Abstract

The collapse dynamics of a structured optical field with a distribution of spatially-variant states of polarization (SoP) and a spiral phase in the field cross section is studied using the two-dimensional coupled nonlinear Schrӧdinger equations. The self-focusing of a structured optical field with an inhomogeneous SoP distribution can give rise to new phenomena of collapse dynamics that is completely different from a scalar field. The collapse patterns are closely related to the topological charges of the vortexas well as the polarization, the initial power, and the SoP distribution in the field cross section. A single on-axis collapse or multiple off-axis partial collapses may occur due to the self-focusing effects of linearly, elliptically and circularly polarized components located at different positions of the field cross-section. The polarization in the core of the collapsing beam is always linearly polarized. The structured collapsing beams, which are driven by the vortex, propagate along a spiral trajectory in a saturated medium.

© 2016 Optical Society of America

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References

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  1. P. A. Robinson, “Nonlinear wave collapse and strong turbulence,” Rev. Mod. Phys. 69(2), 507–574 (1997).
    [Crossref]
  2. L. Bergé, C. Gouédard, J. Schjodt-Eriksen, and H. Ward, “Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states,” Physica D 176(3-4), 181–211 (2003).
    [Crossref]
  3. M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refueled optical filaments,” Nat. Photonics 8(4), 297–301 (2014).
    [Crossref]
  4. R. Chiao, E. Garmire, and C. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
    [Crossref]
  5. L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
    [Crossref] [PubMed]
  6. A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, “Suppression of collapse for spiraling elliptic solitons,” Phys. Rev. Lett. 104(5), 053902 (2010).
    [Crossref] [PubMed]
  7. R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3, 1406 (2013).
    [Crossref] [PubMed]
  8. A. Dubietis, G. Tamosauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29(10), 1126–1128 (2004).
    [Crossref] [PubMed]
  9. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
    [Crossref]
  10. R. P. Chen, Z. Chen, K. H. Chew, P. G. Li, Z. Yu, J. Ding, and S. He, “Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation,” Sci. Rep. 5, 10628 (2015).
    [Crossref] [PubMed]
  11. H.-T. Wang, X.-L. Wang, Y. Li, J. Chen, C.-S. Guo, and J. Ding, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18(10), 10786–10795 (2010).
    [Crossref] [PubMed]
  12. D. Deng, Q. Guo, L. Wu, and X. Yang, “Propagation of radially polarized elegant light beams,” J. Opt. Soc. Am. B 24(3), 636–643 (2007).
    [Crossref]
  13. R. P. Chen and G. Li, “The evanescent wavefield part of a cylindrical vector beam,” Opt. Express 21(19), 22246–22254 (2013).
    [Crossref] [PubMed]
  14. R.-P. Chen, L.-X. Zhong, K.-H. Chew, B. Gu, G. Zhou, and T. Zhao, “Effect of a spiral phase on a vector beam with hybrid polarization states,” J. Opt. 17(6), 065605 (2015).
    [Crossref]
  15. N. M. Litchinitser, “Applied physics. Structured light meets structured matter,” Science 337(6098), 1054–1055 (2012).
    [Crossref] [PubMed]
  16. 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(1), 13–15 (2008).
    [Crossref] [PubMed]
  17. G. Fibich and N. Gavish, “Critical power of collapsing vortices,” Phys. Rev. A 77(4), 045803 (2008).
    [Crossref]
  18. S. M. Li, Y. Li, X. L. Wang, L. J. Kong, K. Lou, C. Tu, Y. Tian, and H. T. Wang, “Taming the collapse of optical fields,” Sci. Rep. 2, 1007 (2012).
    [PubMed]
  19. R. P. Chen, L. X. Zhong, K. H. Chew, T. Y. Zhao, and X. Zhang, “X, Zhang, “Collapse dynamics of a vector vortex optical field with inhomogeneous states of polarization,” Laser Phys. 25(7), 075401 (2015).
    [Crossref]
  20. V. M. Malkin, “On the analytical theory for stationary self-focusing of radiation,” Physica D 38, 537 (1993).
  21. N. A. Panov, V. A. Makarov, V. Y. Fedorov, and O. G. Kosareva, “Filamentation of arbitrary polarized femtosecond laser pulses in case of high-order Kerr effect,” Opt. Lett. 38(4), 537–539 (2013).
    [Crossref] [PubMed]
  22. B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108(4), 043902 (2012).
    [Crossref] [PubMed]
  23. A. S. Desyatnikov, D. E. Pelinovsky, and J. Yang, “Multi-component vortex solutions in symmetric coupled nonlinear Schrodinger equations,” J. Math. Sci. 151(4), 3091–3111 (2008).
    [Crossref]
  24. V. Kruglov, Y. Logvin, and V. M. Volkov, “The theory of spiral laser beams in nonlinear media,” J. Mod. Opt. 39(11), 2277–2291 (1992).
    [Crossref]
  25. V. Prytula, V. Vekslerchik, and V. M. Pérez-García, “Collapse in coupled nonlinear Schrodinger equations: Suffcient conditions and applications,” Physica D 238(15), 1462–1467 (2009).
    [Crossref]
  26. G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25(5), 335–337 (2000).
    [Crossref] [PubMed]

