Abstract

We observe the stabilization of a single-(double-) charge optical vortex propagating in a self-focusing medium. The optical vortex, which carries a phase singularity at its center, usually breaks up in a self-focusing medium due to the so-called azimuthal instability. However, by adding a small rotating azimuthally-periodic intensity modulation on the vortex light beam, which propagates in a noninstantaneous self-focusing medium, we successfully suppress the azimuthal instability. This observation is confirmed by both numerical simulation and perturbational analysis.

© 2007 Optical Society of America

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  1. L. M. Pismen, Vortices in Nonlinear Fields (Clarendon Press, Oxford, 1999).
  2. See, e.g., Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, 2003), Chap. 8.
  3. G. A. Swartzlander and C. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992).
    [CrossRef] [PubMed]
  4. G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, "Dark photorefractive spatial solitons and photorefractive vortex solitons," Phys. Rev. Lett. 74, 1978-1981 (1995).
    [CrossRef] [PubMed]
  5. J. Christou,V. Tikhonenko,Y. S. Kivshar, and B. Luther-Davies, "Vortex soliton motion and steering," Opt. Lett. 21, 1649-1651 (1996).
    [CrossRef] [PubMed]
  6. Z. Chen, M. Shih, M. Segev, D.W. Wilson, R. E. Muller, and P. D. Maker, "Steady-state vortex-screening solitons formed in biased photorefractive media," Opt. Lett. 22, 1751-1753 (1997).
    [CrossRef]
  7. Z. Chen, M. Mitchell, M. Segev, T. Coskun, and D. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889-892 (1998).
    [CrossRef] [PubMed]
  8. V. I. Kruglov and R. A. Vlasov, "Spiral self-trapping propagation of optical beams in media with cubic nonlinearity," Phys. Lett. A 111, 401-404 (1985).
    [CrossRef]
  9. W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450-2453 (1997).
    [CrossRef]
  10. V. Tikhonenko, J. Christou, and B. Luther-Davies, "Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium," J. Opt. Soc. Am. B 12, 2046-2052 (1995).
    [CrossRef]
  11. D. V. Petrov, L. Torner, J. Nartorell, R. Vilaseca, J. P. Torres, and C. Cojocaru, "Observation of azimuthal modulational instability and formation of patterns of optical solitons in a quadratic nonlinear crystal," Opt. Lett. 23, 1444-1446 (1998).
    [CrossRef]
  12. M. Bigelow, P. Zerom and R. Boyd, "Breakup of ring beams carrying orbital angular momentum in sodium vapor," Phys. Rev. Lett. 92, 083902 (2004).
    [CrossRef] [PubMed]
  13. H. Saito and M. Ueda, "Split instability of a vortex in an attractive Bose-Einstein condensate, " Phys. Rev. Lett. 89, 190402 (2002).
    [CrossRef] [PubMed]
  14. M. Quiroga-Teizeiro and H. Michinel, "Stable azimuthal stationary state in quintic nonlinear optical media," J. Opt. Soc. Am. B 14, 2004-2009 (1997).
    [CrossRef]
  15. I. Towers, A. V. Buryak, R. A. Sammut. B. A. Malomed, L.-C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schrodinger equation," Phys. Lett. A 288, 292-298 (2001).
    [CrossRef]
  16. B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of vortex solitons in the cubic-quintic model," Phycisa D  161, 187-201 (2002).
  17. D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
    [CrossRef] [PubMed]
  18. D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, "Ring vortex solitons in nonlocal nonlinear media," Opt. Express 13, 435-443 (2005).
    [CrossRef] [PubMed]
  19. C.-C. Jeng, M.-F. Shih, K. Motzek, and Y. Kivshar, "Partially incoherent optical vortices in self-focusing nonlinear media," Phys. Rev. Lett. 92, 043904 (2004).
    [CrossRef] [PubMed]
  20. C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J.P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
    [CrossRef] [PubMed]
  21. M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal optical modulation instability of coherent light in noninstantaneous nonlinear media," Phys. Rev. Lett. 88, 133902 (2002).
    [CrossRef] [PubMed]
  22. M. Segev, M.-F. Shih, and G. C. Valley, "Photorefractive screening solitons of high and low intensity," J. Opt. Soc. Am. B 13, 706-718 (1996).
    [CrossRef]
  23. For most nonlinearity other than that from electronic polarization, this criterion is satisfied, see R. W. Boyd, Nonlinear Optics, (Academic, San Diego, 1992).
  24. M.-F. Shih and F.-W. Sheu, "Dynamic Soliton-Like Modes," Phys. Rev. Lett. 86, 2281-2284 (2001).
    [CrossRef] [PubMed]
  25. This is the well-known catastrophic self-focusing first predicted by P. L. Kelley," Self-Focusing of Optical Beams," Phys. Rev. Lett. 15, 1005-1008 (1965).
    [CrossRef]
  26. A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric-field," Phys. Rev. A 51, 1520-1531 (1995).
    [CrossRef] [PubMed]
  27. A. S. Desyantnikov, A. A. Sukhorukov, and Y. S. Kivshar, "Azimuthons: spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005).
    [CrossRef]

