Abstract

We study the different families of vortex-type modes that can exist in a photonic crystal fiber with two close defects forming a dual-core coupler and presenting the Kerr nonlinearity. Those complex modes bifurcate from the real double-dipole states leading to different states with different phase structures. When power is high enough, single- and double-vortex modes as well as combinations of vortex and fundamental modes arise. Also, families of discrete vortices formed by multipoles located inside the cores are found. We classify the different families, describe their nontrivial bifurcations, and study the stability of the states identifying different scenarios.

© 2009 Optical Society of America

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  1. Ph. Russell, “Photonic crystals fibers,” Science 299, 358-562 (2003).
    [CrossRef] [PubMed]
  2. J. C. Knight, “Photonic crystals fibers,” Nature 424, 847-851 (2003).
    [CrossRef] [PubMed]
  3. A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 17, 1333-1340 (2000).
    [CrossRef] [PubMed]
  4. A. Ferrando, M. Zacarés, and M. A. García-March, “Vorticity cutoff in nonlinear photonic crystals,” Phys. Rev. Lett. 95, 043901 (2005).
    [CrossRef] [PubMed]
  5. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, 2003).
  6. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47.
    [CrossRef]
  7. A. Ferrando, M. Zacarés, P. Fernández de Córdoba, D. Binosi, and J. A. Monsoriu, “Spatial soliton formation in photonic crystal fibers,” Opt. Express 11, 452-459 (2003).
    [CrossRef] [PubMed]
  8. J. R. Salgueiro, Yu. S. Kivshar, D. E. Pelinovski, V. Simón, and H. Michinel, “Spatial vector solitons in nonlinear photonic crystal fibers,” Stud. Appl. Math. 115, 157-171 (2005).
    [CrossRef]
  9. V. I. Kruglov and R. A. Vlasov, “Spiral self-trapping propagation of optical beams in media with cubic nonlinearity,” Phys. Lett. A 111, 401-404 (1985).
    [CrossRef]
  10. A. S. Desyatnikov and Yu. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88, 053901 (2002).
    [CrossRef] [PubMed]
  11. Y. V. Kartashov, L. C. Crasovan, D. Mihalache, and L. Torner, “Robust propagation of two-color soliton clusters supported by competing nonlinearities,” Phys. Rev. Lett. 89, 273902 (2002).
    [CrossRef]
  12. A. Desyatnikov and Yu. Kivshar, “Spatial optical solitons and soliton clusters carrying an angular momentum,” J. Opt. B: Quantum Semiclassical Opt. 4, S58-S64 (2002).
    [CrossRef]
  13. D. Mihalache, D. Mazilu, L. C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046612 (2003).
    [CrossRef]
  14. A. Ferrando, M. Zacarés, P. Fernández de Córdoba, D. Binosi, and J. A. Monsoriu, “Vortex solitons in photonic crystal fibers,” Opt. Express 12, 817-822 (2004).
    [CrossRef] [PubMed]
  15. J. R. Salgueiro and Yu. S. Kivshar, “Optical vortex solitons and soliton clusters in photonic crystal fibres,” Eur. Phys. J. Spec. Top. 173, 281-288 (2009).
    [CrossRef]
  16. P. Xie, Z. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasi-periodic photonic crystals,” Phys. Rev. E 67, 026607 (2003).
    [CrossRef]
  17. B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63, 642-648 (2003).
    [CrossRef]
  18. J. R. Salgueiro and Yu. S. Kivshar, “Nonlinear dual-core photonic crystal fiber couplers,” Opt. Lett. 30, 1858-1860 (2005).
    [CrossRef] [PubMed]
  19. A. Gubeskys and B. A. Malomed, “Spontaneous soliton symmetry breaking in two-dimensional coupled Bose-Einstein condensates supported by optical lattices,” Phys. Rev. A 76, 043623 (2007).
    [CrossRef]
  20. W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. D. J. Russell, “Two-core photonic crystal fibre for Doppler difference velocimetry,” Opt. Commun. 223, 375-380 (2003).
    [CrossRef]
  21. A. Betlej, S. Suntsov, K. G. Makris, L. Jankovic, D. N. Christodoulides, G. I. Stegeman, J. Fini, R. T. Bise, and D. J. DiGiovanni, “All-optical switching and multifrequency generation in a dual-core photonic crystal fiber,” Opt. Lett. 31, 1480-1482 (2006).
    [CrossRef] [PubMed]
  22. J. Yang and D. E. Pelinovsky, “Stable vortex and dipole vector solitons in a saturable nonlinear medium,” Phys. Rev. E 67, 016608 (2003).
    [CrossRef]
  23. J. R. Salgueiro and Yu. S. Kivshar, “Single- and double-vortex vector solitons in self-focusing nonlinear media,” Phys. Rev. E 70, 056613 (2004).
    [CrossRef]
  24. A. I. Yakimenko, Y. A. Zaliznyak, and Yu. Kivshar, “Stable vortex solitons in nonlocal self-focusing nonlinear media,” Phys. Rev. E 71, 065603 (2005).
    [CrossRef]
  25. D. Briedis, D. E. Petersen, D. Edmundson, W. Krolikowski, and O. Bang, “Ring vortex solitons in nonlocal nonlinear media,” Opt. Express 13, 435-443 (2005).
    [CrossRef] [PubMed]
  26. A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Yu. S. Kivshar, “Stabilization of vortex solitons in nonlocal nonlinear media,” Phys. Rev. A 76, 063803 (2007).
    [CrossRef]
  27. S. Lopez-Aguayo, A. S. Desyatnikov, and Yu. S. Kivshar, “Azimuthons in nonlocal nonlinear media,” Opt. Express 14, 7903-7908 (2006).
    [CrossRef] [PubMed]
  28. D. Buccoliero, S. López-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Yu. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351-356 (2007).
    [CrossRef]
  29. D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Spiraling multivortex solitons in nonlocal nonlinear media,” Opt. Lett. 33, 198-200 (2008).
    [CrossRef] [PubMed]
  30. J. R. Salgueiro, D. Olivieri, and H. Michinel, “Computation of linear and nonlinear stationary states of photonic structures using modern iterative solvers,” Opt. Quantum Electron. 39, 239-260 (2007).
    [CrossRef]
  31. N. N. Akhmediev and A. Ankiewicz, Solitons (Chapman and Hall, 1997).

