Abstract

We discuss the properties of composite (or vector) spatial optical solitons created by the incoherent interaction of two optical beams and associated with higher-order modes guided by a soliton-induced waveguide in a bulk medium. Such stationary (2+1)-dimensional self-trapped localized structures include, in particular, vortex- and dipole-mode vector solitons and also incorporate higher-order multipole spatial solitons in a bulk medium, such as quadrupole solitons and necklace-type composite beams. We overview our theoretical and experimental results for the structure, formation, and stability of these self-trapped composite optical beams and also discuss the effects of anisotropy and of the nonlocality of the photorefractive nonlinearity on their properties. Additionally, we demonstrate, analytically and experimentally, that an array of the dipole-mode vector solitons can be generated as a result of the transverse instability of a quasi-one-dimensional two-hump soliton stripe in a saturable nonlinear optical medium.

© 2002 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  5. D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, “Rotating propeller solitons,” Phys. Rev. Lett. 87, 143901 (2001).
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  19. W. J. Firth and D. V. Skryabin, “Optical solitons carrying orbital angular momentum,” Phys. Rev. Lett. 79, 2450–2453 (1997).
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  26. W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  30. M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
    [CrossRef]
  31. M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
    [CrossRef] [PubMed]
  32. M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
    [CrossRef]
  33. V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Zh. Eskp. Teor. Fiz. 65, 997 (1973) [ Sov. Phys. JETP 38, 494–500 (1974)].
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    [CrossRef]
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    [CrossRef]
  36. A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
    [CrossRef] [PubMed]
  37. V. Tikhonenko, J. Christou, B. Luther-Davies, and Yu. S. Kivshar, “Observation of vortex solitons created by the instability of dark soliton stripes,” Opt. Lett. 21, 1129–1131 (1996).
    [CrossRef] [PubMed]
  38. R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997).
    [CrossRef]
  39. X. Liu, K. Beckwitt, and F. Wise, “Transverse instability of optical spatiotemporal solitons in quadratic media,” Phys. Rev. Lett. 85, 1871–1874 (2000).
    [CrossRef] [PubMed]
  40. C. Anastassiou, M. Soljacić, 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]
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    [CrossRef]
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    [CrossRef]
  43. Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Yu. S. Kivshar, “Suppression of transverse instabilities for vector solitons,” Phys. Rev. E 60, R1170–R1173 (1999).
    [CrossRef]
  44. J. J. García-Ripoll, V. Pérez-García, W. Krolikowski, and Yu. S. Kivshar, “Scattering of light by molecules of light,” arXiv.org # e-print archive, June 29, 2000, http://arXiv.org/ps/ nlin.PS/0006047.
  45. D. Neshev, W. Krolikowski, D. E. Pelinovsky, G. McCarthy, and Yu. S. Kivshar, “Transverse instability of vector solitons and generation of dipole arrays,” Phys. Rev. Lett. 87, 103903 (2001).
    [CrossRef] [PubMed]

2001 (4)

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, “Rotating propeller solitons,” Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef] [PubMed]

D. Neshev, W. Krolikowski, D. E. Pelinovsky, G. McCarthy, and Yu. S. Kivshar, “Transverse instability of vector solitons and generation of dipole arrays,” Phys. Rev. Lett. 87, 103903 (2001).
[CrossRef] [PubMed]

A. Desyatnikov, D. Neshev, E. Ostrovskaya, Yu. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. Perez-García, “Multipole spatial vector solitons,” Opt. Lett. 26, 435–437 (2001).
[CrossRef]

D. Neshev, G. McCarthy, W. Krolikowski, E. A. Ostrovskaya, G. F. Calvo, F. Agullo-Lopez, and Yu. S. Kivshar, “Dipole-mode vector solitons in anisotropic nonlocal self-focusing media,” Opt. Lett. 26, 1185–1187 (2001).
[CrossRef]

2000 (9)

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Observation of two-dimensional multimode solitons,” Opt. Lett. 25, 1113–1115 (2000).
[CrossRef]

H. Fang, R. Malendevich, R. Schiek, and G. I. Stegeman, “Spatial modulational instability in one-dimensional lithium niobate slab waveguides,” Opt. Lett. 25, 1786–1788 (2000).
[CrossRef]

J. N. Malmberg, A. H. Carlsson, D. Anderson, M. Lisak, E. A. Ostrovskaya, and Yu. S. Kivshar, “Vector solitons in (2+1) dimensions,” Opt. Lett. 25, 643–645 (2000).
[CrossRef]

Yu. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331, 118–195 (2000).
[CrossRef]

X. Liu, K. Beckwitt, and F. Wise, “Transverse instability of optical spatiotemporal solitons in quadratic media,” Phys. Rev. Lett. 85, 1871–1874 (2000).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljacić, 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]

W. Krolikowski, E. A. Ostrovskaya, C. Weinau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljačić, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000).
[CrossRef] [PubMed]

