Abstract

We introduce a new class of elliptically modulated self-trapped singular beams in isotropic nonlinear media where nonlocality plays a crucial role in their existence. The analytical expressions in the highly nonlocal nonlinear limit of these elliptically shaped self-trapped beams, or ellipticons, is obtained and their existence in more general nonlocal nonlinear media is demonstrated. We show that the ellipticons represent a generalization of several known self-trapped beams, for example vortex solitons, azimuthons, and the Hermite and Laguerre solitons clusters. For the limit of the highly nonlocal nonlinear medium, the ellipticons are described in close form in terms of the InceGauss functions.

© 2007 Optical Society of America

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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  37. A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “An optical vortex as a rotating body: mechanical features of a singular light beam,” J. Opt. A, Pure Appl. Opt. 6, S170–S174 (2004).
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    [Crossref]
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    [Crossref]

2007 (4)

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Laguerre and Hermite Soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98, 053901 (2007).
[Crossref] [PubMed]

S. Lopez-Aguayo and J. C. Gutiérrez-Vega, “Self-trapped modes in highly nonlocal nonlinear media,” Phys. Rev. A 76, 023814 (2007).
[Crossref]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Rotating multipole vortex solitons in nonlocal media,” ICONO 2007: Nonlinear Space-Time Dynamics 6725, 672507 (2007).

W. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75, 061801 (2007).
[Crossref]

2006 (8)

A. Bekshaev and M. Soskin, “Rotational transformations and transverse energy flow in paraxial light beams: linear azimuthons,” Opt. Lett. 31, 2199–2201 (2006).
[Crossref] [PubMed]

S. Skupin, O. Bang, D. Edmunson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603 (2006).
[Crossref]

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, “Dynamics of two-dimensional coherent structures in nonlocal nonlinear media,” Phys. Rev E  73, 066605 (2006).
[Crossref]

J. B. Bentley, J. A. Davis, M. A. Bandres, and J. C. Gutiérrez-Vega, “Generation of helical Ince-Gaussian beams with a liquid-crystal display,” Opt. Lett. 31, 649-651 (2006).
[Crossref] [PubMed]

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, “Incoherent solitons in instantaneous nonlocal nonlinear media,” Phys. Rev. E 73, 015601 (2006).
[Crossref]

S. Lopez-Aguayo, A. S. Desyatnikov, and Yu. S. Kivshar, “Azimuthons in nonlocal nonlinear media,” Opt. Express 14, 7903–7908 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-17-7903
[Crossref] [PubMed]

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of attraction between dark solitons,” Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

S. Lopez-Aguayo, A. S. Desyatnikov, Yu. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31, 1100–1102 (2006).
[Crossref] [PubMed]

2005 (6)

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First bbservation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

A.I. Yakimenko, Y. A. Zaliznyak, and Yu. S. Kivshar, “Stable vortex solitons in nonlocal self-focusing nonlinear media,” Phys. Rev E 71, 065603 (2005).
[Crossref]

A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, “Azimuthons: Spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).
[Crossref] [PubMed]

J. C. Gutiérrez-Vega and M. A. Bandres, “Ince-Gaussian beam in quadratic index medium,” J. Opt. Soc. Am. A,  22, 306–309 (2005).
[Crossref]

M. A. Bandres and J. C. Gutiérrez-Vega, “InceGaussian series representation of the two-dimensional fractional Fourier transform,” Opt. Lett. 30, 540–542 (2005).
[Crossref] [PubMed]

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, “Ring vortex solitons in nonlocal nonlinear media,” Opt. Express 13, 435–443 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-2-435
[Crossref] [PubMed]

2004 (9)

M. A. Bandres and J. C. Gutiérrez-Vega, “Ince Gaussian beams,” Opt. Lett. 29, 144–146 (2004).
[Crossref] [PubMed]

M. A. Bandres and J. C. Gutiérrez-Vega, “Ince-Gaussian modes of the paraxial wave equation and stable resonators,” J. Opt. Soc. Am. A,  21, 873–880 (2004).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

E. A. Ultanir, G. Stegeman, C. H. Lange, and F. Lederer, “Coherent interactions of dissipative spatial solitons,” Opt. Lett. 29, 283–285 (2004).
[Crossref] [PubMed]

