Abstract

Inhomogeneously polarized optical waves form a class of nonlinear vector wave propagation that has not been widely studied in the literature. We find a modulation instability only when the wave has nonzero ellipticity in a medium where the Kerr nonlinearity possesses opposite handness. Under the modulation instability the wave develops an azimuthally periodic shape with two or four peaks.

© 2006 Optical Society of America

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References

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  1. M. Stalder and M. Schadt, "Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters," Opt. Lett. 21, 1948-1950 (1996).
    [CrossRef] [PubMed]
  2. R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
    [CrossRef]
  3. Q. Zhan, "Radiation forces on a dielectric sphere produced by a highly focused cylindrical vector beam," J. Opt. A: Pure and Appl. Opt. 5, 229-232 (2003).
    [CrossRef]
  4. Q. Zhan and J. R. Leger, "Focus shaping using cylindrical vector beams," Opt. Express 10, 324-331 (2002).
    [PubMed]
  5. L. E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens system," Opt. Commun. 191, 161-172 (2001).
    [CrossRef]
  6. A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, "Plasmon-coupled tip enhance near-field optical microscopy," J. of Microsc. 210, 220-224 (2003).
    [CrossRef]
  7. Q. Zhan, "Trapping metallic Rayleigh particles with radial polarization," Opt. Express,  12, pp. 3377-3382, (2004).
    [CrossRef] [PubMed]
  8. Y. Q. Zhao, Q. Zhan, Y. L. Zhang, and Y. P. Li, "Creation of a three-dimensional optical chain for controllable particle delivery," Opt. Lett. 30, 848-850 (2005).
    [CrossRef] [PubMed]
  9. V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D. 32, 1455-1461 (1999).
    [CrossRef]
  10. Y. Kivshar and G. P. Agrawal, Opitcal solitons: from fiber to photonic crystals (Elsevier, Amsterdam, 2003).
  11. H. Wang and W. She, "Nonparaxial optial Kerr vortex soliton with radial polarization," Opt. Express 14,1590-1595 (2006).
    [CrossRef] [PubMed]
  12. G. A. Swartzlander and C. T. Law, "Optical vortex solitons observed in Kerr nonlinear media," Phys. Rev. Lett. 69, 2503-2506 (1992).
    [CrossRef] [PubMed]
  13. D. Rozas, Z. S. Sacks, and G. A. Swartzlander, "Experimental observation of fluidlike motion of optical vortices," Phys. Rev. Lett. 79, 3399-3402 (1997).
    [CrossRef]
  14. J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, "Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium," Phys. Rev. A 45, 3168-3175 (1992).
    [CrossRef] [PubMed]
  15. A. S. Desyatnikov, A. A. Sukhorukov, and Y. S. Kivshar, "Azimuthons: spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005).
    [CrossRef] [PubMed]
  16. D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, "Azimuthal instability of spinning spatiotemporal solitons," Phys. Rev. E 62,R1505-R1508 (2000).
    [CrossRef]
  17. D. V. Petrov, L. Torner, J. Martorell, R. Vilseca, J. P. Torres, and C. Cojocaru, "Observation of azimuthal modulation instability and formation of patterns of optical solitons in quadratic nonlinear crystal," Opt. Lett 23, 1444-1447 (1998).
    [CrossRef]
  18. P. D. Maker and R. W. Terhune, "Study of Optical effects due to an induced polarization third order in the electric field strength," Phys. Rev. 137, A801 (1965).
    [CrossRef]
  19. R.W. Boyd, Nonlinear Optics (Academic Press, San Diego, CA, 1992).
  20. M. S. Malcuit, D. J. Gauthier, and R. W. Boyd, "Vector phase conjugation by two-photon-resonant degenerate four-wave mixing," Opt. Lett. 13, 663-665 (1988).
    [CrossRef] [PubMed]
  21. D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, "Polarization bistability of counterpropagating laser beams,"Phys. Rev. Lett. 64, 1721-1724 (1990).
    [CrossRef] [PubMed]
  22. J. A. Fleck, J. R. Morris, and M. D. Feit, "Time dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129-160 (1976).
    [CrossRef]
  23. K. D. Moll, A. Gaeta, and G. Fibich, "Self-similar optical wave collapse: Observation of the Townes Profile," Phys. Rev. Lett. 90, 203902 (2003
    [CrossRef] [PubMed]

