Abstract

We present a new type of ring-shaped filaments featured by stationary nonlinear high-order Bessel solutions to the laser beam propagation equation. Two different regimes are identified by direct numerical simulations of the nonlinear propagation of axicon focused Gaussian beams carrying helicity in a Kerr medium with multiphoton absorption: the stable nonlinear propagation regime corresponds to a slow beam reshaping into one of the stationary nonlinear high-order Bessel solutions, called nonlinear Bessel vortices. The region of existence of nonlinear Bessel vortices is found semi-analytically. The influence of the Kerr nonlinearity and nonlinear losses on the beam shape is presented. Direct numerical simulations highlight the role of attractors played by nonlinear Bessel vortices in the stable propagation regime. Large input powers or small cone angles lead to the unstable propagation regime where nonlinear Bessel vortices break up into an helical multiple filament pattern or a more irregular structure. Nonlinear Bessel vortices are shown to be sufficiently intense to generate a ring-shaped filamentary ionized channel in the medium which is foreseen as opening the way to novel applications in laser material processing of transparent dielectrics.

© 2014 Optical Society of America

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References

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  4. P. Polesana, D. Faccio, P. Di Trapani, A. Dubietis, A. Piskarkas, A. Couairon, and M. A. Porras, “High localization, focal depth and contrast by means of nonlinear Bessel Beams,” Opt. Express 13, 6160–6167 (2005).
    [Crossref] [PubMed]
  5. P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E 73, 056612 (2006).
    [Crossref]
  6. P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A 77, 043814 (2008).
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    [Crossref]
  8. M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express,  18, 566–574 (2010).
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  9. M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.,  97, 081102 (2010).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  28. E. Gaizauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31, 80–82 (2006).
    [Crossref] [PubMed]
  29. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover PublicationsNew York, 1972).

2014 (2)

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milián, J. Carbonnel, Y. Liu, A. Couairon, and A. Mysyrowicz, “Superfilamentation in Air,” Phys. Rev. Lett. 112, 223902 (2014).
[Crossref] [PubMed]

K.-M. Lee, C. M. Kim, S. A. Sato, T. Otobe, Y. Shinohara, K. Yabana, and T. M. Jeong, “First-principles simulation of the optical response of bulk and thin-film a-quartz irradiated with an ultrashort intense laser pulse,” J. Appl. Phys. 115, 053519 (2014).
[Crossref]

2013 (3)

F. Courvoisier, J. Zhang, M.K. Bhuyan, M. Jacquot, and J.M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys. A 112 (1), 29–34 (2013).
[Crossref]

P. Polynkin, C. Ament, and J.V. Moloney, “Self-Focusing of Ultraintense Femtosecond Optical Vortices in Air,” Phys. Rev. Lett. 111, 023901 (2013).
[Crossref] [PubMed]

B. Wetzel, C. Xie, P.-A. Lacourt, J. M. Dudley, and F. Courvoisier, “Femtosecond laser fabrication of micro and nano-disks in single layer graphene using vortex Bessel beams,” Appl. Phys. Lett. 103, 241111 (2013).
[Crossref]

2012 (2)

X. Long, W. Zhao, R. Stoian, R. Hui, and G. Cheng, “Writing of stressed waveguides with tubular depressed cladding using femtosecond hollow beams,” Opt. Lett. 37, 3138–3140 (2012).
[Crossref] [PubMed]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A,  86, 013842 (2012).
[Crossref]

2011 (3)

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84021807 (2011).
[Crossref]

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. de J. Ramirez-Gongora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Special Topics 199, 5–76 (2011).
[Crossref]

S. Shiffler, P. Polynkin, and J. Moloney, “Self-focusing of femtosecond diffraction-resistant vortex beams in water,” Opt. Lett.,  36, 3834–3836 (2011).
[Crossref] [PubMed]

2010 (2)

M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express,  18, 566–574 (2010).
[Crossref] [PubMed]

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.,  97, 081102 (2010).
[Crossref]

2009 (1)

G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A: Pure Appl. Opt. 11, 013001 (2009).
[Crossref]

2008 (2)

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008).
[Crossref]

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A 77, 043814 (2008).
[Crossref]

2007 (2)

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

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett. 99 (22), 223902 (2007).
[Crossref]

2006 (2)

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E 73, 056612 (2006).
[Crossref]

E. Gaizauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31, 80–82 (2006).
[Crossref] [PubMed]

2005 (1)

2004 (2)

M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett. 93 (15), 153902 (2004).
[Crossref] [PubMed]

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, “Light Filaments without Self-Channeling,” Phys. Rev. Lett. 92, 253903 (2004).
[Crossref] [PubMed]

2001 (1)

A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 40, 1197–1199 (2001).
[Crossref]

2000 (1)

V. Jarutis, R. Paskauskas, and A. Stabinis, “Focusing of Laguerre-Gaussian beams by axicon,” Optics Commun. 184, 105–112 (2000).
[Crossref]

1987 (3)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
[Crossref] [PubMed]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Optics Commun. 64, 491–495 (1987).
[Crossref]

J. Durnin, “Exact solutions for nondiffracting beams. I. The Scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[Crossref]

Abdollahpour, D.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A,  86, 013842 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84021807 (2011).
[Crossref]

Abramowitz, M.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover PublicationsNew York, 1972).

Ament, C.

P. Polynkin, C. Ament, and J.V. Moloney, “Self-Focusing of Ultraintense Femtosecond Optical Vortices in Air,” Phys. Rev. Lett. 111, 023901 (2013).
[Crossref] [PubMed]

Bhuyan, M. K.

M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express,  18, 566–574 (2010).
[Crossref] [PubMed]

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.,  97, 081102 (2010).
[Crossref]

Bhuyan, M.K.

F. Courvoisier, J. Zhang, M.K. Bhuyan, M. Jacquot, and J.M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys. A 112 (1), 29–34 (2013).
[Crossref]

Brambilla, E.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. de J. Ramirez-Gongora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Special Topics 199, 5–76 (2011).
[Crossref]

Brelet, Y.

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milián, J. Carbonnel, Y. Liu, A. Couairon, and A. Mysyrowicz, “Superfilamentation in Air,” Phys. Rev. Lett. 112, 223902 (2014).
[Crossref] [PubMed]

Carbonnel, J.

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milián, J. Carbonnel, Y. Liu, A. Couairon, and A. Mysyrowicz, “Superfilamentation in Air,” Phys. Rev. Lett. 112, 223902 (2014).
[Crossref] [PubMed]

Cheng, G.

Corti, T.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. de J. Ramirez-Gongora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Special Topics 199, 5–76 (2011).
[Crossref]

Couairon, A.

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milián, J. Carbonnel, Y. Liu, A. Couairon, and A. Mysyrowicz, “Superfilamentation in Air,” Phys. Rev. Lett. 112, 223902 (2014).
[Crossref] [PubMed]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A,  86, 013842 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84021807 (2011).
[Crossref]

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. de J. Ramirez-Gongora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Special Topics 199, 5–76 (2011).
[Crossref]

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A 77, 043814 (2008).
[Crossref]

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

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett. 99 (22), 223902 (2007).
[Crossref]

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E 73, 056612 (2006).
[Crossref]

P. Polesana, D. Faccio, P. Di Trapani, A. Dubietis, A. Piskarkas, A. Couairon, and M. A. Porras, “High localization, focal depth and contrast by means of nonlinear Bessel Beams,” Opt. Express 13, 6160–6167 (2005).
[Crossref] [PubMed]

Courvoisier, F.

B. Wetzel, C. Xie, P.-A. Lacourt, J. M. Dudley, and F. Courvoisier, “Femtosecond laser fabrication of micro and nano-disks in single layer graphene using vortex Bessel beams,” Appl. Phys. Lett. 103, 241111 (2013).
[Crossref]

F. Courvoisier, J. Zhang, M.K. Bhuyan, M. Jacquot, and J.M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys. A 112 (1), 29–34 (2013).
[Crossref]

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.,  97, 081102 (2010).
[Crossref]

M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express,  18, 566–574 (2010).
[Crossref] [PubMed]

Della Valle, G.

G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A: Pure Appl. Opt. 11, 013001 (2009).
[Crossref]

Di Trapani, P.

