Abstract

Femtosecond laser filamentation is generally initialized from unpredictable symmetry breaking caused by random noise, causing it to be barely controlled. However, it is always anticipated for stable and controllable filamentation. We present and demonstrate the idea that hybridly polarized vector fields with axial symmetry broken polarization, associated with a pair of orthogonally linearly polarized vortices carrying the opposite-handed orbital angular momenta, could achieve controllable and robust multiple filamentation. Here, our motivation is to unveil the underlying physics behind such controllable and robust multiple filamentation. The symmetry breaking should first be actively controllable and then be able to effectively inhibit random noise. Robust multiple filamentation is inseparable from the fact that the phases between the multiple filaments are always locked. In contrast, uncontrollable multiple filamentation is always accompanied with loss of phase, i.e., the multiple filaments become incoherent to each other. Our results may offer a suggestion for achieving controllable and robust multiple filamentation in other systems.

© 2016 Chinese Laser Press

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References

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  1. J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
    [Crossref]
  2. P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
    [Crossref]
  3. F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
    [Crossref]
  4. C. D’Amico, A. Houard, M. Franco, B. Prade, and A. Mysyrowicz, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
    [Crossref]
  5. C. P. Hauri, W. Kornelis, F. W. Heibing, 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, 673–677 (2004).
    [Crossref]
  6. A. Couairon and A. Mysyrowicz, “Femtosecond filamentation in transparent media,” Phys. Rep. 441, 47–189 (2007).
    [Crossref]
  7. S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470–5473 (2001).
    [Crossref]
  8. S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70, 033802 (2004).
    [Crossref]
  9. Z. Jin, J. Zhang, M. H. Xu, X. Lu, Y. T. Li, Z. H. Wang, Z. Y. Wei, X. H. Yuan, and W. Yu, “Control of filamentation induced by femtosecond laser pulses propagating in air,” Opt. Express 13, 10424–10430 (2005).
    [Crossref]
  10. A. Dubietis, G. Tamošauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29, 1126–1128 (2004).
    [Crossref]
  11. T. D. Grow and A. L. Gaeta, “Dependence of multiple filamentation on beam ellipticity,” Opt. Express 13, 4594–4599 (2005).
    [Crossref]
  12. T. Pfeifer, L. Gallmann, M. J. Abel, D. M. Neumark, and S. R. Leone, “Circular phase mask for control and stabilization of single optical filaments,” Opt. Lett. 31, 2326–2328 (2006).
    [Crossref]
  13. Z. Q. Hao, K. Stelmaszczyk, P. Rohwetter, W. M. Nakaema, and L. Woeste, “Femtosecond laser filament-fringes in fused silica,” Opt. Express 19, 7799–7806 (2011).
    [Crossref]
  14. A. Trisorio and C. P. Hauri, “Control and characterization of multiple circularly polarized femtosecond filaments in argon,” Opt. Lett. 32, 1650–1652 (2007).
    [Crossref]
  15. G. Fibich and B. Ilan, “Deterministic vectorial effects lead to multiple filamentation,” Opt. Lett. 26, 840–842 (2001).
    [Crossref]
  16. S. Varma, Y. H. Chen, and H. M. Milchberg, “Trapping and destruction of long-range high-intensity optical filaments by molecular quantum wakes in air,” Phys. Rev. Lett. 101, 205001 (2008).
    [Crossref]
  17. F. Calegari, C. Vozzi, S. Gasilov, E. Benedetti, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Rotational Raman effects in the wake of optical filamentation,” Phys. Rev. Lett. 100, 123006 (2008).
    [Crossref]
  18. L. Bergé, M. R. Schmidt, J. Juul Rasmussen, P. L. Christiansen, and K. Ø. Rasmussen, “Amalgamation of interacting light beamlets in Kerr-type,” J. Opt. Soc. Am. B 14, 2550–2562 (1997).
    [Crossref]
  19. T. T. Xi, X. Lu, and J. Zhang, “Interaction of light filaments generated by femtosecond laser pulses in air,” Phys. Rev. Lett. 96, 025003 (2006).
    [Crossref]
  20. G. Fibich and M. Klein, “Continuations of the nonlinear Schrödinger equation beyond the singularity,” Nonlinearity 24, 2003–2045 (2011).
    [Crossref]
  21. A. A. Ishaaya, T. D. Grow, S. Ghosh, L. T. Vuong, and A. L. Gaeta, “Self-focusing dynamics of coupled optical beams,” Phys. Rev. A 75, 023813 (2007).
    [Crossref]
  22. B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803 (2010).
    [Crossref]
  23. B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
    [Crossref]
  24. 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, 133901 (2006).
    [Crossref]
  25. A. A. Ishaaya, L. T. Vuong, T. D. Grow, and A. L. Gaeta, “Self-focusing dynamics of polarization vortices in Kerr media,” Opt. Lett. 33, 13–15 (2008).
    [Crossref]
  26. T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99, 133902 (2007).
    [Crossref]
  27. G. Fibich and B. Ilan, “Multiple filamentation of circularly polarized beams,” Phys. Rev. Lett. 89, 013901 (2002).
    [Crossref]
  28. S. M. Li, Y. N. Li, X. L. Wang, L. J. Kong, K. Lou, C. H. Tu, Y. J. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
    [Crossref]
  29. M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
    [Crossref]
  30. L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
    [Crossref]
  31. X. L. Wang, J. P. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator, a common path interferometric arrangement,” Opt. Lett. 32, 3549–3551 (2007).
    [Crossref]
  32. X. L. Wang, Y. N. Li, J. Chen, C. S. Guo, J. P. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18, 10786–10795 (2010).
    [Crossref]