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
[Crossref]

O. Katz, T. Carmon, T. Schwartz, M. Segev, and D. N. Christodoulides, “Observation of elliptic incoherent spatial solitons,” Opt. Lett. 29, 1248–1250 (2004).
[Crossref] [PubMed]

U. T. Schwarz, M. A. Bandres, and J. C. Gutiérrez-Vega, “Observation of Ince-Gaussian modes in stable resonators,” Opt. Lett. 29, 1870–1872 (2004).
[Crossref] [PubMed]

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A. Pure. Appl. Opt. 6, S157–S161 (2004).
[Crossref]

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “An optical vortex as a rotating body: mechanical features of a singular light beam,” J. Opt. A, Pure Appl. Opt. 6, S170–S174 (2004).
[Crossref]

2003 (1)

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

2002 (1)

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[Crossref]

2001 (1)

1999 (1)

C. A. Sackett, J. M. Gerton, M. Weilling, and R. C. Hulet, “Measurements of collective collapse in a Bose-Einstein condensate with attractive interactions,” Phys. Rev. Lett. 82, 876–879 (1999).
[Crossref]

1997 (1)

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
[Crossref]

1996 (1)

Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E. 54, R50–R53 (1996).
[Crossref]

1992 (1)

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926(1992).
[Crossref] [PubMed]

1987 (1)

J. E. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev.Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

1975 (1)

C. P. Boyer, E. G. Kalnins, and W. Miller, “Lie theory and separation of variables. 7. The harmonic oscillator in ellipic coordinates and the Ince polynomials,” J. Math. Phys. 16, 512–523 (1975).
[Crossref]

1967 (1)

F. M. Arscott, “The Whittaker-Hill equation and the wave equation in paraboloidal coordinates,” Proc. R. Soc. Edinburgh Sect. A 67, 265–276 (1967).

Abramochkin, E. G.

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A. Pure. Appl. Opt. 6, S157–S161 (2004).
[Crossref]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003) p. 540.

Arscott, F. M.

F. M. Arscott, “The Whittaker-Hill equation and the wave equation in paraboloidal coordinates,” Proc. R. Soc. Edinburgh Sect. A 67, 265–276 (1967).

F. M. Arscott, Periodic Differential Equations (Pergamon, Oxford, 1964).

Assanto, G.

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

Bandres, M. A.

Bang, O.

S. Skupin, O. Bang, D. Edmunson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603 (2006).
[Crossref]

S. Lopez-Aguayo, A. S. Desyatnikov, Yu. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31, 1100–1102 (2006).
[Crossref] [PubMed]

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of attraction between dark solitons,” Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, “Ring vortex solitons in nonlocal nonlinear media,” Opt. Express 13, 435–443 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-2-435
[Crossref] [PubMed]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[Crossref]

Bekshaev, A.

Bekshaev, A. Ya.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “An optical vortex as a rotating body: mechanical features of a singular light beam,” J. Opt. A, Pure Appl. Opt. 6, S170–S174 (2004).
[Crossref]

Bentley, J. B.

Boyer, C. P.

C. P. Boyer, E. G. Kalnins, and W. Miller, “Lie theory and separation of variables. 7. The harmonic oscillator in ellipic coordinates and the Ince polynomials,” J. Math. Phys. 16, 512–523 (1975).
[Crossref]

Briedis, D.

Buccoliero, D.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Rotating multipole vortex solitons in nonlocal media,” ICONO 2007: Nonlinear Space-Time Dynamics 6725, 672507 (2007).

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Laguerre and Hermite Soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98, 053901 (2007).
[Crossref] [PubMed]

Buljan, H.

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, “Incoherent solitons in instantaneous nonlocal nonlinear media,” Phys. Rev. E 73, 015601 (2006).
[Crossref]

Carmon, T.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First bbservation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

O. Katz, T. Carmon, T. Schwartz, M. Segev, and D. N. Christodoulides, “Observation of elliptic incoherent spatial solitons,” Opt. Lett. 29, 1248–1250 (2004).
[Crossref] [PubMed]

Chi, S.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
[Crossref]

Christodoulides, D. N.