2006 (1)

2005 (2)

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

Y. Q. Zhao, Q. Zhan, Y. L. Zhang, and Y. P. Li, "Creation of a three-dimensional optical chain for controllable particle delivery," Opt. Lett. 30, 848-850 (2005).
[CrossRef] [PubMed]

2004 (1)

2003 (3)

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, "Plasmon-coupled tip enhance near-field optical microscopy," J. of Microsc. 210, 220-224 (2003).
[CrossRef]

Q. Zhan, "Radiation forces on a dielectric sphere produced by a highly focused cylindrical vector beam," J. Opt. A: Pure and Appl. Opt. 5, 229-232 (2003).
[CrossRef]

K. D. Moll, A. Gaeta, and G. Fibich, "Self-similar optical wave collapse: Observation of the Townes Profile," Phys. Rev. Lett. 90, 203902 (2003
[CrossRef] [PubMed]

2002 (1)

2001 (1)

L. E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens system," Opt. Commun. 191, 161-172 (2001).
[CrossRef]

2000 (2)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, "Azimuthal instability of spinning spatiotemporal solitons," Phys. Rev. E 62,R1505-R1508 (2000).
[CrossRef]

1999 (1)

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D. 32, 1455-1461 (1999).
[CrossRef]

1998 (1)

D. V. Petrov, L. Torner, J. Martorell, R. Vilseca, J. P. Torres, and C. Cojocaru, "Observation of azimuthal modulation instability and formation of patterns of optical solitons in quadratic nonlinear crystal," Opt. Lett 23, 1444-1447 (1998).
[CrossRef]

1997 (1)

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, "Experimental observation of fluidlike motion of optical vortices," Phys. Rev. Lett. 79, 3399-3402 (1997).
[CrossRef]

1996 (1)

1992 (2)

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, "Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium," Phys. Rev. A 45, 3168-3175 (1992).
[CrossRef] [PubMed]

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

1990 (1)

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, "Polarization bistability of counterpropagating laser beams,"Phys. Rev. Lett. 64, 1721-1724 (1990).
[CrossRef] [PubMed]

1988 (1)

1976 (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129-160 (1976).
[CrossRef]

1965 (1)

P. D. Maker and R. W. Terhune, "Study of Optical effects due to an induced polarization third order in the electric field strength," Phys. Rev. 137, A801 (1965).
[CrossRef]

Akhmediev, N. N.

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, "Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium," Phys. Rev. A 45, 3168-3175 (1992).
[CrossRef] [PubMed]

Beversluis, M. R.

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, "Plasmon-coupled tip enhance near-field optical microscopy," J. of Microsc. 210, 220-224 (2003).
[CrossRef]

Blit, S.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Bomzon, Z.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Bouhelier, A.

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, "Plasmon-coupled tip enhance near-field optical microscopy," J. of Microsc. 210, 220-224 (2003).
[CrossRef]

Boyd, R. W.

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, "Polarization bistability of counterpropagating laser beams,"Phys. Rev. Lett. 64, 1721-1724 (1990).
[CrossRef] [PubMed]

M. S. Malcuit, D. J. Gauthier, and R. W. Boyd, "Vector phase conjugation by two-photon-resonant degenerate four-wave mixing," Opt. Lett. 13, 663-665 (1988).
[CrossRef] [PubMed]

Cojocaru, C.

D. V. Petrov, L. Torner, J. Martorell, R. Vilseca, J. P. Torres, and C. Cojocaru, "Observation of azimuthal modulation instability and formation of patterns of optical solitons in quadratic nonlinear crystal," Opt. Lett 23, 1444-1447 (1998).
[CrossRef]

Crasovan, L.-C.

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, "Azimuthal instability of spinning spatiotemporal solitons," Phys. Rev. E 62,R1505-R1508 (2000).
[CrossRef]

Davidson, N.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Desyatnikov, A. S.