2012 (2)

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref]

S. M. Li, Y. N. Li, X. L. Wang, L. J. Kong, K. Lou, C. H. Tu, Y. J. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
[Crossref]

2011 (2)

Z. Q. Hao, K. Stelmaszczyk, P. Rohwetter, W. M. Nakaema, and L. Woeste, “Femtosecond laser filament-fringes in fused silica,” Opt. Express 19, 7799–7806 (2011).
[Crossref]

G. Fibich and M. Klein, “Continuations of the nonlinear Schrödinger equation beyond the singularity,” Nonlinearity 24, 2003–2045 (2011).
[Crossref]

2010 (4)

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

X. L. Wang, Y. N. Li, J. Chen, C. S. Guo, J. P. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18, 10786–10795 (2010).
[Crossref]

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803 (2010).
[Crossref]

2008 (3)

A. A. Ishaaya, L. T. Vuong, T. D. Grow, and A. L. Gaeta, “Self-focusing dynamics of polarization vortices in Kerr media,” Opt. Lett. 33, 13–15 (2008).
[Crossref]

S. Varma, Y. H. Chen, and H. M. Milchberg, “Trapping and destruction of long-range high-intensity optical filaments by molecular quantum wakes in air,” Phys. Rev. Lett. 101, 205001 (2008).
[Crossref]

F. Calegari, C. Vozzi, S. Gasilov, E. Benedetti, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Rotational Raman effects in the wake of optical filamentation,” Phys. Rev. Lett. 100, 123006 (2008).
[Crossref]

2007 (6)

A. A. Ishaaya, T. D. Grow, S. Ghosh, L. T. Vuong, and A. L. Gaeta, “Self-focusing dynamics of coupled optical beams,” Phys. Rev. A 75, 023813 (2007).
[Crossref]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99, 133902 (2007).
[Crossref]

C. D’Amico, A. Houard, M. Franco, B. Prade, and A. Mysyrowicz, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

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

A. Trisorio and C. P. Hauri, “Control and characterization of multiple circularly polarized femtosecond filaments in argon,” Opt. Lett. 32, 1650–1652 (2007).
[Crossref]