J. J. García-Ripoll, V. Perez-García, E. A. Ostrovskaya, and Yu. S. Kivshar, “Dipole-mode vector solitons,” Phys. Rev. Lett. 85, 82–85 (2000).
[CrossRef] [PubMed]

1999 (3)

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiralling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

E. Ostrovskaya, Yu. S. Kivshar, D. Skryabin, and W. J. Firth, “Stability of multihump optical solitons,” Phys. Rev. Lett. 83, 296–299 (1999).
[CrossRef]

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Yu. S. Kivshar, “Suppression of transverse instabilities for vector solitons,” Phys. Rev. E 60, R1170–R1173 (1999).
[CrossRef]

1998 (8)

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

D. V. Skryabin and W. J. Firth, “Modulational instability of solitary waves in nondegenerate three-wave mixing: the role of phase symmetries,” Phys. Rev. Lett. 81, 3379–3382 (1998).
[CrossRef]

M. Soljačić, S. Sears, and M. Segev, “Self-trapping of ‘necklace’ beams in self-focusing Kerr media,” Phys. Rev. Lett. 81, 4851–4854 (1998).
[CrossRef]

D. V. Skryabin and W. J. Firth, “Dynamics of self-trapped beams with phase dislocation in saturable Kerr and quadratic nonlinear media,” Phys. Rev. E 58, 3916–3930 (1998).
[CrossRef]

M. Segev and G. I. Stegeman, “Self-trapping of optical beams: spatial solitons,” Phys. Today 51, 42–48 (1998).
[CrossRef]

M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett. 80, 4657–4560 (1998).
[CrossRef]

V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, and V. A. Vysloukh, “Cross-modulation coupling of incoherent soliton modes in photorefractive crystals,” Phys. Rev. E 57, 6056–6065 (1998).
[CrossRef]

1997 (3)

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

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997).
[CrossRef]

See, e.g., A. W. Snyder and Yu. S. Kivshar, “Bright spatial solitons in non-Kerr media: stationary beams and dynamical evolution,” J. Opt. Soc. Am. B 14, 3025–3031 (1997), and references therein.
[CrossRef]

1996 (4)

V. Tikhonenko, J. Christou, B. Luther-Davies, and Yu. S. Kivshar, “Observation of vortex solitons created by the instability of dark soliton stripes,” Opt. Lett. 21, 1129–1131 (1996).
[CrossRef] [PubMed]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
[CrossRef] [PubMed]

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).
[CrossRef] [PubMed]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

1995 (3)

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

See, e.g., 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]

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]

1994 (5)

A. Barthelemy, C. Froehly, and M. Shalaby, “Nonlinear propagation of picosecond tubular beams: self phase modulation and induced refraction,” in Mode-Locked and Other Ultrashort Laser Designs, Amplifiers, and Applications, M. Piche and P. W. Pace, eds., Proc. SPIE 2041, 104–113 (1994).
[CrossRef]

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

See, e.g., M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).
[CrossRef]

A. W. Snyder, S. J. Hewlett, and J. Mitchell, “Dynamic spatial solitons,” Phys. Rev. Lett. 72, 1012–1015 (1994).
[CrossRef] [PubMed]

1991 (1)

1988 (1)

1986 (1)

E. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, “Soliton stability in plasmas and hydrodynamics,” Phys. Rep. 142, 103–165 (1986).
[CrossRef]

1974 (2)

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Zh. Eskp. Teor. Fiz. 65, 997 (1973) [ Sov. Phys. JETP 38, 494–500 (1974)].

Agullo-Lopez, F.

Anastassiou, C.

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Observation of two-dimensional multimode solitons,” Opt. Lett. 25, 1113–1115 (2000).
[CrossRef]

C. Anastassiou, M. Soljacić, 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.

Anderson, D. Z.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

See, e.g., 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]

Baboiu, D.-M.

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997).
[CrossRef]

Barthelemy, A.

A. Barthelemy, C. Froehly, and M. Shalaby, “Nonlinear propagation of picosecond tubular beams: self phase modulation and induced refraction,” in Mode-Locked and Other Ultrashort Laser Designs, Amplifiers, and Applications, M. Piche and P. W. Pace, eds., Proc. SPIE 2041, 104–113 (1994).
[CrossRef]

Beckwitt, K.

X. Liu, K. Beckwitt, and F. Wise, “Transverse instability of optical spatiotemporal solitons in quadratic media,” Phys. Rev. Lett. 85, 1871–1874 (2000).
[CrossRef] [PubMed]

Buryak, A. V.

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiralling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

Calvo, G. F.

Carlsson, A. H.