2005 (2)

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, "Ring vortex solitons in nonlocal nonlinear media," Opt. Express 13, 435-443 (2005).
[CrossRef] [PubMed]

A. S. Desyantnikov, A. A. Sukhorukov, and Y. S. Kivshar, "Azimuthons: spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef]

2004 (2)

C.-C. Jeng, M.-F. Shih, K. Motzek, and Y. Kivshar, "Partially incoherent optical vortices in self-focusing nonlinear media," Phys. Rev. Lett. 92, 043904 (2004).
[CrossRef] [PubMed]

M. Bigelow, P. Zerom and R. Boyd, "Breakup of ring beams carrying orbital angular momentum in sodium vapor," Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

2002 (4)

H. Saito and M. Ueda, "Split instability of a vortex in an attractive Bose-Einstein condensate, " Phys. Rev. Lett. 89, 190402 (2002).
[CrossRef] [PubMed]

B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of vortex solitons in the cubic-quintic model," Phycisa D  161, 187-201 (2002).

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal optical modulation instability of coherent light in noninstantaneous nonlinear media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

2001 (2)

M.-F. Shih and F.-W. Sheu, "Dynamic Soliton-Like Modes," Phys. Rev. Lett. 86, 2281-2284 (2001).
[CrossRef] [PubMed]

I. Towers, A. V. Buryak, R. A. Sammut. B. A. Malomed, L.-C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schrodinger equation," Phys. Lett. A 288, 292-298 (2001).
[CrossRef]

2000 (1)

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J.P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

1998 (2)

1997 (3)

1996 (2)

1995 (3)

A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric-field," Phys. Rev. A 51, 1520-1531 (1995).
[CrossRef] [PubMed]

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, "Dark photorefractive spatial solitons and photorefractive vortex solitons," Phys. Rev. Lett. 74, 1978-1981 (1995).
[CrossRef] [PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, "Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium," J. Opt. Soc. Am. B 12, 2046-2052 (1995).
[CrossRef]

1992 (1)

G. A. Swartzlander and C. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992).
[CrossRef] [PubMed]

1985 (1)

V. I. Kruglov and R. A. Vlasov, "Spiral self-trapping propagation of optical beams in media with cubic nonlinearity," Phys. Lett. A 111, 401-404 (1985).
[CrossRef]

1965 (1)

This is the well-known catastrophic self-focusing first predicted by P. L. Kelley," Self-Focusing of Optical Beams," Phys. Rev. Lett. 15, 1005-1008 (1965).
[CrossRef]

Anastassiou, C.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J.P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

Anderson, D. Z.

A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric-field," Phys. Rev. A 51, 1520-1531 (1995).
[CrossRef] [PubMed]

Bang, O.

Bigelow, M.