Cohen, O.

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, “Incoherent solitons in instantaneous nonlocal nonlinear media,” Phys. Rev. E 73, 015601 (2006).
[Crossref]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First bbservation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Conti, C.

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

Crosignani, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926(1992).
[Crossref] [PubMed]

Davis, J. A.

Desyatnikov, A. S.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Rotating multipole vortex solitons in nonlocal media,” ICONO 2007: Nonlinear Space-Time Dynamics 6725, 672507 (2007).

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Laguerre and Hermite Soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98, 053901 (2007).
[Crossref] [PubMed]

S. Lopez-Aguayo, A. S. Desyatnikov, and Yu. S. Kivshar, “Azimuthons in nonlocal nonlinear media,” Opt. Express 14, 7903–7908 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-17-7903
[Crossref] [PubMed]

S. Lopez-Aguayo, A. S. Desyatnikov, Yu. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31, 1100–1102 (2006).
[Crossref] [PubMed]

A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, “Azimuthons: Spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).
[Crossref] [PubMed]

Dreischuh, A.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of attraction between dark solitons,” Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

Durnin, J. E.

J. E. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev.Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Eberly, J. H.

J. E. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev.Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Edmundson, D.

Edmunson, D.

S. Skupin, O. Bang, D. Edmunson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603 (2006).
[Crossref]

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926(1992).
[Crossref] [PubMed]

Fleischer, J. W.

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, “Incoherent solitons in instantaneous nonlocal nonlinear media,” Phys. Rev. E 73, 015601 (2006).
[Crossref]

Gerton, J. M.

C. A. Sackett, J. M. Gerton, M. Weilling, and R. C. Hulet, “Measurements of collective collapse in a Bose-Einstein condensate with attractive interactions,” Phys. Rev. Lett. 82, 876–879 (1999).
[Crossref]

Guo, Q.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
[Crossref]

Gutiérrez-Vega, J. C.

Hulet, R. C.

C. A. Sackett, J. M. Gerton, M. Weilling, and R. C. Hulet, “Measurements of collective collapse in a Bose-Einstein condensate with attractive interactions,” Phys. Rev. Lett. 82, 876–879 (1999).
[Crossref]

Kalnins, E. G.

C. P. Boyer, E. G. Kalnins, and W. Miller, “Lie theory and separation of variables. 7. The harmonic oscillator in ellipic coordinates and the Ince polynomials,” J. Math. Phys. 16, 512–523 (1975).
[Crossref]

Katz, O.

Kivshar, Y. S.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003) p. 540.

Kivshar, Yu.

Kivshar, Yu. S.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Rotating multipole vortex solitons in nonlocal media,” ICONO 2007: Nonlinear Space-Time Dynamics 6725, 672507 (2007).

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Laguerre and Hermite Soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98, 053901 (2007).
[Crossref] [PubMed]

S. Lopez-Aguayo, A. S. Desyatnikov, and Yu. S. Kivshar, “Azimuthons in nonlocal nonlinear media,” Opt. Express 14, 7903–7908 (2006). http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-17-7903
[Crossref] [PubMed]

A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, “Azimuthons: Spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).
[Crossref] [PubMed]

A.I. Yakimenko, Y. A. Zaliznyak, and Yu. S. Kivshar, “Stable vortex solitons in nonlocal self-focusing nonlinear media,” Phys. Rev E 71, 065603 (2005).
[Crossref]

Krolikowski, W.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Laguerre and Hermite Soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98, 053901 (2007).
[Crossref] [PubMed]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Rotating multipole vortex solitons in nonlocal media,” ICONO 2007: Nonlinear Space-Time Dynamics 6725, 672507 (2007).

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of attraction between dark solitons,” Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

S. Lopez-Aguayo, A. S. Desyatnikov, Yu. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31, 1100–1102 (2006).
[Crossref] [PubMed]

S. Skupin, O. Bang, D. Edmunson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603 (2006).
[Crossref]

D. Briedis, D. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, “Ring vortex solitons in nonlocal nonlinear media,” Opt. Express 13, 435–443 (2005). http://www.opticsinfobase.org/abstract.cfm?URI=oe-13-2-435
[Crossref] [PubMed]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[Crossref]

Lange, C. H.