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A 77, 043814 (2008).
[Crossref]

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett. 99 (22), 223902 (2007).
[Crossref]

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E 73, 056612 (2006).
[Crossref]

P. Polesana, D. Faccio, P. Di Trapani, A. Dubietis, A. Piskarkas, A. Couairon, and M. A. Porras, “High localization, focal depth and contrast by means of nonlinear Bessel Beams,” Opt. Express 13, 6160–6167 (2005).
[Crossref] [PubMed]

M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett. 93 (15), 153902 (2004).
[Crossref] [PubMed]

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, “Light Filaments without Self-Channeling,” Phys. Rev. Lett. 92, 253903 (2004).
[Crossref] [PubMed]

Dubietis, A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett. 99 (22), 223902 (2007).
[Crossref]

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E 73, 056612 (2006).
[Crossref]

P. Polesana, D. Faccio, P. Di Trapani, A. Dubietis, A. Piskarkas, A. Couairon, and M. A. Porras, “High localization, focal depth and contrast by means of nonlinear Bessel Beams,” Opt. Express 13, 6160–6167 (2005).
[Crossref] [PubMed]

M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett. 93 (15), 153902 (2004).
[Crossref] [PubMed]

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, “Light Filaments without Self-Channeling,” Phys. Rev. Lett. 92, 253903 (2004).
[Crossref] [PubMed]

Dudley, J.

Dudley, J. M.

B. Wetzel, C. Xie, P.-A. Lacourt, J. M. Dudley, and F. Courvoisier, “Femtosecond laser fabrication of micro and nano-disks in single layer graphene using vortex Bessel beams,” Appl. Phys. Lett. 103, 241111 (2013).
[Crossref]

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.,  97, 081102 (2010).
[Crossref]

Dudley, J.M.

F. Courvoisier, J. Zhang, M.K. Bhuyan, M. Jacquot, and J.M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys. A 112 (1), 29–34 (2013).
[Crossref]

Durnin, J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
[Crossref] [PubMed]

J. Durnin, “Exact solutions for nondiffracting beams. I. The Scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[Crossref]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
[Crossref] [PubMed]

Faccio, D.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A,  86, 013842 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84021807 (2011).
[Crossref]

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A 77, 043814 (2008).
[Crossref]

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett. 99 (22), 223902 (2007).
[Crossref]

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E 73, 056612 (2006).
[Crossref]

P. Polesana, D. Faccio, P. Di Trapani, A. Dubietis, A. Piskarkas, A. Couairon, and M. A. Porras, “High localization, focal depth and contrast by means of nonlinear Bessel Beams,” Opt. Express 13, 6160–6167 (2005).
[Crossref] [PubMed]

M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett. 93 (15), 153902 (2004).
[Crossref] [PubMed]

Franco, M.

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A 77, 043814 (2008).
[Crossref]

Furfaro, L.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.,  97, 081102 (2010).
[Crossref]

M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express,  18, 566–574 (2010).
[Crossref] [PubMed]

Gaizauskas, E.

Gaižauskas, E.

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, “Light Filaments without Self-Channeling,” Phys. Rev. Lett. 92, 253903 (2004).
[Crossref] [PubMed]

Gattass, R. R.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008).
[Crossref]

Gori, F.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Optics Commun. 64, 491–495 (1987).
[Crossref]

Guattari, G.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Optics Commun. 64, 491–495 (1987).
[Crossref]

Houard, A.

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milián, J. Carbonnel, Y. Liu, A. Couairon, and A. Mysyrowicz, “Superfilamentation in Air,” Phys. Rev. Lett. 112, 223902 (2014).
[Crossref] [PubMed]

Hui, R.

Jacquot, M.

F. Courvoisier, J. Zhang, M.K. Bhuyan, M. Jacquot, and J.M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys. A 112 (1), 29–34 (2013).
[Crossref]

M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express,  18, 566–574 (2010).
[Crossref] [PubMed]

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.,  97, 081102 (2010).
[Crossref]

Jarutis, V.

Jeong, T. M.

K.-M. Lee, C. M. Kim, S. A. Sato, T. Otobe, Y. Shinohara, K. Yabana, and T. M. Jeong, “First-principles simulation of the optical response of bulk and thin-film a-quartz irradiated with an ultrashort intense laser pulse,” J. Appl. Phys. 115, 053519 (2014).
[Crossref]

Jukna, V.

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milián, J. Carbonnel, Y. Liu, A. Couairon, and A. Mysyrowicz, “Superfilamentation in Air,” Phys. Rev. Lett. 112, 223902 (2014).
[Crossref] [PubMed]

Juodkazis, S.

E. Gaizauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31, 80–82 (2006).
[Crossref] [PubMed]

A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 40, 1197–1199 (2001).
[Crossref]

Kim, C. M.

K.-M. Lee, C. M. Kim, S. A. Sato, T. Otobe, Y. Shinohara, K. Yabana, and T. M. Jeong, “First-principles simulation of the optical response of bulk and thin-film a-quartz irradiated with an ultrashort intense laser pulse,” J. Appl. Phys. 115, 053519 (2014).
[Crossref]

Kolesik, M.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. de J. Ramirez-Gongora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Special Topics 199, 5–76 (2011).
[Crossref]

Kucinskas, E.

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E 73, 056612 (2006).
[Crossref]

Lacourt, P. A.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.,  97, 081102 (2010).
[Crossref]

Lacourt, P.-A.

B. Wetzel, C. Xie, P.-A. Lacourt, J. M. Dudley, and F. Courvoisier, “Femtosecond laser fabrication of micro and nano-disks in single layer graphene using vortex Bessel beams,” Appl. Phys. Lett. 103, 241111 (2013).
[Crossref]

M. K. Bhuyan, F. Courvoisier, P.-A. Lacourt, M. Jacquot, L. Furfaro, M. J. Withford, and J. Dudley, “High aspect ratio taper-free microchannel fabrication using femtosecond Bessel beams,” Opt. Express,  18, 566–574 (2010).
[Crossref] [PubMed]

Laporta, P.

G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A: Pure Appl. Opt. 11, 013001 (2009).
[Crossref]

Lee, K.-M.

K.-M. Lee, C. M. Kim, S. A. Sato, T. Otobe, Y. Shinohara, K. Yabana, and T. M. Jeong, “First-principles simulation of the optical response of bulk and thin-film a-quartz irradiated with an ultrashort intense laser pulse,” J. Appl. Phys. 115, 053519 (2014).
[Crossref]

Liu, Y.

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milián, J. Carbonnel, Y. Liu, A. Couairon, and A. Mysyrowicz, “Superfilamentation in Air,” Phys. Rev. Lett. 112, 223902 (2014).
[Crossref] [PubMed]

Long, X.

Lotti, A.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A,  86, 013842 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84021807 (2011).
[Crossref]

Majus, D.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. de J. Ramirez-Gongora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Special Topics 199, 5–76 (2011).
[Crossref]

Marcinkevicius, A.

A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 40, 1197–1199 (2001).
[Crossref]

Matsuo, S.

A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 40, 1197–1199 (2001).
[Crossref]

Mazur, E.

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008).
[Crossref]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
[Crossref] [PubMed]

Milián, C.

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milián, J. Carbonnel, Y. Liu, A. Couairon, and A. Mysyrowicz, “Superfilamentation in Air,” Phys. Rev. Lett. 112, 223902 (2014).
[Crossref] [PubMed]

Misawa, H.

E. Gaizauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31, 80–82 (2006).
[Crossref] [PubMed]

A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 40, 1197–1199 (2001).
[Crossref]

Mizeikis, V.

E. Gaizauskas, E. Vanagas, V. Jarutis, S. Juodkazis, V. Mizeikis, and H. Misawa, “Discrete damage traces from filamentation of Gauss-Bessel pulses,” Opt. Lett. 31, 80–82 (2006).
[Crossref] [PubMed]

A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 40, 1197–1199 (2001).
[Crossref]

Moloney, J.

Moloney, J.V.

P. Polynkin, C. Ament, and J.V. Moloney, “Self-Focusing of Ultraintense Femtosecond Optical Vortices in Air,” Phys. Rev. Lett. 111, 023901 (2013).
[Crossref] [PubMed]

Mysyrowicz, A.

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milián, J. Carbonnel, Y. Liu, A. Couairon, and A. Mysyrowicz, “Superfilamentation in Air,” Phys. Rev. Lett. 112, 223902 (2014).
[Crossref] [PubMed]

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

Osellame, R.

G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A: Pure Appl. Opt. 11, 013001 (2009).
[Crossref]

Otobe, T.

K.-M. Lee, C. M. Kim, S. A. Sato, T. Otobe, Y. Shinohara, K. Yabana, and T. M. Jeong, “First-principles simulation of the optical response of bulk and thin-film a-quartz irradiated with an ultrashort intense laser pulse,” J. Appl. Phys. 115, 053519 (2014).
[Crossref]

Padovani, C.