Carmon, T.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, “Rotating propeller solitons,” Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef] [PubMed]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Observation of two-dimensional multimode solitons,” Opt. Lett. 25, 1113–1115 (2000).
[CrossRef]

Carvalho, M. I.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

Christodoulides, D. N.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljačić, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljacić, 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]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Observation of two-dimensional multimode solitons,” Opt. Lett. 25, 1113–1115 (2000).
[CrossRef]

M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett. 80, 4657–4560 (1998).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

D. N. Christodoulides and R. I. Joseph, “Vector solitons in birefringent nonlinear dispersive media,” Opt. Lett. 13, 53–55 (1988).
[CrossRef] [PubMed]

Christou, J.

Crosignani, B.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

Denz, C.

W. Krolikowski, E. A. Ostrovskaya, C. Weinau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

Desyatnikov, A.

DiPorto, P.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

Eugenieva, E. D.

C. Anastassiou, M. Soljacić, 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]

Fang, H.

Firth, W. J.

E. Ostrovskaya, Yu. S. Kivshar, D. Skryabin, and W. J. Firth, “Stability of multihump optical solitons,” Phys. Rev. Lett. 83, 296–299 (1999).
[CrossRef]

D. V. Skryabin and W. J. Firth, “Dynamics of self-trapped beams with phase dislocation in saturable Kerr and quadratic nonlinear media,” Phys. Rev. E 58, 3916–3930 (1998).
[CrossRef]

D. V. Skryabin and W. J. Firth, “Modulational instability of solitary waves in nondegenerate three-wave mixing: the role of phase symmetries,” Phys. Rev. Lett. 81, 3379–3382 (1998).
[CrossRef]

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

Froehly, C.

A. Barthelemy, C. Froehly, and M. Shalaby, “Nonlinear propagation of picosecond tubular beams: self phase modulation and induced refraction,” in Mode-Locked and Other Ultrashort Laser Designs, Amplifiers, and Applications, M. Piche and P. W. Pace, eds., Proc. SPIE 2041, 104–113 (1994).
[CrossRef]

Fuerst, R. A.

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997).
[CrossRef]

Gagnon, L.

García-Ripoll, J. J.

Geisser, M.

W. Krolikowski, E. A. Ostrovskaya, C. Weinau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

Haelterman, M.

See, e.g., M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).
[CrossRef]

Hewlett, S. J.

A. W. Snyder, S. J. Hewlett, and J. Mitchell, “Dynamic spatial solitons,” Phys. Rev. Lett. 72, 1012–1015 (1994).
[CrossRef] [PubMed]

Iturbe-Castillo, M. D.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[CrossRef]

Joseph, R. I.

Kip, D.

C. Anastassiou, M. Soljacić, 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]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Observation of two-dimensional multimode solitons,” Opt. Lett. 25, 1113–1115 (2000).
[CrossRef]

Kivshar, Yu. S.

A. Desyatnikov, D. Neshev, E. Ostrovskaya, Yu. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. Perez-García, “Multipole spatial vector solitons,” Opt. Lett. 26, 435–437 (2001).
[CrossRef]

D. Neshev, G. McCarthy, W. Krolikowski, E. A. Ostrovskaya, G. F. Calvo, F. Agullo-Lopez, and Yu. S. Kivshar, “Dipole-mode vector solitons in anisotropic nonlocal self-focusing media,” Opt. Lett. 26, 1185–1187 (2001).
[CrossRef]

D. Neshev, W. Krolikowski, D. E. Pelinovsky, G. McCarthy, and Yu. S. Kivshar, “Transverse instability of vector solitons and generation of dipole arrays,” Phys. Rev. Lett. 87, 103903 (2001).
[CrossRef] [PubMed]

W. Krolikowski, E. A. Ostrovskaya, C. Weinau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

J. N. Malmberg, A. H. Carlsson, D. Anderson, M. Lisak, E. A. Ostrovskaya, and Yu. S. Kivshar, “Vector solitons in (2+1) dimensions,” Opt. Lett. 25, 643–645 (2000).
[CrossRef]

Yu. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331, 118–195 (2000).
[CrossRef]

J. J. García-Ripoll, V. Perez-García, E. A. Ostrovskaya, and Yu. S. Kivshar, “Dipole-mode vector solitons,” Phys. Rev. Lett. 85, 82–85 (2000).
[CrossRef] [PubMed]

E. Ostrovskaya, Yu. S. Kivshar, D. Skryabin, and W. J. Firth, “Stability of multihump optical solitons,” Phys. Rev. Lett. 83, 296–299 (1999).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiralling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Yu. S. Kivshar, “Suppression of transverse instabilities for vector solitons,” Phys. Rev. E 60, R1170–R1173 (1999).
[CrossRef]

See, e.g., A. W. Snyder and Yu. S. Kivshar, “Bright spatial solitons in non-Kerr media: stationary beams and dynamical evolution,” J. Opt. Soc. Am. B 14, 3025–3031 (1997), and references therein.
[CrossRef]

V. Tikhonenko, J. Christou, B. Luther-Davies, and Yu. S. Kivshar, “Observation of vortex solitons created by the instability of dark soliton stripes,” Opt. Lett. 21, 1129–1131 (1996).
[CrossRef] [PubMed]

Krolikowski, W.