2015 (3)

R. P. Chen, Z. Chen, K. H. Chew, P. G. Li, Z. Yu, J. Ding, and S. He, “Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation,” Sci. Rep. 5, 10628 (2015).
[Crossref] [PubMed]

R.-P. Chen, L.-X. Zhong, K.-H. Chew, B. Gu, G. Zhou, and T. Zhao, “Effect of a spiral phase on a vector beam with hybrid polarization states,” J. Opt. 17(6), 065605 (2015).
[Crossref]

R. P. Chen, L. X. Zhong, K. H. Chew, T. Y. Zhao, and X. Zhang, “X, Zhang, “Collapse dynamics of a vector vortex optical field with inhomogeneous states of polarization,” Laser Phys. 25(7), 075401 (2015).
[Crossref]

2014 (1)

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refueled optical filaments,” Nat. Photonics 8(4), 297–301 (2014).
[Crossref]

2013 (3)

2012 (3)

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108(4), 043902 (2012).
[Crossref] [PubMed]

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

N. M. Litchinitser, “Applied physics. Structured light meets structured matter,” Science 337(6098), 1054–1055 (2012).
[Crossref] [PubMed]

2010 (2)

H.-T. Wang, X.-L. Wang, Y. Li, J. Chen, C.-S. Guo, and J. Ding, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18(10), 10786–10795 (2010).
[Crossref] [PubMed]

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, “Suppression of collapse for spiraling elliptic solitons,” Phys. Rev. Lett. 104(5), 053902 (2010).
[Crossref] [PubMed]

2009 (2)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

V. Prytula, V. Vekslerchik, and V. M. Pérez-García, “Collapse in coupled nonlinear Schrodinger equations: Suffcient conditions and applications,” Physica D 238(15), 1462–1467 (2009).
[Crossref]

2008 (3)

A. S. Desyatnikov, D. E. Pelinovsky, and J. Yang, “Multi-component vortex solutions in symmetric coupled nonlinear Schrodinger equations,” J. Math. Sci. 151(4), 3091–3111 (2008).
[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(1), 13–15 (2008).
[Crossref] [PubMed]

G. Fibich and N. Gavish, “Critical power of collapsing vortices,” Phys. Rev. A 77(4), 045803 (2008).
[Crossref]

2007 (1)

2006 (1)

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref] [PubMed]

2004 (1)

2003 (1)

L. Bergé, C. Gouédard, J. Schjodt-Eriksen, and H. Ward, “Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states,” Physica D 176(3-4), 181–211 (2003).
[Crossref]

2000 (1)

1997 (1)

P. A. Robinson, “Nonlinear wave collapse and strong turbulence,” Rev. Mod. Phys. 69(2), 507–574 (1997).
[Crossref]

1993 (1)

V. M. Malkin, “On the analytical theory for stationary self-focusing of radiation,” Physica D 38, 537 (1993).

1992 (1)

V. Kruglov, Y. Logvin, and V. M. Volkov, “The theory of spiral laser beams in nonlinear media,” J. Mod. Opt. 39(11), 2277–2291 (1992).
[Crossref]

1964 (1)

R. Chiao, E. Garmire, and C. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[Crossref]

’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(13), 133901 (2006).
[Crossref] [PubMed]

Bergé, L.

L. Bergé, C. Gouédard, J. Schjodt-Eriksen, and H. Ward, “Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states,” Physica D 176(3-4), 181–211 (2003).
[Crossref]

Buccoliero, D.

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, “Suppression of collapse for spiraling elliptic solitons,” Phys. Rev. Lett. 104(5), 053902 (2010).
[Crossref] [PubMed]

Chen, J.