2009

J. R. Salgueiro and Yu. S. Kivshar, “Optical vortex solitons and soliton clusters in photonic crystal fibres,” Eur. Phys. J. Spec. Top. 173, 281-288 (2009).
[CrossRef]

2008

2007

J. R. Salgueiro, D. Olivieri, and H. Michinel, “Computation of linear and nonlinear stationary states of photonic structures using modern iterative solvers,” Opt. Quantum Electron. 39, 239-260 (2007).
[CrossRef]

A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Yu. S. Kivshar, “Stabilization of vortex solitons in nonlocal nonlinear media,” Phys. Rev. A 76, 063803 (2007).
[CrossRef]

D. Buccoliero, S. López-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Yu. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351-356 (2007).
[CrossRef]

A. Gubeskys and B. A. Malomed, “Spontaneous soliton symmetry breaking in two-dimensional coupled Bose-Einstein condensates supported by optical lattices,” Phys. Rev. A 76, 043623 (2007).
[CrossRef]

2006

2005

J. R. Salgueiro and Yu. S. Kivshar, “Nonlinear dual-core photonic crystal fiber couplers,” Opt. Lett. 30, 1858-1860 (2005).
[CrossRef] [PubMed]

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

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

A. Ferrando, M. Zacarés, and M. A. García-March, “Vorticity cutoff in nonlinear photonic crystals,” Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef] [PubMed]