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

Feit, M. D.

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129-160 (1976).
[CrossRef]

Fibich, G.

K. D. Moll, A. Gaeta, and G. Fibich, "Self-similar optical wave collapse: Observation of the Townes Profile," Phys. Rev. Lett. 90, 203902 (2003
[CrossRef] [PubMed]

Fleck, J. A.

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129-160 (1976).
[CrossRef]

Friesem, A. A.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Gaeta, A.

K. D. Moll, A. Gaeta, and G. Fibich, "Self-similar optical wave collapse: Observation of the Townes Profile," Phys. Rev. Lett. 90, 203902 (2003
[CrossRef] [PubMed]

Gaeta, A. L.

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, "Polarization bistability of counterpropagating laser beams,"Phys. Rev. Lett. 64, 1721-1724 (1990).
[CrossRef] [PubMed]

Gauthier, D. J.

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, "Polarization bistability of counterpropagating laser beams,"Phys. Rev. Lett. 64, 1721-1724 (1990).
[CrossRef] [PubMed]

M. S. Malcuit, D. J. Gauthier, and R. W. Boyd, "Vector phase conjugation by two-photon-resonant degenerate four-wave mixing," Opt. Lett. 13, 663-665 (1988).
[CrossRef] [PubMed]

Hasman, E.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Helseth, L. E.

L. E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens system," Opt. Commun. 191, 161-172 (2001).
[CrossRef]

Kivshar, Y. S.

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

Law, C. T.

G. A. Swartzlander and C. T. 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, B. A. Malomed, and F. Lederer, "Azimuthal instability of spinning spatiotemporal solitons," Phys. Rev. E 62,R1505-R1508 (2000).
[CrossRef]

Leger, J. R.

Li, Y. P.

Maker, P. D.

P. D. Maker and R. W. Terhune, "Study of Optical effects due to an induced polarization third order in the electric field strength," Phys. Rev. 137, A801 (1965).
[CrossRef]

Malcuit, M. S.

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, "Polarization bistability of counterpropagating laser beams,"Phys. Rev. Lett. 64, 1721-1724 (1990).
[CrossRef] [PubMed]

M. S. Malcuit, D. J. Gauthier, and R. W. Boyd, "Vector phase conjugation by two-photon-resonant degenerate four-wave mixing," Opt. Lett. 13, 663-665 (1988).
[CrossRef] [PubMed]

Malomed, B. A.

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, "Azimuthal instability of spinning spatiotemporal solitons," Phys. Rev. E 62,R1505-R1508 (2000).
[CrossRef]

Martorell, J.

D. V. Petrov, L. Torner, J. Martorell, R. Vilseca, J. P. Torres, and C. Cojocaru, "Observation of azimuthal modulation instability and formation of patterns of optical solitons in quadratic nonlinear crystal," Opt. Lett 23, 1444-1447 (1998).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, "Azimuthal instability of spinning spatiotemporal solitons," Phys. Rev. E 62,R1505-R1508 (2000).
[CrossRef]

Mihalache, D.

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, "Azimuthal instability of spinning spatiotemporal solitons," Phys. Rev. E 62,R1505-R1508 (2000).
[CrossRef]

Moll, K. D.

K. D. Moll, A. Gaeta, and G. Fibich, "Self-similar optical wave collapse: Observation of the Townes Profile," Phys. Rev. Lett. 90, 203902 (2003
[CrossRef] [PubMed]

Morris, J. R.

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129-160 (1976).
[CrossRef]

Nesterov, A. V.

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D. 32, 1455-1461 (1999).
[CrossRef]

Niziev, V. G.

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D. 32, 1455-1461 (1999).
[CrossRef]

Novotny, L.

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, "Plasmon-coupled tip enhance near-field optical microscopy," J. of Microsc. 210, 220-224 (2003).
[CrossRef]

Oron, R.

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

Petrov, D. V.