Chen, R. P.

R. P. Chen, Z. Chen, K. H. Chew, P. G. Li, Z. Yu, J. Ding, and S. He, “Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation,” Sci. Rep. 5, 10628 (2015).
[Crossref] [PubMed]

R. P. Chen, L. X. Zhong, K. H. Chew, T. Y. Zhao, and X. Zhang, “X, Zhang, “Collapse dynamics of a vector vortex optical field with inhomogeneous states of polarization,” Laser Phys. 25(7), 075401 (2015).
[Crossref]

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3, 1406 (2013).
[Crossref] [PubMed]

R. P. Chen and G. Li, “The evanescent wavefield part of a cylindrical vector beam,” Opt. Express 21(19), 22246–22254 (2013).
[Crossref] [PubMed]

Chen, R.-P.

R.-P. Chen, L.-X. Zhong, K.-H. Chew, B. Gu, G. Zhou, and T. Zhao, “Effect of a spiral phase on a vector beam with hybrid polarization states,” J. Opt. 17(6), 065605 (2015).
[Crossref]

Chen, Z.

R. P. Chen, Z. Chen, K. H. Chew, P. G. Li, Z. Yu, J. Ding, and S. He, “Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation,” Sci. Rep. 5, 10628 (2015).
[Crossref] [PubMed]

Cheng, W.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refueled optical filaments,” Nat. Photonics 8(4), 297–301 (2014).
[Crossref]

Chew, K. H.

R. P. Chen, Z. Chen, K. H. Chew, P. G. Li, Z. Yu, J. Ding, and S. He, “Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation,” Sci. Rep. 5, 10628 (2015).
[Crossref] [PubMed]

R. P. Chen, L. X. Zhong, K. H. Chew, T. Y. Zhao, and X. Zhang, “X, Zhang, “Collapse dynamics of a vector vortex optical field with inhomogeneous states of polarization,” Laser Phys. 25(7), 075401 (2015).
[Crossref]

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3, 1406 (2013).
[Crossref] [PubMed]

Chew, K.-H.

R.-P. Chen, L.-X. Zhong, K.-H. Chew, B. Gu, G. Zhou, and T. Zhao, “Effect of a spiral phase on a vector beam with hybrid polarization states,” J. Opt. 17(6), 065605 (2015).
[Crossref]

Chiao, R.

R. Chiao, E. Garmire, and C. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[Crossref]

Christodoulides, D. N.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refueled optical filaments,” Nat. Photonics 8(4), 297–301 (2014).
[Crossref]

Deng, D.

Dennis, M. R.

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, “Suppression of collapse for spiraling elliptic solitons,” Phys. Rev. Lett. 104(5), 053902 (2010).
[Crossref] [PubMed]

Desyatnikov, A. S.

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, “Suppression of collapse for spiraling elliptic solitons,” Phys. Rev. Lett. 104(5), 053902 (2010).
[Crossref] [PubMed]

A. S. Desyatnikov, D. E. Pelinovsky, and J. Yang, “Multi-component vortex solutions in symmetric coupled nonlinear Schrodinger equations,” J. Math. Sci. 151(4), 3091–3111 (2008).
[Crossref]

Ding, J.

R. P. Chen, Z. Chen, K. H. Chew, P. G. Li, Z. Yu, J. Ding, and S. He, “Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation,” Sci. Rep. 5, 10628 (2015).
[Crossref] [PubMed]

H.-T. Wang, X.-L. Wang, Y. Li, J. Chen, C.-S. Guo, and J. Ding, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18(10), 10786–10795 (2010).
[Crossref] [PubMed]

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(13), 133901 (2006).
[Crossref] [PubMed]

Fedorov, V. Y.

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(4), 043902 (2012).
[Crossref] [PubMed]

G. Fibich and N. Gavish, “Critical power of collapsing vortices,” Phys. Rev. A 77(4), 045803 (2008).
[Crossref]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref] [PubMed]

A. Dubietis, G. Tamosauskas, G. Fibich, and B. Ilan, “Multiple filamentation induced by input-beam ellipticity,” Opt. Lett. 29(10), 1126–1128 (2004).
[Crossref] [PubMed]

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25(5), 335–337 (2000).
[Crossref] [PubMed]

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(4), 043902 (2012).
[Crossref] [PubMed]

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(1), 13–15 (2008).
[Crossref] [PubMed]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref] [PubMed]

G. Fibich and A. L. Gaeta, “Critical power for self-focusing in bulk media and in hollow waveguides,” Opt. Lett. 25(5), 335–337 (2000).
[Crossref] [PubMed]

Garmire, E.