Lashkin, V. M.

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, “Dynamics of two-dimensional coherent structures in nonlocal nonlinear media,” Phys. Rev E  73, 066605 (2006).
[Crossref]

Lederer, F.

Lopez-Aguayo, S.

Luo, B.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
[Crossref]

Malomed, B. A.

B. A. Malomed, “Variational methods in nonlinear fiber optics and related fields,” Prog. Opt.43, Ed. E. Wolf (North-Holland, Amsterdam, 2002), p. 71–191.
[Crossref]

Manela, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First bbservation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Miceli, J. J.

J. E. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev.Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Miller, W.

C. P. Boyer, E. G. Kalnins, and W. Miller, “Lie theory and separation of variables. 7. The harmonic oscillator in ellipic coordinates and the Ince polynomials,” J. Math. Phys. 16, 512–523 (1975).
[Crossref]

Mitchell, D. J.

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
[Crossref]

Neshev, D. N.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of attraction between dark solitons,” Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

Peccianti, M.

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

Petersen, D.

Petersen, D. E.

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of attraction between dark solitons,” Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

Piestun, R.

Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E. 54, R50–R53 (1996).
[Crossref]

Prikhodko, O. O.

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, “Dynamics of two-dimensional coherent structures in nonlocal nonlinear media,” Phys. Rev E  73, 066605 (2006).
[Crossref]

Rasmussen, J. J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[Crossref]

Rotschild, C.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First bbservation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Sackett, C. A.

C. A. Sackett, J. M. Gerton, M. Weilling, and R. C. Hulet, “Measurements of collective collapse in a Bose-Einstein condensate with attractive interactions,” Phys. Rev. Lett. 82, 876–879 (1999).
[Crossref]

Schechner, Y. Y.

Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E. 54, R50–R53 (1996).
[Crossref]

Schwartz, T.

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, “Incoherent solitons in instantaneous nonlocal nonlinear media,” Phys. Rev. E 73, 015601 (2006).
[Crossref]

O. Katz, T. Carmon, T. Schwartz, M. Segev, and D. N. Christodoulides, “Observation of elliptic incoherent spatial solitons,” Opt. Lett. 29, 1248–1250 (2004).
[Crossref] [PubMed]

Schwarz, U. T.

Segev, M.

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, “Incoherent solitons in instantaneous nonlocal nonlinear media,” Phys. Rev. E 73, 015601 (2006).
[Crossref]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First bbservation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

O. Katz, T. Carmon, T. Schwartz, M. Segev, and D. N. Christodoulides, “Observation of elliptic incoherent spatial solitons,” Opt. Lett. 29, 1248–1250 (2004).
[Crossref] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926(1992).
[Crossref] [PubMed]

Shamir, J.

Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E. 54, R50–R53 (1996).
[Crossref]

Skupin, S.

S. Skupin, O. Bang, D. Edmunson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603 (2006).
[Crossref]

S. Lopez-Aguayo, A. S. Desyatnikov, Yu. Kivshar, S. Skupin, W. Krolikowski, and O. Bang, “Stable rotating dipole solitons in nonlocal optical media,” Opt. Lett. 31, 1100–1102 (2006).
[Crossref] [PubMed]

Snyder, A. W.

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
[Crossref]

Soskin, M.

Soskin, M. S.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “An optical vortex as a rotating body: mechanical features of a singular light beam,” J. Opt. A, Pure Appl. Opt. 6, S170–S174 (2004).
[Crossref]

Stegeman, G.

Sukhorukov, A. A.

A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, “Azimuthons: Spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).
[Crossref] [PubMed]

Tervo, J.

Turunen, J. P.

Ultanir, E. A.

Vasnetsov, M. V.

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “An optical vortex as a rotating body: mechanical features of a singular light beam,” J. Opt. A, Pure Appl. Opt. 6, S170–S174 (2004).
[Crossref]

Volostnikov, V. G.

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A. Pure. Appl. Opt. 6, S157–S161 (2004).
[Crossref]

Weilling, M.