D. V. Petrov, L. Torner, J. Martorell, R. Vilseca, J. P. Torres, and C. Cojocaru, "Observation of azimuthal modulation instability and formation of patterns of optical solitons in quadratic nonlinear crystal," Opt. Lett 23, 1444-1447 (1998).
[CrossRef]

Renger, J.

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, "Plasmon-coupled tip enhance near-field optical microscopy," J. of Microsc. 210, 220-224 (2003).
[CrossRef]

Rozas, D.

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, "Experimental observation of fluidlike motion of optical vortices," Phys. Rev. Lett. 79, 3399-3402 (1997).
[CrossRef]

Sacks, Z. S.

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, "Experimental observation of fluidlike motion of optical vortices," Phys. Rev. Lett. 79, 3399-3402 (1997).
[CrossRef]

Schadt, M.

She, W.

Soto-Crespo, J. M.

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, "Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium," Phys. Rev. A 45, 3168-3175 (1992).
[CrossRef] [PubMed]

Stalder, M.

Sukhorukov, A. A.

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

Swartzlander, G. A.

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, "Experimental observation of fluidlike motion of optical vortices," Phys. Rev. Lett. 79, 3399-3402 (1997).
[CrossRef]

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

Terhune, R. W.

P. D. Maker and R. W. Terhune, "Study of Optical effects due to an induced polarization third order in the electric field strength," Phys. Rev. 137, A801 (1965).
[CrossRef]

Torner, L.

D. V. Petrov, L. Torner, J. Martorell, R. Vilseca, J. P. Torres, and C. Cojocaru, "Observation of azimuthal modulation instability and formation of patterns of optical solitons in quadratic nonlinear crystal," Opt. Lett 23, 1444-1447 (1998).
[CrossRef]

Torres, J. P.

D. V. Petrov, L. Torner, J. Martorell, R. Vilseca, J. P. Torres, and C. Cojocaru, "Observation of azimuthal modulation instability and formation of patterns of optical solitons in quadratic nonlinear crystal," Opt. Lett 23, 1444-1447 (1998).
[CrossRef]

Vilseca, R.

D. V. Petrov, L. Torner, J. Martorell, R. Vilseca, J. P. Torres, and C. Cojocaru, "Observation of azimuthal modulation instability and formation of patterns of optical solitons in quadratic nonlinear crystal," Opt. Lett 23, 1444-1447 (1998).
[CrossRef]

Wang, H.

Wright, E. M.

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, "Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium," Phys. Rev. A 45, 3168-3175 (1992).
[CrossRef] [PubMed]

Zhan, Q.

Zhang, Y. L.

Zhao, Y. Q.

Appl. Phys. (1)

J. A. Fleck, J. R. Morris, and M. D. Feit, "Time dependent propagation of high energy laser beams through the atmosphere," Appl. Phys. 10, 129-160 (1976).
[CrossRef]

Appl. Phys. Lett. (1)

R. Oron, S. Blit, N. Davidson, A. A. Friesem, Z. Bomzon, and E. Hasman, "The formation of laser beams with pure azimuthal or radial polarization," Appl. Phys. Lett. 77, 3322-3324 (2000).
[CrossRef]

J. of Microsc. (1)

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, "Plasmon-coupled tip enhance near-field optical microscopy," J. of Microsc. 210, 220-224 (2003).
[CrossRef]

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

Q. Zhan, "Radiation forces on a dielectric sphere produced by a highly focused cylindrical vector beam," J. Opt. A: Pure and Appl. Opt. 5, 229-232 (2003).
[CrossRef]

J. Phys. D. (1)

V. G. Niziev and A. V. Nesterov, "Influence of beam polarization on laser cutting efficiency," J. Phys. D. 32, 1455-1461 (1999).
[CrossRef]

Opt. Commun. (1)

L. E. Helseth, "Roles of polarization, phase and amplitude in solid immersion lens system," Opt. Commun. 191, 161-172 (2001).
[CrossRef]

Opt. Express (3)

Opt. Lett (1)

D. V. Petrov, L. Torner, J. Martorell, R. Vilseca, J. P. Torres, and C. Cojocaru, "Observation of azimuthal modulation instability and formation of patterns of optical solitons in quadratic nonlinear crystal," Opt. Lett 23, 1444-1447 (1998).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. (1)