R. Chiao, E. Garmire, and C. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[Crossref]

Gavish, N.

G. Fibich and N. Gavish, “Critical power of collapsing vortices,” Phys. Rev. A 77(4), 045803 (2008).
[Crossref]

Gouédard, C.

L. Bergé, C. Gouédard, J. Schjodt-Eriksen, and H. Ward, “Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states,” Physica D 176(3-4), 181–211 (2003).
[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(1), 13–15 (2008).
[Crossref] [PubMed]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref] [PubMed]

Gu, B.

R.-P. Chen, L.-X. Zhong, K.-H. Chew, B. Gu, G. Zhou, and T. Zhao, “Effect of a spiral phase on a vector beam with hybrid polarization states,” J. Opt. 17(6), 065605 (2015).
[Crossref]

Guo, C.-S.

Guo, Q.

He, S.

R. P. Chen, Z. Chen, K. H. Chew, P. G. Li, Z. Yu, J. Ding, and S. He, “Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation,” Sci. Rep. 5, 10628 (2015).
[Crossref] [PubMed]

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3, 1406 (2013).
[Crossref] [PubMed]

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(13), 133901 (2006).
[Crossref] [PubMed]

Ishaaya, A. A.

Kivshar, Y. S.

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, “Suppression of collapse for spiraling elliptic solitons,” Phys. Rev. Lett. 104(5), 053902 (2010).
[Crossref] [PubMed]

Klein, M.

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108(4), 043902 (2012).
[Crossref] [PubMed]

Kolesik, M.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refueled optical filaments,” Nat. Photonics 8(4), 297–301 (2014).
[Crossref]

Kong, L. J.

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

Kosareva, O. G.

Kruglov, V.

V. Kruglov, Y. Logvin, and V. M. Volkov, “The theory of spiral laser beams in nonlinear media,” J. Mod. Opt. 39(11), 2277–2291 (1992).
[Crossref]

Li, G.

Li, P. G.

R. P. Chen, Z. Chen, K. H. Chew, P. G. Li, Z. Yu, J. Ding, and S. He, “Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation,” Sci. Rep. 5, 10628 (2015).
[Crossref] [PubMed]

Li, S. M.

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

Li, Y.

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

H.-T. Wang, X.-L. Wang, Y. Li, J. Chen, C.-S. Guo, and J. Ding, “A new type of vector fields with hybrid states of polarization,” Opt. Express 18(10), 10786–10795 (2010).
[Crossref] [PubMed]

Litchinitser, N. M.

N. M. Litchinitser, “Applied physics. Structured light meets structured matter,” Science 337(6098), 1054–1055 (2012).
[Crossref] [PubMed]

Logvin, Y.

V. Kruglov, Y. Logvin, and V. M. Volkov, “The theory of spiral laser beams in nonlinear media,” J. Mod. Opt. 39(11), 2277–2291 (1992).
[Crossref]

Lou, K.

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

Makarov, V. A.

Malkin, V. M.

V. M. Malkin, “On the analytical theory for stationary self-focusing of radiation,” Physica D 38, 537 (1993).

Mills, M. S.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refueled optical filaments,” Nat. Photonics 8(4), 297–301 (2014).
[Crossref]

Miri, M. A.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refueled optical filaments,” Nat. Photonics 8(4), 297–301 (2014).
[Crossref]

Moloney, J. V.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refueled optical filaments,” Nat. Photonics 8(4), 297–301 (2014).
[Crossref]

Panov, N. A.

Pelinovsky, D. E.

A. S. Desyatnikov, D. E. Pelinovsky, and J. Yang, “Multi-component vortex solutions in symmetric coupled nonlinear Schrodinger equations,” J. Math. Sci. 151(4), 3091–3111 (2008).
[Crossref]

Pérez-García, V. M.

V. Prytula, V. Vekslerchik, and V. M. Pérez-García, “Collapse in coupled nonlinear Schrodinger equations: Suffcient conditions and applications,” Physica D 238(15), 1462–1467 (2009).
[Crossref]

Polynkin, P.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refueled optical filaments,” Nat. Photonics 8(4), 297–301 (2014).
[Crossref]

Prytula, V.