C. A. Sackett, J. M. Gerton, M. Weilling, and R. C. Hulet, “Measurements of collective collapse in a Bose-Einstein condensate with attractive interactions,” Phys. Rev. Lett. 82, 876–879 (1999).
[Crossref]

Wyller, J.

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[Crossref]

Xie, Y.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
[Crossref]

Yakimenko, A. I.

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, “Dynamics of two-dimensional coherent structures in nonlocal nonlinear media,” Phys. Rev E  73, 066605 (2006).
[Crossref]

Yakimenko, A.I.

A.I. Yakimenko, Y. A. Zaliznyak, and Yu. S. Kivshar, “Stable vortex solitons in nonlocal self-focusing nonlinear media,” Phys. Rev E 71, 065603 (2005).
[Crossref]

Yariv, A.

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926(1992).
[Crossref] [PubMed]

Yi, F.

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
[Crossref]

Yi, L.

W. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75, 061801 (2007).
[Crossref]

Zaliznyak, Y. A.

A.I. Yakimenko, Y. A. Zaliznyak, and Yu. S. Kivshar, “Stable vortex solitons in nonlocal self-focusing nonlinear media,” Phys. Rev E 71, 065603 (2005).
[Crossref]

Zhong, W.

W. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75, 061801 (2007).
[Crossref]

ICONO 2007: Nonlinear Space-Time Dynamics (1)

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Rotating multipole vortex solitons in nonlocal media,” ICONO 2007: Nonlinear Space-Time Dynamics 6725, 672507 (2007).

J. Math. Phys. (1)

C. P. Boyer, E. G. Kalnins, and W. Miller, “Lie theory and separation of variables. 7. The harmonic oscillator in ellipic coordinates and the Ince polynomials,” J. Math. Phys. 16, 512–523 (1975).
[Crossref]

J. Opt. A, Pure Appl. Opt. (1)

A. Ya. Bekshaev, M. S. Soskin, and M. V. Vasnetsov, “An optical vortex as a rotating body: mechanical features of a singular light beam,” J. Opt. A, Pure Appl. Opt. 6, S170–S174 (2004).
[Crossref]

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

E. G. Abramochkin and V. G. Volostnikov, “Generalized Gaussian beams,” J. Opt. A. Pure. Appl. Opt. 6, S157–S161 (2004).
[Crossref]

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

Opt. Express (3)

Opt. Lett. (8)

Phys. Rev E (2)

A.I. Yakimenko, Y. A. Zaliznyak, and Yu. S. Kivshar, “Stable vortex solitons in nonlocal self-focusing nonlinear media,” Phys. Rev E 71, 065603 (2005).
[Crossref]

A. I. Yakimenko, V. M. Lashkin, and O. O. Prikhodko, “Dynamics of two-dimensional coherent structures in nonlocal nonlinear media,” Phys. Rev E  73, 066605 (2006).
[Crossref]

Phys. Rev. A (2)

S. Lopez-Aguayo and J. C. Gutiérrez-Vega, “Self-trapped modes in highly nonlocal nonlinear media,” Phys. Rev. A 76, 023814 (2007).
[Crossref]

W. Zhong and L. Yi, “Two-dimensional Laguerre-Gaussian soliton family in strongly nonlocal nonlinear media,” Phys. Rev. A 75, 061801 (2007).
[Crossref]

Phys. Rev. E (4)

O. Cohen, H. Buljan, T. Schwartz, J. W. Fleischer, and M. Segev, “Incoherent solitons in instantaneous nonlocal nonlinear media,” Phys. Rev. E 73, 015601 (2006).
[Crossref]

Q. Guo, B. Luo, F. Yi, S. Chi, and Y. Xie, “Large phase shift of nonlocal optical spatial solitons,” Phys. Rev. E 69, 016602 (2004).
[Crossref]

O. Bang, W. Krolikowski, J. Wyller, and J. J. Rasmussen, “Collapse arrest and soliton stabilization in nonlocal nonlinear media,” Phys. Rev. E 66, 046619 (2002).
[Crossref]