D. Neshev, W. Krolikowski, D. E. Pelinovsky, G. McCarthy, and Yu. S. Kivshar, “Transverse instability of vector solitons and generation of dipole arrays,” Phys. Rev. Lett. 87, 103903 (2001).
[CrossRef] [PubMed]

D. Neshev, G. McCarthy, W. Krolikowski, E. A. Ostrovskaya, G. F. Calvo, F. Agullo-Lopez, and Yu. S. Kivshar, “Dipole-mode vector solitons in anisotropic nonlocal self-focusing media,” Opt. Lett. 26, 1185–1187 (2001).
[CrossRef]

A. Desyatnikov, D. Neshev, E. Ostrovskaya, Yu. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. Perez-García, “Multipole spatial vector solitons,” Opt. Lett. 26, 435–437 (2001).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weinau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

Kutuzov, V.

V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, and V. A. Vysloukh, “Cross-modulation coupling of incoherent soliton modes in photorefractive crystals,” Phys. Rev. E 57, 6056–6065 (1998).
[CrossRef]

Kuznetsov, E.

E. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, “Soliton stability in plasmas and hydrodynamics,” Phys. Rep. 142, 103–165 (1986).
[CrossRef]

Lan, S.

Lawrence, B.

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997).
[CrossRef]

Lisak, M.

Liu, X.

X. Liu, K. Beckwitt, and F. Wise, “Transverse instability of optical spatiotemporal solitons in quadratic media,” Phys. Rev. Lett. 85, 1871–1874 (2000).
[CrossRef] [PubMed]

Luther-Davies, B.

A. Desyatnikov, D. Neshev, E. Ostrovskaya, Yu. S. Kivshar, W. Krolikowski, B. Luther-Davies, J. J. García-Ripoll, and V. Perez-García, “Multipole spatial vector solitons,” Opt. Lett. 26, 435–437 (2001).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weinau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).
[CrossRef] [PubMed]

V. Tikhonenko, J. Christou, B. Luther-Davies, and Yu. S. Kivshar, “Observation of vortex solitons created by the instability of dark soliton stripes,” Opt. Lett. 21, 1129–1131 (1996).
[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]

Malendevich, R.

Malmberg, J. N.

Mamaev, A. V.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
[CrossRef] [PubMed]

Manakov, S. V.

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).

Marquez-Aguilar, P. A.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[CrossRef]

McCarthy, G.

D. Neshev, W. Krolikowski, D. E. Pelinovsky, G. McCarthy, and Yu. S. Kivshar, “Transverse instability of vector solitons and generation of dipole arrays,” Phys. Rev. Lett. 87, 103903 (2001).
[CrossRef] [PubMed]

D. Neshev, G. McCarthy, W. Krolikowski, E. A. Ostrovskaya, G. F. Calvo, F. Agullo-Lopez, and Yu. S. Kivshar, “Dipole-mode vector solitons in anisotropic nonlocal self-focusing media,” Opt. Lett. 26, 1185–1187 (2001).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weinau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

Mitchell, J.

A. W. Snyder, S. J. Hewlett, and J. Mitchell, “Dynamic spatial solitons,” Phys. Rev. Lett. 72, 1012–1015 (1994).
[CrossRef] [PubMed]

Mitchell, M.

M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett. 80, 4657–4560 (1998).
[CrossRef]

Musslimani, Z. H.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, “Rotating propeller solitons,” Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljačić, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljacić, 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]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Observation of two-dimensional multimode solitons,” Opt. Lett. 25, 1113–1115 (2000).
[CrossRef]

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Yu. S. Kivshar, “Suppression of transverse instabilities for vector solitons,” Phys. Rev. E 60, R1170–R1173 (1999).
[CrossRef]

Nepomnyashchy, A.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, “Rotating propeller solitons,” Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Yu. S. Kivshar, “Suppression of transverse instabilities for vector solitons,” Phys. Rev. E 60, R1170–R1173 (1999).
[CrossRef]

Neshev, D.

Ostrovskaya, E.

Ostrovskaya, E. A.

D. Neshev, G. McCarthy, W. Krolikowski, E. A. Ostrovskaya, G. F. Calvo, F. Agullo-Lopez, and Yu. S. Kivshar, “Dipole-mode vector solitons in anisotropic nonlocal self-focusing media,” Opt. Lett. 26, 1185–1187 (2001).
[CrossRef]

J. J. García-Ripoll, V. Perez-García, E. A. Ostrovskaya, and Yu. S. Kivshar, “Dipole-mode vector solitons,” Phys. Rev. Lett. 85, 82–85 (2000).
[CrossRef] [PubMed]

J. N. Malmberg, A. H. Carlsson, D. Anderson, M. Lisak, E. A. Ostrovskaya, and Yu. S. Kivshar, “Vector solitons in (2+1) dimensions,” Opt. Lett. 25, 643–645 (2000).
[CrossRef]

W. Krolikowski, E. A. Ostrovskaya, C. Weinau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

Paré, C.