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Optics Commun. 64, 491–495 (1987).
[Crossref]

Panagiotopoulos, P.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A,  86, 013842 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84021807 (2011).
[Crossref]

Papazoglou, D. G.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A,  86, 013842 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84021807 (2011).
[Crossref]

Parola, A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett. 99 (22), 223902 (2007).
[Crossref]

M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett. 93 (15), 153902 (2004).
[Crossref] [PubMed]

Paskauskas, R.

V. Jarutis, R. Paskauskas, and A. Stabinis, “Focusing of Laguerre-Gaussian beams by axicon,” Optics Commun. 184, 105–112 (2000).
[Crossref]

Piskarkas, A.

Piskarskas, A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett. 99 (22), 223902 (2007).
[Crossref]

Point, G.

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milián, J. Carbonnel, Y. Liu, A. Couairon, and A. Mysyrowicz, “Superfilamentation in Air,” Phys. Rev. Lett. 112, 223902 (2014).
[Crossref] [PubMed]

Polesana, P.

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A 77, 043814 (2008).
[Crossref]

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett. 99 (22), 223902 (2007).
[Crossref]

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E 73, 056612 (2006).
[Crossref]

P. Polesana, D. Faccio, P. Di Trapani, A. Dubietis, A. Piskarkas, A. Couairon, and M. A. Porras, “High localization, focal depth and contrast by means of nonlinear Bessel Beams,” Opt. Express 13, 6160–6167 (2005).
[Crossref] [PubMed]

Polynkin, P.

P. Polynkin, C. Ament, and J.V. Moloney, “Self-Focusing of Ultraintense Femtosecond Optical Vortices in Air,” Phys. Rev. Lett. 111, 023901 (2013).
[Crossref] [PubMed]

S. Shiffler, P. Polynkin, and J. Moloney, “Self-focusing of femtosecond diffraction-resistant vortex beams in water,” Opt. Lett.,  36, 3834–3836 (2011).
[Crossref] [PubMed]

Porras, M. A.

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett. 99 (22), 223902 (2007).
[Crossref]

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E 73, 056612 (2006).
[Crossref]

P. Polesana, D. Faccio, P. Di Trapani, A. Dubietis, A. Piskarkas, A. Couairon, and M. A. Porras, “High localization, focal depth and contrast by means of nonlinear Bessel Beams,” Opt. Express 13, 6160–6167 (2005).
[Crossref] [PubMed]

Porras, M.A.

M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett. 93 (15), 153902 (2004).
[Crossref] [PubMed]

Ramirez-Gongora, O. de J.

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. de J. Ramirez-Gongora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Special Topics 199, 5–76 (2011).
[Crossref]

Salut, R.

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.,  97, 081102 (2010).
[Crossref]

Sato, S. A.

K.-M. Lee, C. M. Kim, S. A. Sato, T. Otobe, Y. Shinohara, K. Yabana, and T. M. Jeong, “First-principles simulation of the optical response of bulk and thin-film a-quartz irradiated with an ultrashort intense laser pulse,” J. Appl. Phys. 115, 053519 (2014).
[Crossref]

Shcheblanov, N.

N. Shcheblanov, “Numerical study of femtosecond laser interactions with dielectric materials: application to the definition of damage threshold of optical components,” Ph.D. Thesis, Jean Monnet University (2013).

Shiffler, S.

Shinohara, Y.

K.-M. Lee, C. M. Kim, S. A. Sato, T. Otobe, Y. Shinohara, K. Yabana, and T. M. Jeong, “First-principles simulation of the optical response of bulk and thin-film a-quartz irradiated with an ultrashort intense laser pulse,” J. Appl. Phys. 115, 053519 (2014).
[Crossref]

Stabinis, A.

V. Jarutis, R. Paskauskas, and A. Stabinis, “Focusing of Laguerre-Gaussian beams by axicon,” Optics Commun. 184, 105–112 (2000).
[Crossref]

Stegun, I. A.

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover PublicationsNew York, 1972).

Stoian, R.

Tamošauskas, G.