J. R. Salgueiro, Yu. S. Kivshar, D. E. Pelinovski, V. Simón, and H. Michinel, “Spatial vector solitons in nonlinear photonic crystal fibers,” Stud. Appl. Math. 115, 157-171 (2005).
[CrossRef]

2004

A. Ferrando, M. Zacarés, P. Fernández de Córdoba, D. Binosi, and J. A. Monsoriu, “Vortex solitons in photonic crystal fibers,” Opt. Express 12, 817-822 (2004).
[CrossRef] [PubMed]

J. R. Salgueiro and Yu. S. Kivshar, “Single- and double-vortex vector solitons in self-focusing nonlinear media,” Phys. Rev. E 70, 056613 (2004).
[CrossRef]

2003

D. Mihalache, D. Mazilu, L. C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046612 (2003).
[CrossRef]

P. Xie, Z. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasi-periodic photonic crystals,” Phys. Rev. E 67, 026607 (2003).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63, 642-648 (2003).
[CrossRef]

J. Yang and D. E. Pelinovsky, “Stable vortex and dipole vector solitons in a saturable nonlinear medium,” Phys. Rev. E 67, 016608 (2003).
[CrossRef]

W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. D. J. Russell, “Two-core photonic crystal fibre for Doppler difference velocimetry,” Opt. Commun. 223, 375-380 (2003).
[CrossRef]

A. Ferrando, M. Zacarés, P. Fernández de Córdoba, D. Binosi, and J. A. Monsoriu, “Spatial soliton formation in photonic crystal fibers,” Opt. Express 11, 452-459 (2003).
[CrossRef] [PubMed]

Ph. Russell, “Photonic crystals fibers,” Science 299, 358-562 (2003).
[CrossRef] [PubMed]

J. C. Knight, “Photonic crystals fibers,” Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

2002

A. S. Desyatnikov and Yu. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

Y. V. Kartashov, L. C. Crasovan, D. Mihalache, and L. Torner, “Robust propagation of two-color soliton clusters supported by competing nonlinearities,” Phys. Rev. Lett. 89, 273902 (2002).
[CrossRef]

A. Desyatnikov and Yu. Kivshar, “Spatial optical solitons and soliton clusters carrying an angular momentum,” J. Opt. B: Quantum Semiclassical Opt. 4, S58-S64 (2002).
[CrossRef]

2000

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 17, 1333-1340 (2000).
[CrossRef] [PubMed]

1985

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

Agrawal, G. P.

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

Akhmediev, N. N.

N. N. Akhmediev and A. Ankiewicz, Solitons (Chapman and Hall, 1997).

Andrés, P.

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 17, 1333-1340 (2000).
[CrossRef] [PubMed]

Ankiewicz, A.

N. N. Akhmediev and A. Ankiewicz, Solitons (Chapman and Hall, 1997).

Baizakov, B. B.

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63, 642-648 (2003).
[CrossRef]

Bang, O.

D. Buccoliero, S. López-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Yu. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351-356 (2007).
[CrossRef]

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

Betlej, A.

Binosi, D.

Bise, R. T.

Briedis, D.

Buccoliero, D.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Spiraling multivortex solitons in nonlocal nonlinear media,” Opt. Lett. 33, 198-200 (2008).
[CrossRef] [PubMed]

D. Buccoliero, S. López-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Yu. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351-356 (2007).
[CrossRef]

Christodoulides, D. N.

Crasovan, L. C.

D. Mihalache, D. Mazilu, L. C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046612 (2003).
[CrossRef]

Y. V. Kartashov, L. C. Crasovan, D. Mihalache, and L. Torner, “Robust propagation of two-color soliton clusters supported by competing nonlinearities,” Phys. Rev. Lett. 89, 273902 (2002).
[CrossRef]

Desyatnikov, A.

A. Desyatnikov and Yu. Kivshar, “Spatial optical solitons and soliton clusters carrying an angular momentum,” J. Opt. B: Quantum Semiclassical Opt. 4, S58-S64 (2002).
[CrossRef]

Desyatnikov, A. S.