V. Prytula, V. Vekslerchik, and V. M. Pérez-García, “Collapse in coupled nonlinear Schrodinger equations: Suffcient conditions and applications,” Physica D 238(15), 1462–1467 (2009).
[Crossref]

Robinson, P. A.

P. A. Robinson, “Nonlinear wave collapse and strong turbulence,” Rev. Mod. Phys. 69(2), 507–574 (1997).
[Crossref]

Scheller, M.

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refueled optical filaments,” Nat. Photonics 8(4), 297–301 (2014).
[Crossref]

Schjodt-Eriksen, J.

L. Bergé, C. Gouédard, J. Schjodt-Eriksen, and H. Ward, “Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states,” Physica D 176(3-4), 181–211 (2003).
[Crossref]

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(4), 043902 (2012).
[Crossref] [PubMed]

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(4), 043902 (2012).
[Crossref] [PubMed]

Tamosauskas, G.

Tian, Y.

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

Townes, C.

R. Chiao, E. Garmire, and C. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[Crossref]

Tu, C.

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

Vekslerchik, V.

V. Prytula, V. Vekslerchik, and V. M. Pérez-García, “Collapse in coupled nonlinear Schrodinger equations: Suffcient conditions and applications,” Physica D 238(15), 1462–1467 (2009).
[Crossref]

Volkov, V. M.

V. Kruglov, Y. Logvin, and V. M. Volkov, “The theory of spiral laser beams in nonlinear media,” J. Mod. Opt. 39(11), 2277–2291 (1992).
[Crossref]

Vuong, L. T.

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(1), 13–15 (2008).
[Crossref] [PubMed]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref] [PubMed]

Wang, H. T.

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

Wang, H.-T.

Wang, X. L.

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

Wang, X.-L.

Ward, H.

L. Bergé, C. Gouédard, J. Schjodt-Eriksen, and H. Ward, “Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states,” Physica D 176(3-4), 181–211 (2003).
[Crossref]

Wu, L.

Yang, J.

A. S. Desyatnikov, D. E. Pelinovsky, and J. Yang, “Multi-component vortex solutions in symmetric coupled nonlinear Schrodinger equations,” J. Math. Sci. 151(4), 3091–3111 (2008).
[Crossref]

Yang, X.

Yu, Z.

R. P. Chen, Z. Chen, K. H. Chew, P. G. Li, Z. Yu, J. Ding, and S. He, “Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation,” Sci. Rep. 5, 10628 (2015).
[Crossref] [PubMed]

Zhan, Q.

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

Zhang, X.

R. P. Chen, L. X. Zhong, K. H. Chew, T. Y. Zhao, and X. Zhang, “X, Zhang, “Collapse dynamics of a vector vortex optical field with inhomogeneous states of polarization,” Laser Phys. 25(7), 075401 (2015).
[Crossref]

Zhao, T.

R.-P. Chen, L.-X. Zhong, K.-H. Chew, B. Gu, G. Zhou, and T. Zhao, “Effect of a spiral phase on a vector beam with hybrid polarization states,” J. Opt. 17(6), 065605 (2015).
[Crossref]

Zhao, T. Y.

R. P. Chen, L. X. Zhong, K. H. Chew, T. Y. Zhao, and X. Zhang, “X, Zhang, “Collapse dynamics of a vector vortex optical field with inhomogeneous states of polarization,” Laser Phys. 25(7), 075401 (2015).
[Crossref]

Zhong, L. X.

R. P. Chen, L. X. Zhong, K. H. Chew, T. Y. Zhao, and X. Zhang, “X, Zhang, “Collapse dynamics of a vector vortex optical field with inhomogeneous states of polarization,” Laser Phys. 25(7), 075401 (2015).
[Crossref]

Zhong, L.-X.

R.-P. Chen, L.-X. Zhong, K.-H. Chew, B. Gu, G. Zhou, and T. Zhao, “Effect of a spiral phase on a vector beam with hybrid polarization states,” J. Opt. 17(6), 065605 (2015).
[Crossref]

Zhou, G.