A. Dubietis, E. Gaižauskas, G. Tamošauskas, and P. Di Trapani, “Light Filaments without Self-Channeling,” Phys. Rev. Lett. 92, 253903 (2004).
[Crossref] [PubMed]

Tzortzakis, S.

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A,  86, 013842 (2012).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84021807 (2011).
[Crossref]

Vanagas, E.

Wetzel, B.

B. Wetzel, C. Xie, P.-A. Lacourt, J. M. Dudley, and F. Courvoisier, “Femtosecond laser fabrication of micro and nano-disks in single layer graphene using vortex Bessel beams,” Appl. Phys. Lett. 103, 241111 (2013).
[Crossref]

Withford, M. J.

Xie, C.

B. Wetzel, C. Xie, P.-A. Lacourt, J. M. Dudley, and F. Courvoisier, “Femtosecond laser fabrication of micro and nano-disks in single layer graphene using vortex Bessel beams,” Appl. Phys. Lett. 103, 241111 (2013).
[Crossref]

Yabana, K.

K.-M. Lee, C. M. Kim, S. A. Sato, T. Otobe, Y. Shinohara, K. Yabana, and T. M. Jeong, “First-principles simulation of the optical response of bulk and thin-film a-quartz irradiated with an ultrashort intense laser pulse,” J. Appl. Phys. 115, 053519 (2014).
[Crossref]

Zhang, J.

F. Courvoisier, J. Zhang, M.K. Bhuyan, M. Jacquot, and J.M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys. A 112 (1), 29–34 (2013).
[Crossref]

Zhao, W.

Appl. Phys. A (1)

F. Courvoisier, J. Zhang, M.K. Bhuyan, M. Jacquot, and J.M. Dudley, “Applications of femtosecond Bessel beams to laser ablation,” Appl. Phys. A 112 (1), 29–34 (2013).
[Crossref]

Appl. Phys. Lett. (2)

M. K. Bhuyan, F. Courvoisier, P. A. Lacourt, M. Jacquot, R. Salut, L. Furfaro, and J. M. Dudley, “High aspect ratio nanochannel machining using single shot femtosecond Bessel beams,” Appl. Phys. Lett.,  97, 081102 (2010).
[Crossref]

B. Wetzel, C. Xie, P.-A. Lacourt, J. M. Dudley, and F. Courvoisier, “Femtosecond laser fabrication of micro and nano-disks in single layer graphene using vortex Bessel beams,” Appl. Phys. Lett. 103, 241111 (2013).
[Crossref]

Eur. Phys. J. Special Topics (1)

A. Couairon, E. Brambilla, T. Corti, D. Majus, O. de J. Ramirez-Gongora, and M. Kolesik, “Practitioner’s guide to laser pulse propagation models and simulation,” Eur. Phys. J. Special Topics 199, 5–76 (2011).
[Crossref]

J. Appl. Phys. (1)

K.-M. Lee, C. M. Kim, S. A. Sato, T. Otobe, Y. Shinohara, K. Yabana, and T. M. Jeong, “First-principles simulation of the optical response of bulk and thin-film a-quartz irradiated with an ultrashort intense laser pulse,” J. Appl. Phys. 115, 053519 (2014).
[Crossref]

J. Opt. A: Pure Appl. Opt. (1)

G. Della Valle, R. Osellame, and P. Laporta, “Micromachining of photonic devices by femtosecond laser pulses,” J. Opt. A: Pure Appl. Opt. 11, 013001 (2009).
[Crossref]

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

Jpn. J. Appl. Phys. (1)

A. Marcinkevicius, S. Juodkazis, S. Matsuo, V. Mizeikis, and H. Misawa, “Application of Bessel beams for microfabrication of dielectrics by femtosecond laser,” Jpn. J. Appl. Phys. 40, 1197–1199 (2001).
[Crossref]

Nat. Photonics (1)

R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photonics 2, 219–225 (2008).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Optics Commun. (2)

V. Jarutis, R. Paskauskas, and A. Stabinis, “Focusing of Laguerre-Gaussian beams by axicon,” Optics Commun. 184, 105–112 (2000).
[Crossref]

F. Gori, G. Guattari, and C. Padovani, “Bessel-Gauss beams,” Optics Commun. 64, 491–495 (1987).
[Crossref]

Phys. Rep. (1)

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

Phys. Rev. A (3)