S. Skupin, O. Bang, D. Edmunson, and W. Krolikowski, “Stability of two-dimensional spatial solitons in nonlocal nonlinear media,” Phys. Rev. E 73, 066603 (2006).
[Crossref]

Phys. Rev. E. (1)

Y. Y. Schechner, R. Piestun, and J. Shamir, “Wave propagation with rotating intensity distributions,” Phys. Rev. E. 54, R50–R53 (1996).
[Crossref]

Phys. Rev. Lett. (8)

A. Dreischuh, D. N. Neshev, D. E. Petersen, O. Bang, and W. Krolikowski, “Observation of attraction between dark solitons,” Phys. Rev. Lett. 96, 043901 (2006).
[Crossref] [PubMed]

A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, “Azimuthons: Spatially modulated vortex solitons,” Phys. Rev. Lett. 95, 203904 (2005).
[Crossref] [PubMed]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Laguerre and Hermite Soliton clusters in nonlocal nonlinear media,” Phys. Rev. Lett. 98, 053901 (2007).
[Crossref] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, “Solitons in nonlinear media with an infinite range of nonlocality: First bbservation of coherent elliptic solitons and of vortex-ring solitons,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

M. Segev, B. Crosignani, A. Yariv, and B. Fischer, “Spatial solitons in photorefractive media,” Phys. Rev. Lett. 68, 923–926(1992).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

C. A. Sackett, J. M. Gerton, M. Weilling, and R. C. Hulet, “Measurements of collective collapse in a Bose-Einstein condensate with attractive interactions,” Phys. Rev. Lett. 82, 876–879 (1999).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

Phys. Rev.Lett. (1)

J. E. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev.Lett. 58, 1499–1501 (1987).
[Crossref] [PubMed]

Proc. R. Soc. Edinburgh Sect. A (1)

F. M. Arscott, “The Whittaker-Hill equation and the wave equation in paraboloidal coordinates,” Proc. R. Soc. Edinburgh Sect. A 67, 265–276 (1967).

Science (1)

A. W. Snyder and D. J. Mitchell, “Accessible solitons,” Science 276, 1538–1541 (1997).
[Crossref]

Other (3)

Y. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003) p. 540.

F. M. Arscott, Periodic Differential Equations (Pergamon, Oxford, 1964).

B. A. Malomed, “Variational methods in nonlinear fiber optics and related fields,” Prog. Opt.43, Ed. E. Wolf (North-Holland, Amsterdam, 2002), p. 71–191.
[Crossref]

Supplementary Material (11)

» Media 1: AVI (1365 KB)     
» Media 2: AVI (1406 KB)     
» Media 3: AVI (1339 KB)     
» Media 4: AVI (1520 KB)     
» Media 5: AVI (1537 KB)     
» Media 6: AVI (2087 KB)     
» Media 7: AVI (2097 KB)     
» Media 8: AVI (537 KB)     
» Media 9: AVI (1459 KB)     
» Media 10: AVI (1374 KB)     
» Media 11: AVI (454 KB)     

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Figures (7)

Fig. 1.
Fig. 1.

(1.3 Mb) (a) Intensity and phase of a stationary accessible ellipticon given by Ψ+ 5,3(ξ,η) for ε=0,1, and ∞. (b) Phase structure around the interfocal line. (c) Intensity and phase distribution of a stationary accessible ellipticon with parameters p=5 and m=5 in HNN media. The intensity pattern remain invariant in propagation while the phase front rotate around the interfocal line. [Media 1]

Fig. 2.
Fig. 2.

(a) Nodal lines for the pure even and the pure odd part of Ψ+5,3(ξ,η) for ε=1 and ∞ respectively. Red and blue lines represent nodal lines of the even and odd components, respectively. Positive and negative vortices are represented by white and black circles, respectively. (b) Orbital angular momentum carried by Ψ+ p,m in function of ε for p=2n+m and m={1,2, …,7}.

Fig. 3.
Fig. 3.