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Spiraling multivortex solitons in nonlocal nonlinear media,” Opt. Lett. 33, 198-200 (2008).
[CrossRef] [PubMed]

D. Buccoliero, S. López-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Yu. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351-356 (2007).
[CrossRef]

S. Lopez-Aguayo, A. S. Desyatnikov, and Yu. S. Kivshar, “Azimuthons in nonlocal nonlinear media,” Opt. Express 14, 7903-7908 (2006).
[CrossRef] [PubMed]

A. S. Desyatnikov and Yu. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47.
[CrossRef]

DiGiovanni, D. J.

Edmundson, D.

Fernández de Córdoba, P.

Ferrando, A.

A. Ferrando, M. Zacarés, and M. A. García-March, “Vorticity cutoff in nonlinear photonic crystals,” Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef] [PubMed]

A. Ferrando, M. Zacarés, P. Fernández de Córdoba, D. Binosi, and J. A. Monsoriu, “Vortex solitons in photonic crystal fibers,” Opt. Express 12, 817-822 (2004).
[CrossRef] [PubMed]

A. Ferrando, M. Zacarés, P. Fernández de Córdoba, D. Binosi, and J. A. Monsoriu, “Spatial soliton formation in photonic crystal fibers,” Opt. Express 11, 452-459 (2003).
[CrossRef] [PubMed]

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 17, 1333-1340 (2000).
[CrossRef] [PubMed]

Fini, J.

García-March, M. A.

A. Ferrando, M. Zacarés, and M. A. García-March, “Vorticity cutoff in nonlinear photonic crystals,” Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef] [PubMed]

Gubeskys, A.

A. Gubeskys and B. A. Malomed, “Spontaneous soliton symmetry breaking in two-dimensional coupled Bose-Einstein condensates supported by optical lattices,” Phys. Rev. A 76, 043623 (2007).
[CrossRef]

Jankovic, L.

Jones, J. D. C.

W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. D. J. Russell, “Two-core photonic crystal fibre for Doppler difference velocimetry,” Opt. Commun. 223, 375-380 (2003).
[CrossRef]

Kartashov, Y. V.

Y. V. Kartashov, L. C. Crasovan, D. Mihalache, and L. Torner, “Robust propagation of two-color soliton clusters supported by competing nonlinearities,” Phys. Rev. Lett. 89, 273902 (2002).
[CrossRef]

Kivshar, Yu.

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

A. Desyatnikov and Yu. Kivshar, “Spatial optical solitons and soliton clusters carrying an angular momentum,” J. Opt. B: Quantum Semiclassical Opt. 4, S58-S64 (2002).
[CrossRef]

Kivshar, Yu. S.

J. R. Salgueiro and Yu. S. Kivshar, “Optical vortex solitons and soliton clusters in photonic crystal fibres,” Eur. Phys. J. Spec. Top. 173, 281-288 (2009).
[CrossRef]

D. Buccoliero, A. S. Desyatnikov, W. Krolikowski, and Yu. S. Kivshar, “Spiraling multivortex solitons in nonlocal nonlinear media,” Opt. Lett. 33, 198-200 (2008).
[CrossRef] [PubMed]

D. Buccoliero, S. López-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Yu. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351-356 (2007).
[CrossRef]

A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Yu. S. Kivshar, “Stabilization of vortex solitons in nonlocal nonlinear media,” Phys. Rev. A 76, 063803 (2007).
[CrossRef]

S. Lopez-Aguayo, A. S. Desyatnikov, and Yu. S. Kivshar, “Azimuthons in nonlocal nonlinear media,” Opt. Express 14, 7903-7908 (2006).
[CrossRef] [PubMed]

J. R. Salgueiro and Yu. S. Kivshar, “Nonlinear dual-core photonic crystal fiber couplers,” Opt. Lett. 30, 1858-1860 (2005).
[CrossRef] [PubMed]

J. R. Salgueiro, Yu. S. Kivshar, D. E. Pelinovski, V. Simón, and H. Michinel, “Spatial vector solitons in nonlinear photonic crystal fibers,” Stud. Appl. Math. 115, 157-171 (2005).
[CrossRef]

J. R. Salgueiro and Yu. S. Kivshar, “Single- and double-vortex vector solitons in self-focusing nonlinear media,” Phys. Rev. E 70, 056613 (2004).
[CrossRef]

A. S. Desyatnikov and Yu. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

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

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47.
[CrossRef]

Knight, J. C.