Pelinovsky, D. E.

D. Neshev, W. Krolikowski, D. E. Pelinovsky, G. McCarthy, and Yu. S. Kivshar, “Transverse instability of vector solitons and generation of dipole arrays,” Phys. Rev. Lett. 87, 103903 (2001).
[CrossRef] [PubMed]

Yu. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331, 118–195 (2000).
[CrossRef]

Perez-García, V.

Petnikova, V. M.

V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, and V. A. Vysloukh, “Cross-modulation coupling of incoherent soliton modes in photorefractive crystals,” Phys. Rev. E 57, 6056–6065 (1998).
[CrossRef]

Pigier, C.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, “Rotating propeller solitons,” Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef] [PubMed]

Rubenchik, A. M.

E. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, “Soliton stability in plasmas and hydrodynamics,” Phys. Rep. 142, 103–165 (1986).
[CrossRef]

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Zh. Eskp. Teor. Fiz. 65, 997 (1973) [ Sov. Phys. JETP 38, 494–500 (1974)].

Saffman, M.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
[CrossRef] [PubMed]

Salamo, G.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

Sanchez-Mondragon, J. J.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[CrossRef]

Schiek, R.

Sears, S.

M. Soljačić, S. Sears, and M. Segev, “Self-trapping of ‘necklace’ beams in self-focusing Kerr media,” Phys. Rev. Lett. 81, 4851–4854 (1998).
[CrossRef]

Segev, M.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, “Rotating propeller solitons,” Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef] [PubMed]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljačić, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljacić, 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]

T. Carmon, C. Anastassiou, S. Lan, D. Kip, Z. H. Musslimani, M. Segev, and D. N. Christodoulides, “Observation of two-dimensional multimode solitons,” Opt. Lett. 25, 1113–1115 (2000).
[CrossRef]

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Yu. S. Kivshar, “Suppression of transverse instabilities for vector solitons,” Phys. Rev. E 60, R1170–R1173 (1999).
[CrossRef]

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiralling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

M. Segev and G. I. Stegeman, “Self-trapping of optical beams: spatial solitons,” Phys. Today 51, 42–48 (1998).
[CrossRef]

M. Soljačić, S. Sears, and M. Segev, “Self-trapping of ‘necklace’ beams in self-focusing Kerr media,” Phys. Rev. Lett. 81, 4851–4854 (1998).
[CrossRef]

M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett. 80, 4657–4560 (1998).
[CrossRef]

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

Shalaby, M.

A. Barthelemy, C. Froehly, and M. Shalaby, “Nonlinear propagation of picosecond tubular beams: self phase modulation and induced refraction,” in Mode-Locked and Other Ultrashort Laser Designs, Amplifiers, and Applications, M. Piche and P. W. Pace, eds., Proc. SPIE 2041, 104–113 (1994).
[CrossRef]

Sheppard, A. P.

See, e.g., M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).
[CrossRef]

Shih, M.

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiralling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

Shuvalov, V. V.

V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, and V. A. Vysloukh, “Cross-modulation coupling of incoherent soliton modes in photorefractive crystals,” Phys. Rev. E 57, 6056–6065 (1998).
[CrossRef]

Singh, S. R.

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

Skryabin, D.

E. Ostrovskaya, Yu. S. Kivshar, D. Skryabin, and W. J. Firth, “Stability of multihump optical solitons,” Phys. Rev. Lett. 83, 296–299 (1999).
[CrossRef]

Skryabin, D. V.

D. V. Skryabin and W. J. Firth, “Dynamics of self-trapped beams with phase dislocation in saturable Kerr and quadratic nonlinear media,” Phys. Rev. E 58, 3916–3930 (1998).
[CrossRef]

D. V. Skryabin and W. J. Firth, “Modulational instability of solitary waves in nondegenerate three-wave mixing: the role of phase symmetries,” Phys. Rev. Lett. 81, 3379–3382 (1998).
[CrossRef]

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

Snyder, A. W.

Soljacic, M.

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljačić, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljacić, 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. Soljačić, S. Sears, and M. Segev, “Self-trapping of ‘necklace’ beams in self-focusing Kerr media,” Phys. Rev. Lett. 81, 4851–4854 (1998).
[CrossRef]

Stegeman, G. I.

H. Fang, R. Malendevich, R. Schiek, and G. I. Stegeman, “Spatial modulational instability in one-dimensional lithium niobate slab waveguides,” Opt. Lett. 25, 1786–1788 (2000).
[CrossRef]

M. Segev and G. I. Stegeman, “Self-trapping of optical beams: spatial solitons,” Phys. Today 51, 42–48 (1998).
[CrossRef]

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997).
[CrossRef]

Stepanov, S.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[CrossRef]

Tikhonenko, V.