R.-P. Chen, L.-X. Zhong, K.-H. Chew, B. Gu, G. Zhou, and T. Zhao, “Effect of a spiral phase on a vector beam with hybrid polarization states,” J. Opt. 17(6), 065605 (2015).
[Crossref]

Adv. Opt. Photonics (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1(1), 1–57 (2009).
[Crossref]

J. Math. Sci. (1)

A. S. Desyatnikov, D. E. Pelinovsky, and J. Yang, “Multi-component vortex solutions in symmetric coupled nonlinear Schrodinger equations,” J. Math. Sci. 151(4), 3091–3111 (2008).
[Crossref]

J. Mod. Opt. (1)

V. Kruglov, Y. Logvin, and V. M. Volkov, “The theory of spiral laser beams in nonlinear media,” J. Mod. Opt. 39(11), 2277–2291 (1992).
[Crossref]

J. Opt. (1)

R.-P. Chen, L.-X. Zhong, K.-H. Chew, B. Gu, G. Zhou, and T. Zhao, “Effect of a spiral phase on a vector beam with hybrid polarization states,” J. Opt. 17(6), 065605 (2015).
[Crossref]

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

Laser Phys. (1)

R. P. Chen, L. X. Zhong, K. H. Chew, T. Y. Zhao, and X. Zhang, “X, Zhang, “Collapse dynamics of a vector vortex optical field with inhomogeneous states of polarization,” Laser Phys. 25(7), 075401 (2015).
[Crossref]

Nat. Photonics (1)

M. Scheller, M. S. Mills, M. A. Miri, W. Cheng, J. V. Moloney, M. Kolesik, P. Polynkin, and D. N. Christodoulides, “Externally refueled optical filaments,” Nat. Photonics 8(4), 297–301 (2014).
[Crossref]

Opt. Express (2)

Opt. Lett. (4)

Phys. Rev. A (1)

G. Fibich and N. Gavish, “Critical power of collapsing vortices,” Phys. Rev. A 77(4), 045803 (2008).
[Crossref]

Phys. Rev. Lett. (4)

R. Chiao, E. Garmire, and C. Townes, “Self-trapping of optical beams,” Phys. Rev. Lett. 13(15), 479–482 (1964).
[Crossref]

L. T. Vuong, T. D. Grow, A. Ishaaya, A. L. Gaeta, G. W. ’t Hooft, E. R. Eliel, and G. Fibich, “Collapse of optical vortices,” Phys. Rev. Lett. 96(13), 133901 (2006).
[Crossref] [PubMed]

A. S. Desyatnikov, D. Buccoliero, M. R. Dennis, and Y. S. Kivshar, “Suppression of collapse for spiraling elliptic solitons,” Phys. Rev. Lett. 104(5), 053902 (2010).
[Crossref] [PubMed]

B. Shim, S. E. Schrauth, A. L. Gaeta, M. Klein, and G. Fibich, “Loss of phase of collapsing beams,” Phys. Rev. Lett. 108(4), 043902 (2012).
[Crossref] [PubMed]

Physica D (3)

V. M. Malkin, “On the analytical theory for stationary self-focusing of radiation,” Physica D 38, 537 (1993).

V. Prytula, V. Vekslerchik, and V. M. Pérez-García, “Collapse in coupled nonlinear Schrodinger equations: Suffcient conditions and applications,” Physica D 238(15), 1462–1467 (2009).
[Crossref]

L. Bergé, C. Gouédard, J. Schjodt-Eriksen, and H. Ward, “Filamentation patterns in Kerr media vs. beam shape robustness, nonlinear saturation and polarization states,” Physica D 176(3-4), 181–211 (2003).
[Crossref]

Rev. Mod. Phys. (1)

P. A. Robinson, “Nonlinear wave collapse and strong turbulence,” Rev. Mod. Phys. 69(2), 507–574 (1997).
[Crossref]

Sci. Rep. (3)

R. P. Chen, Z. Chen, K. H. Chew, P. G. Li, Z. Yu, J. Ding, and S. He, “Structured caustic vector vortex optical field: manipulating optical angular momentum flux and polarization rotation,” Sci. Rep. 5, 10628 (2015).
[Crossref] [PubMed]

R. P. Chen, K. H. Chew, and S. He, “Dynamic control of collapse in a vortex Airy beam,” Sci. Rep. 3, 1406 (2013).
[Crossref] [PubMed]

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

Science (1)

N. M. Litchinitser, “Applied physics. Structured light meets structured matter,” Science 337(6098), 1054–1055 (2012).
[Crossref] [PubMed]

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Figures (5)

