Abstract

We suggest a novel type of composite spatial optical soliton created by a coherent vortex beam guiding a partially incoherent light beam in a self-focusing nonlinear medium. We show that the incoherence of the guided mode may enhance, rather than suppress, the vortex azimuthal instability, and we also demonstrate strong destabilization of dipole-mode solitons by partially incoherent light.

© 2004 Optical Society of America

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References

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  1. See M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001), Vol. 42, pp. 219–276.
    [CrossRef]
  2. G. A. Swartzlander and C. Law, Phys. Rev. Lett. 69, 2503 (1992).
    [CrossRef] [PubMed]
  3. See, e.g., Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, Calif., 2003), Chap. 8.
  4. Such beams were suggested by V. I. Kruglov and R. A. Vlasov, Phys. Lett. A 111, 401 (1985).
    [CrossRef]
  5. W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
    [CrossRef]
  6. C. C. Jeng, M. Shih, K. Motzek, and Yu. Kivshar, Phys. Rev. Lett. 94, 043904 (2004).
    [CrossRef]
  7. A. P. Sheppard and M. Haelterman, Opt. Lett. 19, 859 (1993).
    [CrossRef]
  8. C. T. Law, X. Zhang, and G. A. Swartzlander, Opt. Lett. 25, 55 (2000).
    [CrossRef]
  9. A. H. Carlsson, J. N. Malmberg, D. Anderson, M. Lisak, E. A. Ostrovskaya, T. J. Alexander, and Yu. S. Kivshar, Opt. Lett. 25, 660 (2000).
    [CrossRef]
  10. Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
    [CrossRef] [PubMed]
  11. J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrov-skaya, and Yu. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
    [CrossRef]
  12. J. Yang and D. E. Pelinovsky, Phys. Rev. E 67, 016608 (2003).
    [CrossRef]
  13. See, e.g., D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
    [CrossRef]

2004 (1)

C. C. Jeng, M. Shih, K. Motzek, and Yu. Kivshar, Phys. Rev. Lett. 94, 043904 (2004).
[CrossRef]

2003 (1)

J. Yang and D. E. Pelinovsky, Phys. Rev. E 67, 016608 (2003).
[CrossRef]

2000 (4)

C. T. Law, X. Zhang, and G. A. Swartzlander, Opt. Lett. 25, 55 (2000).
[CrossRef]

A. H. Carlsson, J. N. Malmberg, D. Anderson, M. Lisak, E. A. Ostrovskaya, T. J. Alexander, and Yu. S. Kivshar, Opt. Lett. 25, 660 (2000).
[CrossRef]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrov-skaya, and Yu. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
[CrossRef]

1997 (2)

See, e.g., D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

1993 (1)

1992 (1)

G. A. Swartzlander and C. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

1985 (1)

Such beams were suggested by V. I. Kruglov and R. A. Vlasov, Phys. Lett. A 111, 401 (1985).
[CrossRef]

Agrawal, G. P.

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

Alexander, T. J.

Anderson, D.

Carlsson, A. H.

Christodoulides, D. N.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

See, e.g., D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Coskun, T. H.

See, e.g., D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Firth, W. J.

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

García-Ripoll, J. J.

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrov-skaya, and Yu. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
[CrossRef]

Haelterman, M.

Jeng, C. C.

C. C. Jeng, M. Shih, K. Motzek, and Yu. Kivshar, Phys. Rev. Lett. 94, 043904 (2004).
[CrossRef]

Kivshar, Yu.

C. C. Jeng, M. Shih, K. Motzek, and Yu. Kivshar, Phys. Rev. Lett. 94, 043904 (2004).
[CrossRef]

Kivshar, Yu. S.

A. H. Carlsson, J. N. Malmberg, D. Anderson, M. Lisak, E. A. Ostrovskaya, T. J. Alexander, and Yu. S. Kivshar, Opt. Lett. 25, 660 (2000).
[CrossRef]

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrov-skaya, and Yu. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
[CrossRef]

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

Kruglov, V. I.

Such beams were suggested by V. I. Kruglov and R. A. Vlasov, Phys. Lett. A 111, 401 (1985).
[CrossRef]

Law, C.

G. A. Swartzlander and C. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

Law, C. T.

Lisak, M.

Malmberg, J. N.

Mitchell, M.