Torres, J. P.

C. Anastassiou, M. Soljacić, 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]

Torruellas, W. E.

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997).
[CrossRef]

Trillo, S.

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997).
[CrossRef]

Uzdin, R.

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, “Rotating propeller solitons,” Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef] [PubMed]

Valley, G. C.

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

Vysloukh, V.

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[CrossRef]

Vysloukh, V. A.

V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, and V. A. Vysloukh, “Cross-modulation coupling of incoherent soliton modes in photorefractive crystals,” Phys. Rev. E 57, 6056–6065 (1998).
[CrossRef]

Wabnitz, S.

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997).
[CrossRef]

Weinau, C.

W. Krolikowski, E. A. Ostrovskaya, C. Weinau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

Wise, F.

X. Liu, K. Beckwitt, and F. Wise, “Transverse instability of optical spatiotemporal solitons in quadratic media,” Phys. Rev. Lett. 85, 1871–1874 (2000).
[CrossRef] [PubMed]

Yariv, A.

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

Zakharov, V. E.

E. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, “Soliton stability in plasmas and hydrodynamics,” Phys. Rep. 142, 103–165 (1986).
[CrossRef]

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Zh. Eskp. Teor. Fiz. 65, 997 (1973) [ Sov. Phys. JETP 38, 494–500 (1974)].

Zozulya, A. A.

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
[CrossRef] [PubMed]

See, e.g., 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]

Appl. Phys. Lett. (2)

D. N. Christodoulides, S. R. Singh, M. I. Carvalho, and M. Segev, “Incoherently coupled soliton pairs in biased photorefractive crystals,” Appl. Phys. Lett. 68, 1763–1765 (1996).
[CrossRef]

M. D. Iturbe-Castillo, P. A. Marquez-Aguilar, J. J. Sanchez-Mondragon, S. Stepanov, and V. Vysloukh, “Spatial solitons in photorefractive Bi12TiO20 with drift mechanism of nonlinearity,” Appl. Phys. Lett. 64, 408–410 (1994).
[CrossRef]

Electron. Lett. (1)

M. Shih, M. Segev, G. C. Valley, G. Salamo, B. Crosignani, and P. DiPorto, “Observation of two-dimensional steady-state photorefractive screening solitons,” Electron. Lett. 31, 826–827 (1995).
[CrossRef]

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

J. Opt. Soc. Am. B (2)

Opt. Lett. (7)

Phys. Rep. (2)

E. Kuznetsov, A. M. Rubenchik, and V. E. Zakharov, “Soliton stability in plasmas and hydrodynamics,” Phys. Rep. 142, 103–165 (1986).
[CrossRef]

Yu. S. Kivshar and D. E. Pelinovsky, “Self-focusing and transverse instabilities of solitary waves,” Phys. Rep. 331, 118–195 (2000).
[CrossRef]

Phys. Rev. A (2)

See, e.g., 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]

A. A. Zozulya, D. Z. Anderson, A. V. Mamaev, and M. Saffman, “Solitary attractors and low-order filamentation in anisotropic self-focusing media,” Phys. Rev. A 57, 522–534 (1998).
[CrossRef]

Phys. Rev. E (4)

D. V. Skryabin and W. J. Firth, “Dynamics of self-trapped beams with phase dislocation in saturable Kerr and quadratic nonlinear media,” Phys. Rev. E 58, 3916–3930 (1998).
[CrossRef]

Z. H. Musslimani, M. Segev, A. Nepomnyashchy, and Yu. S. Kivshar, “Suppression of transverse instabilities for vector solitons,” Phys. Rev. E 60, R1170–R1173 (1999).
[CrossRef]

See, e.g., M. Haelterman and A. P. Sheppard, “Bifurcation phenomena and multiple soliton-bound states in isotropic Kerr media,” Phys. Rev. E 49, 3376–3381 (1994).
[CrossRef]

V. Kutuzov, V. M. Petnikova, V. V. Shuvalov, and V. A. Vysloukh, “Cross-modulation coupling of incoherent soliton modes in photorefractive crystals,” Phys. Rev. E 57, 6056–6065 (1998).
[CrossRef]

Phys. Rev. Lett. (19)

E. Ostrovskaya, Yu. S. Kivshar, D. Skryabin, and W. J. Firth, “Stability of multihump optical solitons,” Phys. Rev. Lett. 83, 296–299 (1999).
[CrossRef]

Z. H. Musslimani, M. Segev, D. N. Christodoulides, and M. Soljačić, “Composite multihump vector solitons carrying topological charge,” Phys. Rev. Lett. 84, 1164–1167 (2000).
[CrossRef] [PubMed]

J. J. García-Ripoll, V. Perez-García, E. A. Ostrovskaya, and Yu. S. Kivshar, “Dipole-mode vector solitons,” Phys. Rev. Lett. 85, 82–85 (2000).
[CrossRef] [PubMed]