M. Bigelow, P. Zerom and R. Boyd, "Breakup of ring beams carrying orbital angular momentum in sodium vapor," Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Boyd, R.

M. Bigelow, P. Zerom and R. Boyd, "Breakup of ring beams carrying orbital angular momentum in sodium vapor," Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Briedis, D.

Buryak, A. V.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

I. Towers, A. V. Buryak, R. A. Sammut. B. A. Malomed, L.-C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schrodinger equation," Phys. Lett. A 288, 292-298 (2001).
[CrossRef]

Chen, Z.

Z. Chen, M. Mitchell, M. Segev, T. Coskun, and D. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889-892 (1998).
[CrossRef] [PubMed]

Z. Chen, M. Shih, M. Segev, D.W. Wilson, R. E. Muller, and P. D. Maker, "Steady-state vortex-screening solitons formed in biased photorefractive media," Opt. Lett. 22, 1751-1753 (1997).
[CrossRef]

Christodoulides, D.

Z. Chen, M. Mitchell, M. Segev, T. Coskun, and D. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889-892 (1998).
[CrossRef] [PubMed]

Christodoulides, D. N.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J.P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

Christou, J.

Cojocaru, C.

Coskun, T.

Z. Chen, M. Mitchell, M. Segev, T. Coskun, and D. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889-892 (1998).
[CrossRef] [PubMed]

Crasovan, L. C.

B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of vortex solitons in the cubic-quintic model," Phycisa D  161, 187-201 (2002).

Crasovan, L.-C.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Crosignani, B.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, "Dark photorefractive spatial solitons and photorefractive vortex solitons," Phys. Rev. Lett. 74, 1978-1981 (1995).
[CrossRef] [PubMed]

Desyantnikov, A. S.

A. S. Desyantnikov, A. A. Sukhorukov, and Y. S. Kivshar, "Azimuthons: spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef]

Di Porto, P.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, "Dark photorefractive spatial solitons and photorefractive vortex solitons," Phys. Rev. Lett. 74, 1978-1981 (1995).
[CrossRef] [PubMed]

Duree, G.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, "Dark photorefractive spatial solitons and photorefractive vortex solitons," Phys. Rev. Lett. 74, 1978-1981 (1995).
[CrossRef] [PubMed]

Edmundson, D.

Eugenieva, E. D.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J.P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

Firth, W. J.

W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450-2453 (1997).
[CrossRef]

Jeng, C.-C.

C.-C. Jeng, M.-F. Shih, K. Motzek, and Y. Kivshar, "Partially incoherent optical vortices in self-focusing nonlinear media," Phys. Rev. Lett. 92, 043904 (2004).
[CrossRef] [PubMed]

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal optical modulation instability of coherent light in noninstantaneous nonlinear media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

Kip, D.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J.P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

Kivshar, Y.

C.-C. Jeng, M.-F. Shih, K. Motzek, and Y. Kivshar, "Partially incoherent optical vortices in self-focusing nonlinear media," Phys. Rev. Lett. 92, 043904 (2004).
[CrossRef] [PubMed]

Kivshar, Y. S.

A. S. Desyantnikov, A. A. Sukhorukov, and Y. S. Kivshar, "Azimuthons: spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef]

J. Christou,V. Tikhonenko,Y. S. Kivshar, and B. Luther-Davies, "Vortex soliton motion and steering," Opt. Lett. 21, 1649-1651 (1996).
[CrossRef] [PubMed]

Krolikowski, W.

Kruglov, V. I.

V. I. Kruglov and R. A. Vlasov, "Spiral self-trapping propagation of optical beams in media with cubic nonlinearity," Phys. Lett. A 111, 401-404 (1985).
[CrossRef]

Law, C.

G. A. Swartzlander and C. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992).
[CrossRef] [PubMed]

Lederer, F.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Lin, C.-Y.

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal optical modulation instability of coherent light in noninstantaneous nonlinear media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

Luther-Davies, B.

Maker, P. D.

