Abstract

We study the effect of Two-Photon Absorption (TPA) nonlinear losses on Gaussian pulses, with power that exceeds the critical power for self-focusing, propagating in bulk kerr media. Experiments performed in fused silica and silicon highlight a spontaneous reshaping of the input pulse into a pulsed Bessel beam. A filament is formed in which sub-diffractive propagation is sustained by the Bessel-nature of the pulse.

© 2008 Optical Society of America

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  1. R. Boyd, Nonlinear Optics (Academic Press, 1992).
  2. G. G. Luther, J. V. Moloney, and A. C. Newell, "Self-focusing threshold in normally dispersive media," Opt. Lett. 19, 862-864 (1994).
    [CrossRef]
  3. A. Couairon, "Dynamics of femtosecond filamentation from saturation of self-focusing laser pulses," Phys. Rev. A 68, 015801 (2003).
    [CrossRef]
  4. L.W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, "Spatiotemporal instabilities in dispersive nonlinear media," Phys. Rev. A 46, 4202-4208 (1992).
    [CrossRef] [PubMed]
  5. A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441, 47-189 (2007).
    [CrossRef]
  6. M. Kolesik, E. Wright, and J. Moloney, "Dynamic nonlinear X waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901 (2004).
    [CrossRef] [PubMed]
  7. D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
    [CrossRef] [PubMed]
  8. D. Faccio, A. Averchi, A. Lotti, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, "Ultrashort laser pulse filamentation from spontaneous X Wave formation in air," Opt. Express 16, 1565-1570 (2008).
    [CrossRef] [PubMed]
  9. D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon, and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601 (2005).
    [CrossRef]
  10. S. Tzortzakis, D. G. Papazoglou, and I. Zergioti, "Long-range filamentary propagation of subpicosecond ultraviolet laser pulses in fused silica," Opt. Lett. 31, 796-798 (2006).
    [CrossRef] [PubMed]
  11. D. G. Papazoglou, I. Zergioti, and S. Tzortzakis, "Plasma strings from ultraviolet laser filaments drive permanent structural modifications in fused silica," Opt. Lett. 32, 2055-2057 (2007).
    [CrossRef] [PubMed]
  12. R. Alfano, Supercontinuum Laser Source (Springer, 2005).
  13. Q. Lin, O. J. Painter, and G. P. Agrawal, "Nonlinear optical phenomena in silicon waveguides: Modeling and applications," Opt. Express 15, 16604-16644 (2007).
    [CrossRef] [PubMed]
  14. 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, 223902 (2007).
    [CrossRef]
  15. 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, 153902 (2004).
    [CrossRef] [PubMed]
  16. D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
    [CrossRef] [PubMed]

2008 (1)

2007 (5)

2006 (2)

S. Tzortzakis, D. G. Papazoglou, and I. Zergioti, "Long-range filamentary propagation of subpicosecond ultraviolet laser pulses in fused silica," Opt. Lett. 31, 796-798 (2006).
[CrossRef] [PubMed]

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

2005 (1)

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon, and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601 (2005).
[CrossRef]

2004 (2)

M. Kolesik, E. Wright, and J. Moloney, "Dynamic nonlinear X waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901 (2004).
[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, 153902 (2004).
[CrossRef] [PubMed]

2003 (1)

A. Couairon, "Dynamics of femtosecond filamentation from saturation of self-focusing laser pulses," Phys. Rev. A 68, 015801 (2003).
[CrossRef]

1994 (1)

1992 (1)

L.W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, "Spatiotemporal instabilities in dispersive nonlinear media," Phys. Rev. A 46, 4202-4208 (1992).
[CrossRef] [PubMed]

Agrawal, G. P.

Q. Lin, O. J. Painter, and G. P. Agrawal, "Nonlinear optical phenomena in silicon waveguides: Modeling and applications," Opt. Express 15, 16604-16644 (2007).
[CrossRef] [PubMed]

L.W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, "Spatiotemporal instabilities in dispersive nonlinear media," Phys. Rev. A 46, 4202-4208 (1992).
[CrossRef] [PubMed]

Averchi, A.

Bragheri, F.

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

Cao, X. D.

L.W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, "Spatiotemporal instabilities in dispersive nonlinear media," Phys. Rev. A 46, 4202-4208 (1992).
[CrossRef] [PubMed]

Couairon, A.

D. Faccio, A. Averchi, A. Lotti, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, "Ultrashort laser pulse filamentation from spontaneous X Wave formation in air," Opt. Express 16, 1565-1570 (2008).
[CrossRef] [PubMed]

A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441, 47-189 (2007).
[CrossRef]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[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, 223902 (2007).
[CrossRef]

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon, and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601 (2005).
[CrossRef]

A. Couairon, "Dynamics of femtosecond filamentation from saturation of self-focusing laser pulses," Phys. Rev. A 68, 015801 (2003).
[CrossRef]

Di Trapani, P.

D. Faccio, A. Averchi, A. Lotti, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, "Ultrashort laser pulse filamentation from spontaneous X Wave formation in air," Opt. Express 16, 1565-1570 (2008).
[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, 223902 (2007).
[CrossRef]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon, and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601 (2005).
[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, 153902 (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, 223902 (2007).
[CrossRef]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon, and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601 (2005).
[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, 153902 (2004).
[CrossRef] [PubMed]

Faccio, D.

D. Faccio, A. Averchi, A. Lotti, P. Di Trapani, A. Couairon, D. Papazoglou, and S. Tzortzakis, "Ultrashort laser pulse filamentation from spontaneous X Wave formation in air," Opt. Express 16, 1565-1570 (2008).
[CrossRef] [PubMed]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[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, 223902 (2007).
[CrossRef]

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon, and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601 (2005).
[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, 153902 (2004).
[CrossRef] [PubMed]

Gaizauskas, E.