P. Polesana, M. Franco, A. Couairon, D. Faccio, and P. Di Trapani, “Filamentation in Kerr media from pulsed Bessel beams,” Phys. Rev. A 77, 043814 (2008).
[Crossref]

A. Lotti, D. Faccio, A. Couairon, D. G. Papazoglou, P. Panagiotopoulos, D. Abdollahpour, and S. Tzortzakis, “Stationary nonlinear Airy beams,” Phys. Rev. A 84021807 (2011).
[Crossref]

P. Panagiotopoulos, D. Abdollahpour, A. Lotti, A. Couairon, D. Faccio, D. G. Papazoglou, and S. Tzortzakis, “Nonlinear propagation dynamics of finite-energy Airy beams,” Phys. Rev. A,  86, 013842 (2012).
[Crossref]

Phys. Rev. E (1)

P. Polesana, A. Dubietis, M. A. Porras, E. Kucinskas, D. Faccio, A. Couairon, and P. Di Trapani, “Near-field dynamics of ultrashort pulsed Bessel beams in media with Kerr nonlinearity,” Phys. Rev. E 73, 056612 (2006).
[Crossref]

Phys. Rev. Lett. (6)

M.A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. Di Trapani, “Nonlinear Unbalanced Bessel Beams: Stationary Conical Waves Supported by Nonlinear Losses,” Phys. Rev. Lett. 93 (15), 153902 (2004).
[Crossref] [PubMed]

P. Polesana, A. Couairon, D. Faccio, A. Parola, M. A. Porras, A. Dubietis, A. Piskarskas, and P. Di Trapani, “Observation of Conical Waves in Focusing, Dispersive, and Dissipative Kerr Media,” Phys. Rev. Lett. 99 (22), 223902 (2007).
[Crossref]

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P. Polynkin, C. Ament, and J.V. Moloney, “Self-Focusing of Ultraintense Femtosecond Optical Vortices in Air,” Phys. Rev. Lett. 111, 023901 (2013).
[Crossref] [PubMed]

G. Point, Y. Brelet, A. Houard, V. Jukna, C. Milián, J. Carbonnel, Y. Liu, A. Couairon, and A. Mysyrowicz, “Superfilamentation in Air,” Phys. Rev. Lett. 112, 223902 (2014).
[Crossref] [PubMed]

Other (2)

N. Shcheblanov, “Numerical study of femtosecond laser interactions with dielectric materials: application to the definition of damage threshold of optical components,” Ph.D. Thesis, Jean Monnet University (2013).

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover PublicationsNew York, 1972).

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Figures (6)

Fig. 1
Fig. 1 Zero-order (a-c) and first order (d-f) Bessel beam propagation through Corning 0211 glass. Intensity profiles for (a,d) linear propagation, (b,e) nonlinear propagation. (c,f) Plasma density profile for nonlinear propagation. The slope of the white lines is equal to the cone half-angle. The Bessel zone lies between the continuous lines. The extended Bessel zone in the nonlinear regime is marked by dashed lines. The input beam power is 64.1 MW and the corresponding pulse energy is 7.8 μJ.
Fig. 2
Fig. 2 Nonlinear propagation regimes for BV. Figures show intensity maps of the propagation of the beam sliced in one transverse direction. (a) Stable propagation when plasma defocusing and absorption terms are active, (b) unstable propagation when the plasma terms are switched off keeping the same initial beam power, and (c) stable propagation when plasma terms are switched off but initial power lowered from 64.1 MW to 38.5 MW.
Fig. 3
Fig. 3 (a) Stable nonlinear propagation regime for a first order nonlinear Bessel beam was reached with 38.5 MW power. (b, c) Unstable propagation for a NBV beam with the same cone angle but power 57.7 MW and 76.9 MW. (d) Unstable propagation for a third order NBV 153.8 MW. Each intensity slice was normalized to its maximum intensity. Different isosurface colors represents intensity levels. Blue color: 0.5×Imax. Green color: 0.7×Imax. Red color: 0.9×Imax. Zone 1: stable nonlinear propagation (beam smooth shrinkage and relaxation). Zone 2: break-up into rotating peaks: Zone 3: irregular rotation of the peaks.
Fig. 4
Fig. 4 Estimated intensity threshold for various cone angles defining the frontier between the decaying and non decaying NBV amplitude profiles for glass. NLL coefficient βK = 4.7 × 10−27 cm3/W2, nonlinear refractive index n2 = 3.45 × 10−16 cm2/W. The light gray zone depicts the area where the NBV amplitude does not decay as 1 / r , but the increase of amplitude is not observed in computation window. Horizontal black line depicts 16.4° angle and black dots depict maximum intensity of NBV shown in Fig. 5(c).
Fig. 5
Fig. 5 Comparison of the stationary NBV when the NLL coefficient is changed. (a)βK is changed (from 4.7 × 10−27 to 42.3 × 10−27 cm3/W2). The black arrow represents increasing βK values while n2 is fixed at 3.45 × 10−16. (b,d) The nonlinear refractive index n2 is changed (from 3.45 × 10−16 to 17.25 × 10−16 cm2/W) and βK = 4.7 × 10−27 cm3/W2. The black arrow represents increasing nonlinear index coefficients. The higher maximum intensity in case (d) induces a stronger influence of NLL compared to case (b). (c) βK and n2 coefficients are fixed, while leaving free the maximum intensity. For all figures, the Bessel beam angle is θ = 16.4°.
Fig. 6
Fig. 6 Position rmax dependence on intensity Imax for the peak intensity obtained by direct numerical simulation (a) with and (b) without plasma terms. The colored curves represent direct numerical simulations with different initial peak powers (6.4, 19.2, 38.5, 57.7 MW). The thick blue line represents the position-intensity dependence of the peak for stationary NBV. Position vs intensity for the peak intensity of stationary NBV profiles calculated for different cone angles is shown in (c) (blue solid curve). The black dotted curves are obtained by the analytical representation for the rmax vs Imax characterization proposed in text.

