed]
- J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. Andre, A. Mysyrowicz, R. Sauerbrey, J.-P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301(5629), 61–64 (2003). [CrossRef] [PubMed]
- A. L. Gaeta, “Optics. Collapsing light really shines,” Science 301(5629), 54–55 (2003). [CrossRef] [PubMed]
- L. Sudrie, A. Couairon, M. Franco, B. Lamouroux, B. Prade, S. Tzortzakis, and A. Mysyrowicz, “Femtosecond laser-induced damage and filamentary propagation in fused silica,” Phys. Rev. Lett. 89(18), 186601 (2002). [CrossRef] [PubMed]
- H. S. Eisenberg, R. Morandotti, Y. Silberberg, S. Bar-Ad, D. Ross, and J. S. Aitchison, “Kerr spatiotemporal self-focusing in a planar glass waveguide,” Phys. Rev. Lett. 87(4), 043902 (2001). [CrossRef] [PubMed]
- X. Liu, K. Beckwitt, and F. W. Wise, “Transverse instability of optical spatiotemporal solitons in quadratic media,” Phys. Rev. Lett. 85(9), 1871–1874 (2000). [CrossRef] [PubMed]
- G. Tamošauskas, A. Dubietis, and G. Valiulis, “Soliton-effect optical pulse compression in bulk media with χ(3) nonlinerity,” Nonlinear Anal. Modelling Control 5, 99–105 (2000).
- X. Liu, L. J. Qian, and F. W. Wise, “Generation of optical spatiotemporal solitons,” Phys. Rev. Lett. 82(23), 4631–4634 (1999). [CrossRef]
- K. Kennedy, “A first-order model of computation of laser-induced breakdown thresholds in ocular and aqueous media: Part I – theory,” IEEE J. Quantum Electron. 31(12), 2241–2249 (1995). [CrossRef]
- P. Audebert, Ph. Daguzan, A. Dos Santos, J. C. Gauthier, J. P. Geindre, S. Guizard, G. Hamoniaux, K. Krastev, P. Martin, G. Petite, and A. Antonetti, “Space-time observation of an electron gas in SiO2.,” Phys. Rev. Lett. 73(14), 1990–1993 (1994). [CrossRef] [PubMed]
- J. W. Grantham, H. M. Gibbs, G. Khitrova, J. F. Valley, and X. Jiajin, “Kaleidoscopic spatial instability: Bifurcations of optical transverse solitary waves,” Phys. Rev. Lett. 66(11), 1422–1425 (1991). [CrossRef] [PubMed]
- V. I. Bespalov and V. I. Talanov, “Filamentary structure of light beams in non-linear liquids,” JETP Lett. 3, 307–310 (1966).
- R. Y. Chiao, E. Garmire, and C. H. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964). [CrossRef]
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