X. L. Wang, J. P. Ding, W. J. Ni, C. S. Guo, and H. T. Wang, “Generation of arbitrary vector beams with a spatial light modulator, a common path interferometric arrangement,” Opt. Lett. 32, 3549–3551 (2007).
[Crossref]

2006 (3)

T. Pfeifer, L. Gallmann, M. J. Abel, D. M. Neumark, and S. R. Leone, “Circular phase mask for control and stabilization of single optical filaments,” Opt. Lett. 31, 2326–2328 (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, 133901 (2006).
[Crossref]

T. T. Xi, X. Lu, and J. Zhang, “Interaction of light filaments generated by femtosecond laser pulses in air,” Phys. Rev. Lett. 96, 025003 (2006).
[Crossref]

2005 (2)

2004 (4)

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref]

A. Dubietis, G. Tamošauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29, 1126–1128 (2004).
[Crossref]

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70, 033802 (2004).
[Crossref]

C. P. Hauri, W. Kornelis, F. W. Heibing, 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, 673–677 (2004).
[Crossref]

2003 (1)

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref]

2002 (1)

G. Fibich and B. Ilan, “Multiple filamentation of circularly polarized beams,” Phys. Rev. Lett. 89, 013901 (2002).
[Crossref]

2001 (2)

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470–5473 (2001).
[Crossref]

G. Fibich and B. Ilan, “Deterministic vectorial effects lead to multiple filamentation,” Opt. Lett. 26, 840–842 (2001).
[Crossref]

1999 (1)

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
[Crossref]

1997 (1)

’t Hooft, G. W.

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, 133901 (2006).
[Crossref]

Abel, M. J.

Aközbek, N.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70, 033802 (2004).
[Crossref]

André, Y. B.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref]

Belgiorno, F.

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Benedetti, E.

F. Calegari, C. Vozzi, S. Gasilov, E. Benedetti, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Rotational Raman effects in the wake of optical filamentation,” Phys. Rev. Lett. 100, 123006 (2008).
[Crossref]

Bergé, L.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470–5473 (2001).
[Crossref]

L. Bergé, M. R. Schmidt, J. Juul Rasmussen, P. L. Christiansen, and K. Ø. Rasmussen, “Amalgamation of interacting light beamlets in Kerr-type,” J. Opt. Soc. Am. B 14, 2550–2562 (1997).
[Crossref]

Biegert, J.

C. P. Hauri, W. Kornelis, F. W. Heibing, 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, 673–677 (2004).
[Crossref]

Bourayou, R.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref]

Cacciatori, S. L.

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Calegari, F.

F. Calegari, C. Vozzi, S. Gasilov, E. Benedetti, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Rotational Raman effects in the wake of optical filamentation,” Phys. Rev. Lett. 100, 123006 (2008).
[Crossref]

Chen, J.

Chen, Y. H.

S. Varma, Y. H. Chen, and H. M. Milchberg, “Trapping and destruction of long-range high-intensity optical filaments by molecular quantum wakes in air,” Phys. Rev. Lett. 101, 205001 (2008).
[Crossref]

Chin, S. L.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70, 033802 (2004).
[Crossref]

Christiansen, P. L.

Clerici, M.

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Couairon, A.

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

C. P. Hauri, W. Kornelis, F. W. Heibing, 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, 673–677 (2004).
[Crossref]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470–5473 (2001).
[Crossref]

D’Amico, C.

C. D’Amico, A. Houard, M. Franco, B. Prade, and A. Mysyrowicz, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

De Silvestri, S.

F. Calegari, C. Vozzi, S. Gasilov, E. Benedetti, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Rotational Raman effects in the wake of optical filamentation,” Phys. Rev. Lett. 100, 123006 (2008).
[Crossref]

Ding, J. P.

Dubietis, A.

Eliel, E. R.

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, 133901 (2006).
[Crossref]

Faccio, D.

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Ferland, B.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70, 033802 (2004).
[Crossref]

Fibich, G.