See, e.g., D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Motzek, K.

C. C. Jeng, M. Shih, K. Motzek, and Yu. Kivshar, Phys. Rev. Lett. 94, 043904 (2004).
[CrossRef]

Musslimani, Z. H.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

Ostrovskaya, E. A.

Ostrov-skaya, E. A.

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrov-skaya, and Yu. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
[CrossRef]

Pelinovsky, D. E.

J. Yang and D. E. Pelinovsky, Phys. Rev. E 67, 016608 (2003).
[CrossRef]

Pérez-García, V. M.

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrov-skaya, and Yu. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
[CrossRef]

Segev, M.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

See, e.g., D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

Sheppard, A. P.

Shih, M.

C. C. Jeng, M. Shih, K. Motzek, and Yu. Kivshar, Phys. Rev. Lett. 94, 043904 (2004).
[CrossRef]

Skryabin, D. V.

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

Soljacic, M.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

Soskin, M. S.

See M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001), Vol. 42, pp. 219–276.
[CrossRef]

Swartzlander, G. A.

C. T. Law, X. Zhang, and G. A. Swartzlander, Opt. Lett. 25, 55 (2000).
[CrossRef]

G. A. Swartzlander and C. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

Vasnetsov, M. V.

See M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001), Vol. 42, pp. 219–276.
[CrossRef]

Vlasov, R. A.

Such beams were suggested by V. I. Kruglov and R. A. Vlasov, Phys. Lett. A 111, 401 (1985).
[CrossRef]

Yang, J.

J. Yang and D. E. Pelinovsky, Phys. Rev. E 67, 016608 (2003).
[CrossRef]

Zhang, X.

Opt. Lett. (3)

Phys. Lett. A (1)

Such beams were suggested by V. I. Kruglov and R. A. Vlasov, Phys. Lett. A 111, 401 (1985).
[CrossRef]

Phys. Rev. E (1)

J. Yang and D. E. Pelinovsky, Phys. Rev. E 67, 016608 (2003).
[CrossRef]

Phys. Rev. Lett. (6)

See, e.g., D. N. Christodoulides, T. H. Coskun, M. Mitchell, and M. Segev, Phys. Rev. Lett. 78, 646 (1997).
[CrossRef]

G. A. Swartzlander and C. Law, Phys. Rev. Lett. 69, 2503 (1992).
[CrossRef] [PubMed]

W. J. Firth and D. V. Skryabin, Phys. Rev. Lett. 79, 2450 (1997).
[CrossRef]

C. C. Jeng, M. Shih, K. Motzek, and Yu. Kivshar, Phys. Rev. Lett. 94, 043904 (2004).
[CrossRef]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljacic, Phys. Rev. Lett. 84, 1164 (2000).
[CrossRef] [PubMed]

J. J. García-Ripoll, V. M. Pérez-García, E. A. Ostrov-skaya, and Yu. S. Kivshar, Phys. Rev. Lett. 85, 82 (2000).
[CrossRef]

Other (2)

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

See M. S. Soskin and M. V. Vasnetsov, in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 2001), Vol. 42, pp. 219–276.
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Propagation of the vortex-mode two-component composite soliton with β1=1.0. Top, coherent guided mode with β2=1.5. Bottom, the same for a partially incoherent guided mode (at θ0=0.7); both beams have the same power as in the coherent case described above.

Fig. 2
Fig. 2

Comparison of the unstable propagation of coherent and partially incoherent vortex-mode solitons. Top, coherent vortex at β1=1.0 and coherent guided mode at β2=1.45. The vortex-mode soliton evolves into a rotating dipole-mode soliton. Bottom, the same for the partially incoherent guided mode (at θ0=0.35); the vortex decays into two separate beams.

Fig. 3
Fig. 3

Propagation of the dipole-mode vector solitons with coherent and incoherent fundamental beams. The initial profile of the beams corresponds to a solitary solution with propagation constants β1=1.0 for the dipole and β2=1.15 for the fundamental component. Top, the evolution of the fundamental; bottom, that of the dipole. Although the degree of incoherence is not very high θ0=0.1°, it is enough to destabilize the soliton and leads to the soliton’s decay.

Equations (2)

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iuz+Δu+FItotu=0, ivz+Δv+FItotv=0,
Gθ=πθ0-1/2exp-θ2/θ02

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