P. D. Maker and R. W. Terhune, "Study of Optical effects due to an induced polarization third order in the electric field strength," Phys. Rev. 137, A801 (1965).
[CrossRef]

Phys. Rev. A (1)

J. M. Soto-Crespo, E. M. Wright, and N. N. Akhmediev, "Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium," Phys. Rev. A 45, 3168-3175 (1992).
[CrossRef] [PubMed]

Phys. Rev. E (1)

D. Mihalache, D. Mazilu, L.-C. Crasovan, B. A. Malomed, and F. Lederer, "Azimuthal instability of spinning spatiotemporal solitons," Phys. Rev. E 62,R1505-R1508 (2000).
[CrossRef]

Phys. Rev. Lett. (5)

K. D. Moll, A. Gaeta, and G. Fibich, "Self-similar optical wave collapse: Observation of the Townes Profile," Phys. Rev. Lett. 90, 203902 (2003
[CrossRef] [PubMed]

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

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

D. Rozas, Z. S. Sacks, and G. A. Swartzlander, "Experimental observation of fluidlike motion of optical vortices," Phys. Rev. Lett. 79, 3399-3402 (1997).
[CrossRef]

D. J. Gauthier, M. S. Malcuit, A. L. Gaeta, and R. W. Boyd, "Polarization bistability of counterpropagating laser beams,"Phys. Rev. Lett. 64, 1721-1724 (1990).
[CrossRef] [PubMed]

Other (2)

R.W. Boyd, Nonlinear Optics (Academic Press, San Diego, CA, 1992).

Y. Kivshar and G. P. Agrawal, Opitcal solitons: from fiber to photonic crystals (Elsevier, Amsterdam, 2003).

Supplementary Material (5)

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Figures (8)

Fig. 1.
Fig. 1.

Scalar case showing donut initial profile (right) and final profile (left). The parameters are B=6 and E0=1.5.

Fig. 2.
Fig. 2.

ector wave propagation for the case B=0 and E0=1.5. The intensity remains rotationally symmetric and the intensity monotonically falls. Other parameters are θ=0, and φ=π/4.

Fig. 3.
Fig. 3.

Intensity versus amplitude after propagation a distance z=2 through the medium. Other parameters are: B=6 θ=0 and φ=π/4 (Movie).

Fig. 4.
Fig. 4.

Evolution of the initial beam on the axis for the following parameter values: B=6, E0=2, θ=0, φ=π/4 (Movie).

Fig. 5.
Fig. 5.

The maximum intensity relative to its initial value versus z. The initial amplitudes are near the critical power for the given retardance values. The critical power lies between the amplitude values 2.3, shown by a dotted line, and 2.4, shown by a dashed line. The parameters are B=6, θ=0, and φ=π/4.

Fig. 6.
Fig. 6.

Intensity profile as a function of the phase retardance angle φ for B=6, E0=2 and θ=0. The propagation distance is z=2 (Movie).

Fig. 7.
Fig. 7.

The component, S3 , of the Stokes vector defined in Eq. (7) after propagating to z=2; the change of S3 with retardation angle is shown. The parameter values are: B=6, E0=2 and θ=0 (Movie).

Fig. 8.
Fig. 8.

Intensity profile as a function of the cylindrical orientation angle θ for B=6, E0=2 φ=π/4. The propagation distance is z=2 (Movie).

Equations (7)

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E α z = i 2 2 E α + i ( E x 2 + E y 2 ) E a + i B 2 ( E x 2 + E y 2 ) E α * ,
E ± z = i 2 2 E ± + i ( E ± 2 + ( 1 + B ) E 2 ) E ± .
E x = E 0 ( cos θ x + sin θ y ) e r 2 ,
E y = E 0 e i ϕ ( sin θ x + cos θ y ) e r 2 ,
E = E 0 r exp ( r 2 ) ,
E z = i 2 2 E + i ( 1 + B 2 ) E 2 E ,
S 3 = E + 2 E 2 .

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