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref]

G. Fibich and M. Klein, “Continuations of the nonlinear Schrödinger equation beyond the singularity,” Nonlinearity 24, 2003–2045 (2011).
[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, 133901 (2006).
[Crossref]

A. Dubietis, G. Tamošauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29, 1126–1128 (2004).
[Crossref]

G. Fibich and B. Ilan, “Multiple filamentation of circularly polarized beams,” Phys. Rev. Lett. 89, 013901 (2002).
[Crossref]

G. Fibich and B. Ilan, “Deterministic vectorial effects lead to multiple filamentation,” Opt. Lett. 26, 840–842 (2001).
[Crossref]

Franco, M.

C. D’Amico, A. Houard, M. Franco, B. Prade, and A. Mysyrowicz, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470–5473 (2001).
[Crossref]

Frey, S.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref]

Gaeta, A. L.

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref]

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803 (2010).
[Crossref]

A. A. Ishaaya, L. T. Vuong, T. D. Grow, and A. L. Gaeta, “Self-focusing dynamics of polarization vortices in Kerr media,” Opt. Lett. 33, 13–15 (2008).
[Crossref]

A. A. Ishaaya, T. D. Grow, S. Ghosh, L. T. Vuong, and A. L. Gaeta, “Self-focusing dynamics of coupled optical beams,” Phys. Rev. A 75, 023813 (2007).
[Crossref]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99, 133902 (2007).
[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, 133901 (2006).
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T. D. Grow and A. L. Gaeta, “Dependence of multiple filamentation on beam ellipticity,” Opt. Express 13, 4594–4599 (2005).
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Gallmann, L.

Gasilov, S.

F. Calegari, C. Vozzi, S. Gasilov, E. Benedetti, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Rotational Raman effects in the wake of optical filamentation,” Phys. Rev. Lett. 100, 123006 (2008).
[Crossref]

Ghosh, S.

A. A. Ishaaya, T. D. Grow, S. Ghosh, L. T. Vuong, and A. L. Gaeta, “Self-focusing dynamics of coupled optical beams,” Phys. Rev. A 75, 023813 (2007).
[Crossref]

Gorini, V.

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Grow, T. D.

A. A. Ishaaya, L. T. Vuong, T. D. Grow, and A. L. Gaeta, “Self-focusing dynamics of polarization vortices in Kerr media,” Opt. Lett. 33, 13–15 (2008).
[Crossref]

A. A. Ishaaya, T. D. Grow, S. Ghosh, L. T. Vuong, and A. L. Gaeta, “Self-focusing dynamics of coupled optical beams,” Phys. Rev. A 75, 023813 (2007).
[Crossref]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99, 133902 (2007).
[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, 133901 (2006).
[Crossref]

T. D. Grow and A. L. Gaeta, “Dependence of multiple filamentation on beam ellipticity,” Opt. Express 13, 4594–4599 (2005).
[Crossref]

Guo, C. S.

Hao, Z. Q.

Z. Q. Hao, K. Stelmaszczyk, P. Rohwetter, W. M. Nakaema, and L. Woeste, “Femtosecond laser filament-fringes in fused silica,” Opt. Express 19, 7799–7806 (2011).
[Crossref]

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
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Hauri, C. P.

A. Trisorio and C. P. Hauri, “Control and characterization of multiple circularly polarized femtosecond filaments in argon,” Opt. Lett. 32, 1650–1652 (2007).
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C. P. Hauri, W. Kornelis, F. W. Heibing, 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, 673–677 (2004).
[Crossref]

Heibing, F. W.

C. P. Hauri, W. Kornelis, F. W. Heibing, 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, 673–677 (2004).
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Heinrich, A.

C. P. Hauri, W. Kornelis, F. W. Heibing, 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, 673–677 (2004).
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Henin, S.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
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Hensley, C. J.

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803 (2010).
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Hosseini, S. A.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70, 033802 (2004).
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Houard, A.

C. D’Amico, A. Houard, M. Franco, B. Prade, and A. Mysyrowicz, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

Hui, P.

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803 (2010).
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Ilan, B.