J. C. Knight, “Photonic crystals fibers,” Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. D. J. Russell, “Two-core photonic crystal fibre for Doppler difference velocimetry,” Opt. Commun. 223, 375-380 (2003).
[CrossRef]

Krolikowski, W.

Kruglov, V. I.

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

Lederer, F.

D. Mihalache, D. Mazilu, L. C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046612 (2003).
[CrossRef]

Lopez-Aguayo, S.

López-Aguayo, S.

D. Buccoliero, S. López-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Yu. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351-356 (2007).
[CrossRef]

MacPherson, W. N.

W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. D. J. Russell, “Two-core photonic crystal fibre for Doppler difference velocimetry,” Opt. Commun. 223, 375-380 (2003).
[CrossRef]

Makris, K. G.

Malomed, B. A.

A. Gubeskys and B. A. Malomed, “Spontaneous soliton symmetry breaking in two-dimensional coupled Bose-Einstein condensates supported by optical lattices,” Phys. Rev. A 76, 043623 (2007).
[CrossRef]

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63, 642-648 (2003).
[CrossRef]

D. Mihalache, D. Mazilu, L. C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046612 (2003).
[CrossRef]

Mangan, B. J.

W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. D. J. Russell, “Two-core photonic crystal fibre for Doppler difference velocimetry,” Opt. Commun. 223, 375-380 (2003).
[CrossRef]

Mazilu, D.

D. Mihalache, D. Mazilu, L. C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046612 (2003).
[CrossRef]

Michinel, H.

J. R. Salgueiro, D. Olivieri, and H. Michinel, “Computation of linear and nonlinear stationary states of photonic structures using modern iterative solvers,” Opt. Quantum Electron. 39, 239-260 (2007).
[CrossRef]

J. R. Salgueiro, Yu. S. Kivshar, D. E. Pelinovski, V. Simón, and H. Michinel, “Spatial vector solitons in nonlinear photonic crystal fibers,” Stud. Appl. Math. 115, 157-171 (2005).
[CrossRef]

Mihalache, D.

D. Mihalache, D. Mazilu, L. C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046612 (2003).
[CrossRef]

Y. V. Kartashov, L. C. Crasovan, D. Mihalache, and L. Torner, “Robust propagation of two-color soliton clusters supported by competing nonlinearities,” Phys. Rev. Lett. 89, 273902 (2002).
[CrossRef]

Minzoni, A. A.

A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Yu. S. Kivshar, “Stabilization of vortex solitons in nonlocal nonlinear media,” Phys. Rev. A 76, 063803 (2007).
[CrossRef]

Miret, J. J.

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 17, 1333-1340 (2000).
[CrossRef] [PubMed]

Monsoriu, J. A.

Olivieri, D.

J. R. Salgueiro, D. Olivieri, and H. Michinel, “Computation of linear and nonlinear stationary states of photonic structures using modern iterative solvers,” Opt. Quantum Electron. 39, 239-260 (2007).
[CrossRef]

Pelinovski, D. E.

J. R. Salgueiro, Yu. S. Kivshar, D. E. Pelinovski, V. Simón, and H. Michinel, “Spatial vector solitons in nonlinear photonic crystal fibers,” Stud. Appl. Math. 115, 157-171 (2005).
[CrossRef]

Pelinovsky, D. E.

J. Yang and D. E. Pelinovsky, “Stable vortex and dipole vector solitons in a saturable nonlinear medium,” Phys. Rev. E 67, 016608 (2003).
[CrossRef]

Petersen, D. E.