M. Mitchell, M. Segev, and D. N. Christodoulides, “Observation of multihump multimode solitons,” Phys. Rev. Lett. 80, 4657–4560 (1998).
[CrossRef]

A. W. Snyder, S. J. Hewlett, and J. Mitchell, “Dynamic spatial solitons,” Phys. Rev. Lett. 72, 1012–1015 (1994).
[CrossRef] [PubMed]

M. Segev, G. C. Valley, B. Crosignani, P. DiPorto, and A. Yariv, “Steady-state spatial screening solitons in photorefractive materials with external applied field,” Phys. Rev. Lett. 73, 3211–3214 (1994).
[CrossRef] [PubMed]

T. Carmon, R. Uzdin, C. Pigier, Z. H. Musslimani, M. Segev, and A. Nepomnyashchy, “Rotating propeller solitons,” Phys. Rev. Lett. 87, 143901 (2001).
[CrossRef] [PubMed]

A. V. Buryak, Yu. S. Kivshar, M. Shih, and M. Segev, “Induced coherence and stable soliton spiralling,” Phys. Rev. Lett. 82, 81–84 (1999).
[CrossRef]

V. Tikhonenko, J. Christou, and B. Luther-Davies, “Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium,” Phys. Rev. Lett. 76, 2698–2701 (1996).
[CrossRef] [PubMed]

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

M. Soljačić, S. Sears, and M. Segev, “Self-trapping of ‘necklace’ beams in self-focusing Kerr media,” Phys. Rev. Lett. 81, 4851–4854 (1998).
[CrossRef]

D. Neshev, W. Krolikowski, D. E. Pelinovsky, G. McCarthy, and Yu. S. Kivshar, “Transverse instability of vector solitons and generation of dipole arrays,” Phys. Rev. Lett. 87, 103903 (2001).
[CrossRef] [PubMed]

W. Krolikowski, E. A. Ostrovskaya, C. Weinau, M. Geisser, G. McCarthy, Yu. S. Kivshar, C. Denz, and B. Luther-Davies, “Observation of dipole-mode vector solitons,” Phys. Rev. Lett. 85, 1424–1427 (2000).
[CrossRef] [PubMed]

W. Krolikowski, M. Saffman, B. Luther-Davies, and C. Denz, “Anomalous interaction of spatial solitons in photorefractive media,” Phys. Rev. Lett. 80, 3240–3243 (1998).
[CrossRef]

R. A. Fuerst, D.-M. Baboiu, B. Lawrence, W. E. Torruellas, G. I. Stegeman, S. Trillo, and S. Wabnitz, “Spatial modulational instability and multisolitonlike generation in a quadratically nonlinear optical medium,” Phys. Rev. Lett. 78, 2756–2759 (1997).
[CrossRef]

X. Liu, K. Beckwitt, and F. Wise, “Transverse instability of optical spatiotemporal solitons in quadratic media,” Phys. Rev. Lett. 85, 1871–1874 (2000).
[CrossRef] [PubMed]

C. Anastassiou, M. Soljacić, 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]

D. V. Skryabin and W. J. Firth, “Modulational instability of solitary waves in nondegenerate three-wave mixing: the role of phase symmetries,” Phys. Rev. Lett. 81, 3379–3382 (1998).
[CrossRef]

A. V. Mamaev, M. Saffman, and A. A. Zozulya, “Propagation of dark stripe beams in nonlinear media: snake instability and creation of optical vortices,” Phys. Rev. Lett. 76, 2262–2265 (1996).
[CrossRef] [PubMed]

Phys. Today (1)

M. Segev and G. I. Stegeman, “Self-trapping of optical beams: spatial solitons,” Phys. Today 51, 42–48 (1998).
[CrossRef]

Proc. SPIE (1)

A. Barthelemy, C. Froehly, and M. Shalaby, “Nonlinear propagation of picosecond tubular beams: self phase modulation and induced refraction,” in Mode-Locked and Other Ultrashort Laser Designs, Amplifiers, and Applications, M. Piche and P. W. Pace, eds., Proc. SPIE 2041, 104–113 (1994).
[CrossRef]

Sov. Phys. JETP (2)

S. V. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).

V. E. Zakharov and A. M. Rubenchik, “Instability of waveguides and solitons in nonlinear media,” Zh. Eskp. Teor. Fiz. 65, 997 (1973) [ Sov. Phys. JETP 38, 494–500 (1974)].

Other (1)

J. J. García-Ripoll, V. Pérez-García, W. Krolikowski, and Yu. S. Kivshar, “Scattering of light by molecules of light,” arXiv.org # e-print archive, June 29, 2000, http://arXiv.org/ps/ nlin.PS/0006047.

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Figures (12)

Fig. 1
Fig. 1

Examples of constituents of (a) dipole-mode (s=0.3) and (b) vortex-mode (s=0.65) vector solitons (top and middle row) shown with the phase distributions needed to generate the w-modes experimentally (bottom row).