Different scenarios for the propagation of accessible rotating ellipticons given by the combination of two stationary accessible ellipticons: (a) (1.4 Mb) self-imaging phenomenon in the case of p 1=6, m 1=2, p 2=2, and m 2=2, (b) (1.3 Mb) stationary behavior; p 1=3, m 1=1, p 2=3, and m 2=3, (c) (1.5 Mb) rotation of the intensity pattern and the phase front in opposite directions, here p 1=8, m 1=4, p 2=6, and m 2=6, and (d) (1.5 Mb) rotation of the intensity pattern and the phase front in the same direction; p 1=8, m 1=4, p 2=10, and m 2=10. In all the cases ε=1 and L=2π/a. [Media 2] [Media 3][Media 4] [Media 5]

Fig. 4.
Fig. 4.

Propagation dynamics of an elliptcon with parameters p=4, m=4, ε=1, and P 0=103 in an xy box of 2.6×2.6 in a nonlocal nonlinear medium. (a) Using directly the accessible ellipticon solution the beam diffracts and the maximum normalized intensity decays [see (b)]. (c) Using the same trial function but modified with the variational approach (A=1.6066) the beam remain self-trapped and the maximum normalized intensity oscillates remaining within a finite and small range [see (d)].

Fig. 5.
Fig. 5.

Intensity and phase of two ellipticons in nonlocal nonlinear media with parameters (a) (2 Mb) p=2, m=2, ε=0.75, and P0=103 in an xy box of 4.2×4.2, and (b) (2.1 Mb) p=3, m=3, ε=1, and P0=103 in an xy box of 4.8×4.8.

Fig. 6.
Fig. 6.

(a) Propagation in nonlocal nonlinear media of a vortex soliton of single charge and double ring (or soliton Laguerre mode L 11). (b) Different modes that also coexist in the propagation before mentioned.

Fig. 7.
Fig. 7.

(a) (1.4 Mb) Elliptically intensity-rotating beam with ε=0 close to the HNN limit (P0=106) in a xy box of 0.8×0.8 produced by two ellipticons with parameters p1=10, m1=10, p2=2, and m2=2. (b) (1.4 Mb) Intensity rotating beam produced by three ellipticons with parameters p1=5, m1=5, p2=5, m 2=3, p 3=5, and m 3=1 close to the HNN limit (P 0=106) in a xy box of 0.8×0.8, here ε=1, for all the three beams. [Media 8] [Media 11]

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

2 i k n 0 z E ( r , z ) + n 0 2 E ( r , z ) + 2 k 2 n ( I , z ) E ( r , z ) = 0 ,
n ( I , z ) = R ( r r ) E ( r , z ) 2 d r ,
R ( r ) = 1 π σ 2 exp ( r 2 σ 2 ) ,
R ( r r ' ) = R 0 + ( r r ) · R 0 + 1 2 [ ( r r ) · ] 2 R 0 + ,
n ( I , z ) P 0 π σ 2 ( 1 r 2 σ 2 ) ,
2 i k z U ( r , z ) + 2 U ( r , z ) k 2 a 2 r 2 U ( r , z ) = 0 ,
Ψ p , m ± ( ξ , η ) = [ C C p m ( i ξ ; ε ) C p m ( η ; ε ) ± i S S p m ( i ξ ; ε ) S p m ( η ; ε ) ] exp ( a k r 2 2 ) ,
β = ( p + 1 ) a ,
P 0 = π n 0 k 2 σ 4 ( p + 1 ) 2 β 2 .
J z = h ¯ r × Im ( U * U ) d x d y U 2 d x d y ,
Φ ( ξ , η ) = A 1 Ψ p 1 , m 1 + ( ξ , η ) + A 2 Ψ p 2 , m 2 + ( ξ , η ) ,
p p = τ ( m m ) ,
ω = a τ .
= 2 k n 0 Γ E ( r ) 2 n 0 E ( r ) 2 + k 2 E ( r ) 2 2 R ( r r ) E ( r ) 2 d r ,
A = P 0 2 ( p + 1 ) π n 0 P 0 3 2 k 2 + ( π σ 2 n 0 2 k 2 ) Ψ p , m ± ( ξ , η ) 2 d r Ψ p , m ± ( ξ , η ) 2 [ exp ( r r ' 2 σ 2 ) Ψ p , m ± ( ξ ' , η ' ) 2 d r ' ] d r .

Metrics