Ishaaya, A.

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, 133901 (2006).
[Crossref]

Ishaaya, A. A.

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803 (2010).
[Crossref]

A. A. Ishaaya, L. T. Vuong, T. D. Grow, and A. L. Gaeta, “Self-focusing dynamics of polarization vortices in Kerr media,” Opt. Lett. 33, 13–15 (2008).
[Crossref]

A. A. Ishaaya, T. D. Grow, S. Ghosh, L. T. Vuong, and A. L. Gaeta, “Self-focusing dynamics of coupled optical beams,” Phys. Rev. A 75, 023813 (2007).
[Crossref]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99, 133902 (2007).
[Crossref]

Jin, Z.

Juul Rasmussen, J.

Kandidov, V. P.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70, 033802 (2004).
[Crossref]

Kasparian, J.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref]

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C. P. Hauri, W. Kornelis, F. W. Heibing, 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, 673–677 (2004).
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B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
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G. Fibich and M. Klein, “Continuations of the nonlinear Schrödinger equation beyond the singularity,” Nonlinearity 24, 2003–2045 (2011).
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M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
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Kong, L. J.

S. M. Li, Y. N. Li, X. L. Wang, L. J. Kong, K. Lou, C. H. Tu, Y. J. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
[Crossref]

Kornelis, W.

C. P. Hauri, W. Kornelis, F. W. Heibing, 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, 673–677 (2004).
[Crossref]

Kosareva, O. G.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70, 033802 (2004).
[Crossref]

Lascoux, N.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

Lederer, F.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref]

Leone, S. R.

Li, S. M.

S. M. Li, Y. N. Li, X. L. Wang, L. J. Kong, K. Lou, C. H. Tu, Y. J. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
[Crossref]

Li, Y. N.

S. M. Li, Y. N. Li, X. L. Wang, L. J. Kong, K. Lou, C. H. Tu, Y. J. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
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X. L. Wang, Y. N. Li, J. Chen, C. S. Guo, J. P. Ding, and H. T. Wang, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18, 10786–10795 (2010).
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Li, Y. T.

Liu, W.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70, 033802 (2004).
[Crossref]

Lou, K.

S. M. Li, Y. N. Li, X. L. Wang, L. J. Kong, K. Lou, C. H. Tu, Y. J. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
[Crossref]

Lu, X.

Luo, Q.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70, 033802 (2004).
[Crossref]

Méjean, G.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
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S. Varma, Y. H. Chen, and H. M. Milchberg, “Trapping and destruction of long-range high-intensity optical filaments by molecular quantum wakes in air,” Phys. Rev. Lett. 101, 205001 (2008).
[Crossref]

Mlejnek, M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
[Crossref]

Moloney, J. V.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
[Crossref]

Mysyrowicz, A.

C. D’Amico, A. Houard, M. Franco, B. Prade, and A. Mysyrowicz, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

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

C. P. Hauri, W. Kornelis, F. W. Heibing, 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, 673–677 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470–5473 (2001).
[Crossref]

Nakaema, W. M.

Z. Q. Hao, K. Stelmaszczyk, P. Rohwetter, W. M. Nakaema, and L. Woeste, “Femtosecond laser filament-fringes in fused silica,” Opt. Express 19, 7799–7806 (2011).
[Crossref]

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

Neumark, D. M.

Ni, W. J.

Nisoli, M.

F. Calegari, C. Vozzi, S. Gasilov, E. Benedetti, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Rotational Raman effects in the wake of optical filamentation,” Phys. Rev. Lett. 100, 123006 (2008).
[Crossref]

Ortenzi, G.

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Panov, N. A.

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70, 033802 (2004).
[Crossref]

Petit, Y.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

Pfeifer, T.

Prade, B.

C. D’Amico, A. Houard, M. Franco, B. Prade, and A. Mysyrowicz, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470–5473 (2001).
[Crossref]

Queißer, M.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

Rasmussen, K. Ø.

Rizzi, L.