Fig. 1
Fig. 1 (a) The polarization states distribution in the field cross-section of the initial field with n = 1, m = 1, Δθ = π/2 and φ0 = 0. The intensity distribution with the propagation distance for different initial powers: (b) Pin = 2.3PG, (c) Pin = 5.3PG. (d) The corresponding normalized peak intensity as a function of propagation distance for different initial powers. The Stokes polarization parameters for input powers (e) Pin = 2.3PG and (f) Pin = 5.3PG at different propagation distances. Positive and negative S1 (or S2) Stokes values represent horizontal (or 45°) and vertical (or 135°) linear polarization components, respectively, whereas positive and negative S3 values represent opposite circular components. Black circles indicate the corresponding locations of the collapse. Note here that Pin = 2.3PG and 5.3PG are the threshold power for the occurrence of an on-axis and off-axis partial collapses.
Fig. 2
Fig. 2 the evolution of on-axis intensity in the structured optical field as a function of propagation distances for a pure linear propagation or a nonlinear propagation with different initial powers. (a) n = m = 1, Pin = 1.15PG; (b) n = m = 1, Pin = 2.3PG; (c) n = m = 2, Pin = 1.45PG; (d) n = m = 2, Pin = 2.9PG.
Fig. 3
Fig. 3 (a) The polarization states distribution in the cross-section of the initial field. (b) The intensity distribution of the vortex vector field (n = 1, m = 2, Δθ = π/2 and φ0 = 0) for Pin = 8.2 PG at different propagation distances. (c) The Stokes polarization parameters at different propagation distances.
Fig. 4
Fig. 4 (a) Iso-surface I = 3 of the data in Stokes parameter S0 for n = 1, m = 1 with initial power Pin = 8Pcr. (b) The corresponding central and neighboring peak intensity as a function of the propagation distance. Vertical dashed lines mark corresponding propagation distances of the maximum amplitudes, and (c) The corresponding Stokes polarization parameters at different propagation distances as marked by the vertical dashed lines.
Fig. 5
Fig. 5 (a) Iso-surface I = 2.7 of the intensity distribution data (Stokes parameter S0) for n = 2, m = 1 with initial power Pin = 8Pcr; (b) The corresponding peak intensity as a function of the propagation distance.

Tables (1)

Tables Icon

Table 1 Critical powers for single on-axial collapse and multiple off-axial collapse when nm, Δθ = π/2 and φ0 = 0

Equations (8)

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2 E ± 2ik E ± z + 4 n 2 k 2 3 n 0 ( | E ± | 2 +2 | E | 2 ) E ± 2 n 4 k 2 5 n 0 ( | E ± | 4 +6 | E ± | 2 | E | 2 +3 | E | 4 ) E ± =0,
P(z)= s ( | E + | 2 + | E | 2 )dxdy ,
H(z)= 1 4 k 2 s [ | E + | 2 + | E | 2 2 k 2 n 2 3 n 0 ( | E + | 4 + | E | 4 +4 | E + | 2 | E | 2 ) + k 2 n 4 15 n 0 ( 2 | E + | 6 +2 | E | 6 +6 | E + | 4 | E | 2 +6 | E + | 2 | E | 4 ) ]dxdy,
I(z)= s ( x 2 + y 2 )( | E + | 2 + | E | 2 )dxdy ,
I(z)=I(z=0)+ dI(z=0) dz z+4H(z=0) z 2 ,
E(x,y;z=0)= A 0 r n exp( r 2 / w 0 2 )(cos(mφ+ φ 0 ) e x +sin(mφ+ φ 0 )exp(iΔθ) e y )exp(inφ) = A 0 r n exp( r 2 / w 0 2 )([cos(mφ+ φ 0 )+exp(iπ/2+iΔθ)sin(mφ+ φ 0 )] e + +[cos(mφ+ φ 0 )exp(iπ/2+iΔθ)sin(mφ+ φ 0 )] e )exp(inφ)/ 2 ,
P cr = 6 5 4 n ( m 2 +n)n!Γ[n] (2n)! P G ,
A 0 r n exp( r 2 / w 0 2 )[cos(mφ+ φ 0 ) e x +sin(mφ+ φ 0 )exp(iΔθ) e y ]exp(inφ) = A 0 r n exp( r 2 / w 0 2 )[exp(i(n+m)φ+i φ 0 )+exp(i(nm)φi φ 0 )] e x /2 i A 0 r n exp( r 2 / w 0 2 )[exp(i(n+m)φ+i φ 0 )exp(i(nm)φi φ 0 )]exp(iΔθ) e y /2.

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