Fig. 2
Fig. 2

Characteristics of a single-charged vortex-mode vector soliton. (a) Power diagram for s=0.5; dashed curve - power of a scalar vortex; dotted curve - power of the fundamental scalar soliton; (b) Existence domain in the (λ, s) parameter space. A and B are the bifurcations points (cut-off) for s=0.5; (c, d) Amplitude profiles for s=0.5 near the bifurcation points A (λ=0.3) and B (λ=0.75), respectively.

Fig. 3
Fig. 3

(a) Dipole-mode soliton components obtained numerically for s=0.5. (b) Profiles of the dipole-mode vector soliton components at s=0.5; solid - numerical solutions, dashed -variational solutions for λ=0.5. (c) The power diagram of the dipole-mode soliton family shown for the partial (Pu and Pw) and total (Ptot) powers. Solid curves: results of the variational approach; points: numerical results; dotted line denotes power of the fundamental scalar soliton.

Fig. 4
Fig. 4

Examples of two-component solitons of Eqs. (2) at s=0.5 for (a, b) a quadrupole (m=2), at λ=0.46, and (c, d) a dodecagon multipole (m=6), at λ=0.6 (see Ref. 21).

Fig. 5
Fig. 5

Examples of higher-order modes for m=2 and m=3. Corresponding variational solutions of Eq. (3) for p=0 were used as initial conditions for the numerical propagation are shown at z=0. Quadrupole vector soliton for s=0.5 and λ=0.5. (b) Hexapole vector soliton for s=0.7 and λ=0.3. (c) and (d) First-order modes of the quadrupole and hexapole vector solitons, respectively.

Fig. 6
Fig. 6

Example of the numerical solution of Eqs. (5) for a dipole-mode vector soliton (g=0.5, E0=2.5, λ2/λ1=0.5). Electric field is applied along y-axis.

Fig. 7
Fig. 7

Experimental setup. M1, M2 - mirrors; BS1, BS2 beam splitters, PZT - piezoelectric transducer.

Fig. 8
Fig. 8

Experimental demonstration of two-component solitons: (a) dipole soliton (V=2kV,Pu=Pv=0.3µW); (b) quadrupole soliton (V=2.3kV,Pu=Pv=0.3µW); and (c) hexapole vector soliton (V=2kV,Pu=Pv=0.3µW). In all cases, the propagation distance is z=10mm.

Fig. 9
Fig. 9

Images of the quadrupole vector solitons for two different orientations. (a, b) Numerical results obtained for the model (5) input and output after 8mm of propagation, |u1|peak2/|u2|peak2=1.6. (c, d) Experimental results: the beam powers are 5.0µW and 6.0µW, respectively.

Fig. 10
Fig. 10

Growth rate λ(p) of the transverse modulational instability found numerically (filled circles) and analytically (dashed line). Solid curve shows an approximate fitting to the curve λ=αp(1-p/pc)1/2.

Fig. 11
Fig. 11

Generation of an array of the dipole-mode vector solitons via the transverse modulational instability - numerical simulations. (a) Intensity distribution at z=10. (b),  (c) Intensity and phase distribution at z=60, respectively.

Fig. 12
Fig. 12

Experimental observation of the transverse modulational instability of a two-component soliton stripe, which decays into an array of the dipole-mode solitons. Input powers for both components are 20.0 and 8.0µW, respectively.

Equations (19)

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iE1,2z+ΔE1,2+E1,21+|E1|2+|E2|2=0,
E1=β1u(x, y)exp(iβ1z),
E2=β1w(x, y)exp(iβ2z),
Δu-u+F(I)u=0,
Δw-λw+F(I)w=0,
w(r, φ)=Km(λr)[A cos(mφ)+B sin(mφ)],
L=rur2+wr2+1r2wφ2+1r2uφ2+|u|2+λ|w|2-Is+1s2 ln(1+sI),
Δru˜+s-1[1-s-f1(u˜, w˜)]u˜=0,
Δrw˜+s-11-sλ-m2sr2-f2(u˜, w˜)w˜=0,
Δr=d2dr2+1rddr
f1(u˜, w˜)=1(1+su˜2+p2sw˜2)1/2(1+su˜2+sw˜2)1/2,
f2(u˜, w˜)=g(u˜, w˜)f1(u˜, w˜),
g(u˜, w˜)=f1(1+su˜2)+p2sf1w˜2+[f1(1+su˜2)+f1sw˜2+1],
iE1,2z+122E1,2=-g2φyE1,2,
2φ+φ ln(1+I)=E0x0y ln(1+I),
E1(x, y)=u(x, y)exp(iλ1z),
E2(x, y)=w(x, y)exp(iλzz)
E1(x, y;0)=[1+εq(x, y)]Φ1(x),
E2(x, y;0)=Φ2(x),

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