Tables (1)

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Table 1 Material and beam parameters.

Equations (22)

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E ^ z = i ( k 0 2 k 2 k 0 ) E ^ + i ω 0 2 n 0 c ε 0 1 ( P ^ + i J ^ ω 0 ) .
ε 0 1 P = 2 n 0 n 2 | E | 2 E ,
ε 0 1 J = n 0 c [ σ ( 1 + i ω 0 τ c ) ρ W P I U g | E | 2 ( 1 ρ ρ n t ) ] E ,
ρ t = W P I ( ρ n t ρ ) + σ U g | E | 2 ρ ( 1 ρ ρ n t ) ρ τ rec ,
E ( x , y , z = 0 ) E 0 exp [ r 2 / w 0 2 + i ( k 0 sin θ r + m ϑ ) ] ,
E z = i 2 k 0 2 E + i k 0 n 2 n 0 | E | 2 E β K 2 | E | 2 K 2 E , 2 E = 1 r E r + 2 E r 2 + 1 r 2 2 E ϑ 2 .
a ¨ q 2 a = a ˙ r 2 k 0 δ a 2 k 0 2 n 2 n 0 a 3 + m 2 r 2 a ,
q ˙ + 2 a ˙ a q = q r k 0 β K a 2 K 2 ,
r 2 a ¨ + r a ˙ + ( 2 k 0 δ r 2 m 2 ) a = 0 .
r q ( r ) a 2 ( r ) = k 0 β K 0 r a 2 K r d r .
z | E | 2 = i 2 k 0 ( E * 2 E E 2 E * ) β K | E | 2 K
= 1 k 0 J β K | E | 2 K
δ > max { g K β K I 0 K 1 k 0 n 2 I 0 / n 0 , 0 } ,
a ( r ) = a 0 2 [ α out H m ( 1 ) ( 2 k 0 δ r ) + α in H m ( 2 ) ( 2 k 0 δ r ) ]
a 2 ( r ) a 0 2 2 ( | α in | 2 + | α out | 2 ) π 2 k 0 δ r [ 1 + C sin ( 2 2 k 0 δ r + arg ( α out / α in ) π m ) ] ,
a 0 2 ( | α in | 2 | α out | 2 ) = k 0 β K 0 + a 2 K r d r .
a ( r = 0 ) = a 0 ,
a ˙ ( r = 0 ) = 0 ,
q 0 = 0 .
a ( r 0 ) ~ a m r m ,
a ˙ ( r 0 ) ~ m a m r m 1 ,
q ( r 0 ) ~ k 0 β K 2 ( m K + 1 ) a m 2 K 2 r 2 m ( K 1 ) + 1 .

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