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Rodriguez, M.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref]

Rohwetter, P.

Z. Q. Hao, K. Stelmaszczyk, P. Rohwetter, W. M. Nakaema, and L. Woeste, “Femtosecond laser filament-fringes in fused silica,” Opt. Express 19, 7799–7806 (2011).
[Crossref]

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

Rubino, E.

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Sala, V. G.

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

Salamé, R.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

Salmon, E.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref]

Sansone, G.

F. Calegari, C. Vozzi, S. Gasilov, E. Benedetti, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Rotational Raman effects in the wake of optical filamentation,” Phys. Rev. Lett. 100, 123006 (2008).
[Crossref]

Sauerbrey, R.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref]

Schmidt, M. R.

Schrauth, S. E.

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref]

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803 (2010).
[Crossref]

Shim, B.

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[Crossref]

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803 (2010).
[Crossref]

Skupin, S.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref]

Stagira, S.

F. Calegari, C. Vozzi, S. Gasilov, E. Benedetti, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Rotational Raman effects in the wake of optical filamentation,” Phys. Rev. Lett. 100, 123006 (2008).
[Crossref]

Stelmaszczyk, K.

Z. Q. Hao, K. Stelmaszczyk, P. Rohwetter, W. M. Nakaema, and L. Woeste, “Femtosecond laser filament-fringes in fused silica,” Opt. Express 19, 7799–7806 (2011).
[Crossref]

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

Tamošauskas, G.

Tian, Y. J.

S. M. Li, Y. N. Li, X. L. Wang, L. J. Kong, K. Lou, C. H. Tu, Y. J. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
[Crossref]

Trisorio, A.

Tu, C. H.

S. M. Li, Y. N. Li, X. L. Wang, L. J. Kong, K. Lou, C. H. Tu, Y. J. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
[Crossref]

Tzortzakis, S.

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470–5473 (2001).
[Crossref]

Varma, S.

S. Varma, Y. H. Chen, and H. M. Milchberg, “Trapping and destruction of long-range high-intensity optical filaments by molecular quantum wakes in air,” Phys. Rev. Lett. 101, 205001 (2008).
[Crossref]

Vozzi, C.

F. Calegari, C. Vozzi, S. Gasilov, E. Benedetti, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Rotational Raman effects in the wake of optical filamentation,” Phys. Rev. Lett. 100, 123006 (2008).
[Crossref]

Vuong, L. T.

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803 (2010).
[Crossref]

A. A. Ishaaya, L. T. Vuong, T. D. Grow, and A. L. Gaeta, “Self-focusing dynamics of polarization vortices in Kerr media,” Opt. Lett. 33, 13–15 (2008).
[Crossref]

A. A. Ishaaya, T. D. Grow, S. Ghosh, L. T. Vuong, and A. L. Gaeta, “Self-focusing dynamics of coupled optical beams,” Phys. Rev. A 75, 023813 (2007).
[Crossref]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99, 133902 (2007).
[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, 133901 (2006).
[Crossref]

Wang, H. T.

Wang, X. L.

Wang, Z. H.

Wei, Z. Y.

Wille, H.

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref]

Woeste, L.

Wolf, J. P.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref]

Wöste, L.

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref]

Wright, E. M.

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
[Crossref]

Xi, T. T.

T. T. Xi, X. Lu, and J. Zhang, “Interaction of light filaments generated by femtosecond laser pulses in air,” Phys. Rev. Lett. 96, 025003 (2006).
[Crossref]

Xu, M. H.

Yu, J.

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref]

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref]

Yu, W.

Yuan, X. H.

Zhang, J.