Malomed, B. A.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of vortex solitons in the cubic-quintic model," Phycisa D  161, 187-201 (2002).

Mazilu, D.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Michinel, H.

Mihalache, D.

B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of vortex solitons in the cubic-quintic model," Phycisa D  161, 187-201 (2002).

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

Mitchell, M.

Z. Chen, M. Mitchell, M. Segev, T. Coskun, and D. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889-892 (1998).
[CrossRef] [PubMed]

Morin, M.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, "Dark photorefractive spatial solitons and photorefractive vortex solitons," Phys. Rev. Lett. 74, 1978-1981 (1995).
[CrossRef] [PubMed]

Motzek, K.

C.-C. Jeng, M.-F. Shih, K. Motzek, and Y. Kivshar, "Partially incoherent optical vortices in self-focusing nonlinear media," Phys. Rev. Lett. 92, 043904 (2004).
[CrossRef] [PubMed]

Muller, R. E.

Musslimani, Z. H.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J.P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

Nartorell, J.

Petersen, D.

Petrov, D. V.

Quiroga-Teizeiro, M.

Saito, H.

H. Saito and M. Ueda, "Split instability of a vortex in an attractive Bose-Einstein condensate, " Phys. Rev. Lett. 89, 190402 (2002).
[CrossRef] [PubMed]

Salamo, G.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, "Dark photorefractive spatial solitons and photorefractive vortex solitons," Phys. Rev. Lett. 74, 1978-1981 (1995).
[CrossRef] [PubMed]

Sammut, R. A.

I. Towers, A. V. Buryak, R. A. Sammut. B. A. Malomed, L.-C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schrodinger equation," Phys. Lett. A 288, 292-298 (2001).
[CrossRef]

Segev, M.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J.P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

Z. Chen, M. Mitchell, M. Segev, T. Coskun, and D. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889-892 (1998).
[CrossRef] [PubMed]

Z. Chen, M. Shih, M. Segev, D.W. Wilson, R. E. Muller, and P. D. Maker, "Steady-state vortex-screening solitons formed in biased photorefractive media," Opt. Lett. 22, 1751-1753 (1997).
[CrossRef]

M. Segev, M.-F. Shih, and G. C. Valley, "Photorefractive screening solitons of high and low intensity," J. Opt. Soc. Am. B 13, 706-718 (1996).
[CrossRef]

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, "Dark photorefractive spatial solitons and photorefractive vortex solitons," Phys. Rev. Lett. 74, 1978-1981 (1995).
[CrossRef] [PubMed]

Sharp, E.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, "Dark photorefractive spatial solitons and photorefractive vortex solitons," Phys. Rev. Lett. 74, 1978-1981 (1995).
[CrossRef] [PubMed]

Sheu, F.-W.

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal optical modulation instability of coherent light in noninstantaneous nonlinear media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

M.-F. Shih and F.-W. Sheu, "Dynamic Soliton-Like Modes," Phys. Rev. Lett. 86, 2281-2284 (2001).
[CrossRef] [PubMed]

Shih, M.

Shih, M.-F.

C.-C. Jeng, M.-F. Shih, K. Motzek, and Y. Kivshar, "Partially incoherent optical vortices in self-focusing nonlinear media," Phys. Rev. Lett. 92, 043904 (2004).
[CrossRef] [PubMed]

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal optical modulation instability of coherent light in noninstantaneous nonlinear media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

M.-F. Shih and F.-W. Sheu, "Dynamic Soliton-Like Modes," Phys. Rev. Lett. 86, 2281-2284 (2001).
[CrossRef] [PubMed]

M. Segev, M.-F. Shih, and G. C. Valley, "Photorefractive screening solitons of high and low intensity," J. Opt. Soc. Am. B 13, 706-718 (1996).
[CrossRef]

Skryabin, D. V.

W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450-2453 (1997).
[CrossRef]

Soljacic, M.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J.P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

Sukhorukov, A. A.

A. S. Desyantnikov, A. A. Sukhorukov, and Y. S. Kivshar, "Azimuthons: spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef]

Swartzlander, G. A.