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon, and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601 (2005).
[CrossRef]

Kolesik, M.

Lin, Q.

Liou, L.W.

L.W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, "Spatiotemporal instabilities in dispersive nonlinear media," Phys. Rev. A 46, 4202-4208 (1992).
[CrossRef] [PubMed]

Lotti, A.

Luther, G. G.

Matijosius, A.

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon, and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601 (2005).
[CrossRef]

McKinstrie, C. J.

L.W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, "Spatiotemporal instabilities in dispersive nonlinear media," Phys. Rev. A 46, 4202-4208 (1992).
[CrossRef] [PubMed]

Moloney, J.

M. Kolesik, E. Wright, and J. Moloney, "Dynamic nonlinear X waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

Moloney, J. V.

Mysyrowicz, A.

A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441, 47-189 (2007).
[CrossRef]

Newell, A. C.

Painter, O. J.

Papazoglou, D.

Papazoglou, D. G.

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, 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, 153902 (2004).
[CrossRef] [PubMed]

Piskarkas, A.

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon, and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601 (2005).
[CrossRef]

Piskarkas, R.

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon, and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601 (2005).
[CrossRef]

Piskarskas, A.

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[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, 223902 (2007).
[CrossRef]

Polesana, P.

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, 223902 (2007).
[CrossRef]

D. Faccio, A. Averchi, A. Couairon, M. Kolesik, J. V. Moloney, A. Dubietis, G. Tamosauskas, P. Polesana, A. Piskarskas, and P. Di Trapani, "Spatio-temporal reshaping and X Wave dynamics in optical filaments," Opt. Express 15, 13077-13095 (2007).
[CrossRef] [PubMed]

Porras, M.

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[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, 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, 153902 (2004).
[CrossRef] [PubMed]

Tamosauskas, G.

Tzortzakis, S.

Varanavicius, A.

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon, and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601 (2005).
[CrossRef]

Wright, E.

M. Kolesik, E. Wright, and J. Moloney, "Dynamic nonlinear X waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901 (2004).
[CrossRef] [PubMed]

Zergioti, I.

Opt. Express (3)

Opt. Lett. (3)

Phys. Rep. (1)

A. Couairon and A. Mysyrowicz, "Femtosecond filamentation in transparent media," Phys. Rep. 441, 47-189 (2007).
[CrossRef]

Phys. Rev. A (2)

A. Couairon, "Dynamics of femtosecond filamentation from saturation of self-focusing laser pulses," Phys. Rev. A 68, 015801 (2003).
[CrossRef]

L.W. Liou, X. D. Cao, C. J. McKinstrie, and G. P. Agrawal, "Spatiotemporal instabilities in dispersive nonlinear media," Phys. Rev. A 46, 4202-4208 (1992).
[CrossRef] [PubMed]

Phys. Rev. E (1)

D. Faccio, A. Matijosius, A. Dubietis, R. Piskarkas, A. Varanavicius, E. Gaizauskas, A. Piskarkas, A. Couairon, and P. Di Trapani, "Near and Far-Field evolution of laser pulse filaments in Kerr media," Phys. Rev. E 72, 037601 (2005).
[CrossRef]

Phys. Rev. Lett. (4)

M. Kolesik, E. Wright, and J. Moloney, "Dynamic nonlinear X waves for femtosecond pulse propagation in water," Phys. Rev. Lett. 92, 253901 (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, 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, 153902 (2004).
[CrossRef] [PubMed]

D. Faccio, M. Porras, A. Dubietis, F. Bragheri, A. Couairon, and P. Di Trapani, "Conical emission, pulse splitting, and x-wave parametric amplification in nonlinear dynamics of ultrashort light pulses," Phys. Rev. Lett. 96, 193901 (2006).
[CrossRef] [PubMed]

Other (2)

R. Boyd, Nonlinear Optics (Academic Press, 1992).

R. Alfano, Supercontinuum Laser Source (Springer, 2005).

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Figures (4)

Fig. 1.
Fig. 1.

Near field intensity profiles in (a) linear (1.5 nJ) and (b) nonlinear (70 nJ) regime respectively, of a 1550 nm, 100 fs pulse, after propagation in a 8 mm long Silicon bulk sample. (c) and (d) are the angularly resolved power spectra recorded for the same input conditions as (a) and (b), respectively.

Fig. 2.
Fig. 2.

Angularly resolved power spectrum (2 decade logarithmic scale) of a 264 nm, 200 fs pulse after propagation in a 13 mm long fused silica bulk sample for: (a) PP crit, (b) P ~1.5 P crit and (c) P~3.5P crit.

Fig. 3.
Fig. 3.

Numerical simulations. (a) and (c) show the output pulsed Bessel beam spectrum and near-field profile in conditions that reproduce the experiments in fused silica. (e) and (f) show the fluence and radius at FWHM evolution along the propagation direction z. (b) and (d) show the results in exactly the same conditions as in (a) and (c) but with a nonlinear Kerr coefficient that is 5 times larger. All figures show the profiles over 3 decades in logarithmic scale.

Fig. 4.
Fig. 4.

Numerically evaluated evolution of L tpa, L diff and L kerr. The simulations were performed using the same input pulse conditions of the experiment and (a) n 2=2.6×10-16 cm2/W, β 2=5.6×10-11 cm/W, (b) n 2=13×10-16 cm2/W, β 2=5.6×10-11 cm/W, (c) n 2=2.6×10-16 cm2/W, β 2=1.12×10-11 cm/W.

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