Appl. Phys. B (1)

C. P. Hauri, W. Kornelis, F. W. Heibing, 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, 673–677 (2004).
[Crossref]

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

Nat. Photonics (1)

P. Rohwetter, J. Kasparian, K. Stelmaszczyk, Z. Q. Hao, S. Henin, N. Lascoux, W. M. Nakaema, Y. Petit, M. Queißer, R. Salamé, E. Salmon, L. Wöste, and J. P. Wolf, “Laser-induced water condensation in air,” Nat. Photonics 4, 451–456 (2010).
[Crossref]

Nonlinearity (1)

G. Fibich and M. Klein, “Continuations of the nonlinear Schrödinger equation beyond the singularity,” Nonlinearity 24, 2003–2045 (2011).
[Crossref]

Opt. Express (4)

Opt. Lett. (6)

Phys. Rep. (1)

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

Phys. Rev. A (3)

S. A. Hosseini, Q. Luo, B. Ferland, W. Liu, S. L. Chin, O. G. Kosareva, N. A. Panov, N. Aközbek, and V. P. Kandidov, “Competition of multiple filaments during the propagation of intense femtosecond laser pulses,” Phys. Rev. A 70, 033802 (2004).
[Crossref]

A. A. Ishaaya, T. D. Grow, S. Ghosh, L. T. Vuong, and A. L. Gaeta, “Self-focusing dynamics of coupled optical beams,” Phys. Rev. A 75, 023813 (2007).
[Crossref]

B. Shim, S. E. Schrauth, C. J. Hensley, L. T. Vuong, P. Hui, A. A. Ishaaya, and A. L. Gaeta, “Controlled interactions of femtosecond light filaments in air,” Phys. Rev. A 81, 061803 (2010).
[Crossref]

Phys. Rev. Lett. (12)

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108, 043902 (2012).
[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, 133901 (2006).
[Crossref]

T. D. Grow, A. A. Ishaaya, L. T. Vuong, and A. L. Gaeta, “Collapse and stability of necklace beams in Kerr media,” Phys. Rev. Lett. 99, 133902 (2007).
[Crossref]

G. Fibich and B. Ilan, “Multiple filamentation of circularly polarized beams,” Phys. Rev. Lett. 89, 013901 (2002).
[Crossref]

M. Mlejnek, M. Kolesik, J. V. Moloney, and E. M. Wright, “Optically turbulent femtosecond light guide in air,” Phys. Rev. Lett. 83, 2938–2941 (1999).
[Crossref]

L. Bergé, S. Skupin, F. Lederer, G. Méjean, J. Yu, J. Kasparian, E. Salmon, J. P. Wolf, M. Rodriguez, L. Wöste, R. Bourayou, and R. Sauerbrey, “Multiple filamentation of terawatt laser pulses in air,” Phys. Rev. Lett. 92, 225002 (2004).
[Crossref]

S. Tzortzakis, L. Bergé, A. Couairon, M. Franco, B. Prade, and A. Mysyrowicz, “Breakup and fusion of self-guided femtosecond light pulses in air,” Phys. Rev. Lett. 86, 5470–5473 (2001).
[Crossref]

F. Belgiorno, S. L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V. G. Sala, and D. Faccio, “Hawking radiation from ultrashort laser pulse filaments,” Phys. Rev. Lett. 105, 203901 (2010).
[Crossref]

C. D’Amico, A. Houard, M. Franco, B. Prade, and A. Mysyrowicz, “Conical forward THz emission from femtosecond-laser-beam filamentation in air,” Phys. Rev. Lett. 98, 235002 (2007).
[Crossref]

T. T. Xi, X. Lu, and J. Zhang, “Interaction of light filaments generated by femtosecond laser pulses in air,” Phys. Rev. Lett. 96, 025003 (2006).
[Crossref]

S. Varma, Y. H. Chen, and H. M. Milchberg, “Trapping and destruction of long-range high-intensity optical filaments by molecular quantum wakes in air,” Phys. Rev. Lett. 101, 205001 (2008).
[Crossref]

F. Calegari, C. Vozzi, S. Gasilov, E. Benedetti, G. Sansone, M. Nisoli, S. De Silvestri, and S. Stagira, “Rotational Raman effects in the wake of optical filamentation,” Phys. Rev. Lett. 100, 123006 (2008).
[Crossref]