G. A. Swartzlander and C. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992).
[CrossRef] [PubMed]

Tikhonenko, V.

Torner, L.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

D. V. Petrov, L. Torner, J. Nartorell, R. Vilaseca, J. P. Torres, and C. Cojocaru, "Observation of azimuthal modulational instability and formation of patterns of optical solitons in a quadratic nonlinear crystal," Opt. Lett. 23, 1444-1446 (1998).
[CrossRef]

Torres, J. P.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

D. V. Petrov, L. Torner, J. Nartorell, R. Vilaseca, J. P. Torres, and C. Cojocaru, "Observation of azimuthal modulational instability and formation of patterns of optical solitons in a quadratic nonlinear crystal," Opt. Lett. 23, 1444-1446 (1998).
[CrossRef]

Torres, J.P.

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J.P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

Towers, I.

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

I. Towers, A. V. Buryak, R. A. Sammut. B. A. Malomed, L.-C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schrodinger equation," Phys. Lett. A 288, 292-298 (2001).
[CrossRef]

Ueda, M.

H. Saito and M. Ueda, "Split instability of a vortex in an attractive Bose-Einstein condensate, " Phys. Rev. Lett. 89, 190402 (2002).
[CrossRef] [PubMed]

Valley, G. C.

Vilaseca, R.

Vlasov, R. A.

V. I. Kruglov and R. A. Vlasov, "Spiral self-trapping propagation of optical beams in media with cubic nonlinearity," Phys. Lett. A 111, 401-404 (1985).
[CrossRef]

Wilson, D.W.

Yariv, A.

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, "Dark photorefractive spatial solitons and photorefractive vortex solitons," Phys. Rev. Lett. 74, 1978-1981 (1995).
[CrossRef] [PubMed]

Zerom, P.

M. Bigelow, P. Zerom and R. Boyd, "Breakup of ring beams carrying orbital angular momentum in sodium vapor," Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

Zozulya, A. A.

A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric-field," Phys. Rev. A 51, 1520-1531 (1995).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (3)

Opt. Express (1)

Opt. Lett. (3)

Phycisa (1)

B. A. Malomed, L. C. Crasovan, and D. Mihalache, "Stability of vortex solitons in the cubic-quintic model," Phycisa D  161, 187-201 (2002).

Phys. Lett. A (2)

I. Towers, A. V. Buryak, R. A. Sammut. B. A. Malomed, L.-C. Crasovan, and D. Mihalache, "Stability of spinning ring solitons of the cubic-quintic nonlinear Schrodinger equation," Phys. Lett. A 288, 292-298 (2001).
[CrossRef]

V. I. Kruglov and R. A. Vlasov, "Spiral self-trapping propagation of optical beams in media with cubic nonlinearity," Phys. Lett. A 111, 401-404 (1985).
[CrossRef]

Phys. Rev. A (1)

A. A. Zozulya and D. Z. Anderson, "Propagation of an optical beam in a photorefractive medium in the presence of a photogalvanic nonlinearity or an externally applied electric-field," Phys. Rev. A 51, 1520-1531 (1995).
[CrossRef] [PubMed]

Phys. Rev. Lett. (12)

A. S. Desyantnikov, A. A. Sukhorukov, and Y. S. Kivshar, "Azimuthons: spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005).
[CrossRef]

C.-C. Jeng, M.-F. Shih, K. Motzek, and Y. Kivshar, "Partially incoherent optical vortices in self-focusing nonlinear media," Phys. Rev. Lett. 92, 043904 (2004).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljacic, M. Segev, E. D. Eugenieva, D. N. Christodoulides, D. Kip, Z. H. Musslimani, and J.P. Torres, "Eliminating the transverse instabilities of Kerr solitons," Phys. Rev. Lett. 85, 4888-4891 (2000).
[CrossRef] [PubMed]