Sci. Rep. (1)

S. M. Li, Y. N. Li, X. L. Wang, L. J. Kong, K. Lou, C. H. Tu, Y. J. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
[Crossref]

Science (1)

J. Kasparian, M. Rodriguez, G. Méjean, J. Yu, E. Salmon, H. Wille, R. Bourayou, S. Frey, Y. B. André, A. Mysyrowicz, R. Sauerbrey, J. P. Wolf, and L. Wöste, “White-light filaments for atmospheric analysis,” Science 301, 61–64 (2003).
[Crossref]

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Figures (4)

Fig. 1.
Fig. 1. (a) Simulated intensity pattern and SoP distribution of the focused AV-HP-VF with m = 2 and φ 0 = 0 , and 10% amplitude random noise. (b) Simulated filamentation pattern of the AV-HP-VF shown in (a) under the conditions of P = 12 P C , ζ = 1.6 , ε = 0.33 , and ε = 10 4 . (c)–(e) Simulated on-axis accumulated phases for three filaments labeled H 1 , H 2 , and H 3 under the same conditions as (b). (f) Simulated relative phases between H 1 and H 2 as well as H 1 and H 3 . For comparison, the simulated on-axis phases of the perfect AV-HP-VF with m = 2 and φ 0 = 0 are given in (c)–(f).
Fig. 2.
Fig. 2. Simulated evolution of the peak intensity of filament with the propagation distance for AV-HP-VF with m = 2 and φ 0 = 0 , under the conditions of ε = 0.33 and ε = 10 4 (a) at different random noise levels of no noise, 5% noise, and 10% noise at P = 12 P C and (b) at different input powers of P = 10 P C , 11 P C , and 12 P C without random noise.
Fig. 3.
Fig. 3. Simulated collapsing evolution and multiple filamentation of the AV-HP-VFs by Eq. (3) under the conditions of ε = 0.33 , ε = 10 4 , and P = 12 P C with 10% amplitude random noise. (a) AV-HP-VF with m = 1 and φ 0 = 0 . (b) AV-HP-VF with m = 2 and φ 0 = 0 .
Fig. 4.
Fig. 4. Measured six consecutive, 10-shot average CCD images of filamentation of AV-HP-VFs at 2.0 μJ pulse energy for two AV-HP-VFs with (a)  m = 1 and (b)  m = 2 .

Equations (8)

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| Ψ = E 0 circ ( ρ / r 0 ) { exp [ j ( m ϕ + ϕ 0 ) ] ( | H + | V ) + exp [ j ( m ϕ + ϕ 0 ) ] ( | H | V ) } ,
= 2 E 0 circ ( ρ / r 0 ) { cos ( m ϕ + ϕ 0 ) | H + exp ( j π / 2 ) sin ( m ϕ + ϕ 0 ) | V } ,
| ψ = A 0 Q [ cos ( m φ + φ 0 ) | H + exp ( j π / 2 ) sin ( m φ + φ 0 ) | V ] ,
Q = ( p / 2 ) m 1 F 2 [ 1 + m / 2 ; 2 + m / 2,1 + m ; ( p / 2 ) 2 ] ( m + 2 ) m ! ,
ψ H / ζ = ( j / 4 ) 2 ψ H + j P H ( 3 ) j P H ( 5 ) ,
ψ V / ζ = ( j / 4 ) 2 ψ V + j P V ( 3 ) j P V ( 5 ) ,
P H ( 3 ) = ε P P C 1 ( 3 | ψ H | 2 ψ H + 2 | ψ V | 2 ψ H + ψ V 2 ψ H * ) ,
P H ( 5 ) = ε P 2 P C 2 ( 5 | ψ H | 4 ψ H + 3 | ψ V | 4 ψ H + 2 | ψ V | 2 ψ V 2 ψ H * + 3 | ψ H | 2 ψ V 2 ψ H * + ψ H 3 ψ V * 2 + 6 | ψ H | 2 | ψ V | 2 ψ H ) ,

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