M.-F. Shih, C.-C. Jeng, F.-W. Sheu, and C.-Y. Lin, "Spatiotemporal optical modulation instability of coherent light in noninstantaneous nonlinear media," Phys. Rev. Lett. 88, 133902 (2002).
[CrossRef] [PubMed]

M.-F. Shih and F.-W. Sheu, "Dynamic Soliton-Like Modes," Phys. Rev. Lett. 86, 2281-2284 (2001).
[CrossRef] [PubMed]

This is the well-known catastrophic self-focusing first predicted by P. L. Kelley," Self-Focusing of Optical Beams," Phys. Rev. Lett. 15, 1005-1008 (1965).
[CrossRef]

W. J. Firth and D. V. Skryabin, "Optical solitons carrying orbital angular momentum," Phys. Rev. Lett. 79, 2450-2453 (1997).
[CrossRef]

G. A. Swartzlander and C. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992).
[CrossRef] [PubMed]

G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, and A. Yariv, "Dark photorefractive spatial solitons and photorefractive vortex solitons," Phys. Rev. Lett. 74, 1978-1981 (1995).
[CrossRef] [PubMed]

D. Mihalache, D. Mazilu, L.-C. Crasovan, I. Towers, A. V. Buryak, B. A. Malomed, L. Torner, J. P. Torres, and F. Lederer, "Stable spinning optical solitons in three dimensions," Phys. Rev. Lett. 88, 073902 (2002).
[CrossRef] [PubMed]

M. Bigelow, P. Zerom and R. Boyd, "Breakup of ring beams carrying orbital angular momentum in sodium vapor," Phys. Rev. Lett. 92, 083902 (2004).
[CrossRef] [PubMed]

H. Saito and M. Ueda, "Split instability of a vortex in an attractive Bose-Einstein condensate, " Phys. Rev. Lett. 89, 190402 (2002).
[CrossRef] [PubMed]

Science (1)

Z. Chen, M. Mitchell, M. Segev, T. Coskun, and D. Christodoulides, "Self-trapping of dark incoherent light beams," Science 280, 889-892 (1998).
[CrossRef] [PubMed]

Other (3)

L. M. Pismen, Vortices in Nonlinear Fields (Clarendon Press, Oxford, 1999).

See, e.g., Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, 2003), Chap. 8.

For most nonlinearity other than that from electronic polarization, this criterion is satisfied, see R. W. Boyd, Nonlinear Optics, (Academic, San Diego, 1992).

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Figures (5)

Fig. 1.
Fig. 1.

The experimental setup.

Fig. 2.
Fig. 2.

Single-charge optical vortex: (a) at the input face; (b) at the output face without nonlinearity; at the output face with the nonlinearity turned on when the mask is (c) not rotating, (d) rotating at 0.05 turn per second, and (e) rotating at 5 turns per second. The arrow indicates the direction of the biasing field.

Fig. 3.
Fig. 3.

Double-charge optical vortex: (a) at the input face; (b) at the output face without nonlinearity; at the output face with the nonlinearity when the modulation mask is (c) not rotating, (d) rotating at 0.05 turn per second, and (e) rotating at 5 turns per second.

Fig. 4.
Fig. 4.

(a). The intensity mask. Intensity of the single-charge optical vortex in the computer simulation: (b) at the input face; at the output face when (c) f = 0, (d) f = 0.015/τ, and (e) f = 0.15/τ, at which frequency the phase at the output face is shown in (f).

Fig. 5.
Fig. 5.

The growth rates of the perturbation with different vorticity J for (a) the single-charge, and (b) the double-charge optical vortex in the noninstantaneous Kerr self-focusing medium.

Equations (2)

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2 A 2 ik A z ( 2 k 2 n 0 ) δ n ( A 2 ) A = 0 .
0 = ( 2 r 2 + 1 r r ) εe i ( θ γz ) + 1 r 2 2 θ 2 ( εe i ( θ γz ) ) + f ( u 2 ) εe i ( θ γz ) 2 ik [ ε z iγε ] e i ( θ γz ) .

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