Russell, P. D. J.

W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. D. J. Russell, “Two-core photonic crystal fibre for Doppler difference velocimetry,” Opt. Commun. 223, 375-380 (2003).
[CrossRef]

Russell, Ph.

Ph. Russell, “Photonic crystals fibers,” Science 299, 358-562 (2003).
[CrossRef] [PubMed]

Salerno, M.

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63, 642-648 (2003).
[CrossRef]

Salgueiro, J. R.

J. R. Salgueiro and Yu. S. Kivshar, “Optical vortex solitons and soliton clusters in photonic crystal fibres,” Eur. Phys. J. Spec. Top. 173, 281-288 (2009).
[CrossRef]

J. R. Salgueiro, D. Olivieri, and H. Michinel, “Computation of linear and nonlinear stationary states of photonic structures using modern iterative solvers,” Opt. Quantum Electron. 39, 239-260 (2007).
[CrossRef]

J. R. Salgueiro and Yu. S. Kivshar, “Nonlinear dual-core photonic crystal fiber couplers,” Opt. Lett. 30, 1858-1860 (2005).
[CrossRef] [PubMed]

J. R. Salgueiro, Yu. S. Kivshar, D. E. Pelinovski, V. Simón, and H. Michinel, “Spatial vector solitons in nonlinear photonic crystal fibers,” Stud. Appl. Math. 115, 157-171 (2005).
[CrossRef]

J. R. Salgueiro and Yu. S. Kivshar, “Single- and double-vortex vector solitons in self-focusing nonlinear media,” Phys. Rev. E 70, 056613 (2004).
[CrossRef]

Silvestre, E.

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 17, 1333-1340 (2000).
[CrossRef] [PubMed]

Simón, V.

J. R. Salgueiro, Yu. S. Kivshar, D. E. Pelinovski, V. Simón, and H. Michinel, “Spatial vector solitons in nonlinear photonic crystal fibers,” Stud. Appl. Math. 115, 157-171 (2005).
[CrossRef]

Skupin, S.

D. Buccoliero, S. López-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Yu. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351-356 (2007).
[CrossRef]

Smyth, N. F.

A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Yu. S. Kivshar, “Stabilization of vortex solitons in nonlocal nonlinear media,” Phys. Rev. A 76, 063803 (2007).
[CrossRef]

Stegeman, G. I.

Suntsov, S.

Torner, L.

D. Mihalache, D. Mazilu, L. C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046612 (2003).
[CrossRef]

Y. V. Kartashov, L. C. Crasovan, D. Mihalache, and L. Torner, “Robust propagation of two-color soliton clusters supported by competing nonlinearities,” Phys. Rev. Lett. 89, 273902 (2002).
[CrossRef]

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47.
[CrossRef]

Vlasov, R. A.

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

Worthy, A. L.

A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Yu. S. Kivshar, “Stabilization of vortex solitons in nonlocal nonlinear media,” Phys. Rev. A 76, 063803 (2007).
[CrossRef]

Xie, P.

P. Xie, Z. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasi-periodic photonic crystals,” Phys. Rev. E 67, 026607 (2003).
[CrossRef]

Yakimenko, A. I.

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

Yang, J.

J. Yang and D. E. Pelinovsky, “Stable vortex and dipole vector solitons in a saturable nonlinear medium,” Phys. Rev. E 67, 016608 (2003).
[CrossRef]

Zacarés, M.

Zaliznyak, Y. A.

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

Zhang, X.

P. Xie, Z. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasi-periodic photonic crystals,” Phys. Rev. E 67, 026607 (2003).
[CrossRef]

Zhang, Z.

P. Xie, Z. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasi-periodic photonic crystals,” Phys. Rev. E 67, 026607 (2003).
[CrossRef]

Eur. Phys. J. Spec. Top.

J. R. Salgueiro and Yu. S. Kivshar, “Optical vortex solitons and soliton clusters in photonic crystal fibres,” Eur. Phys. J. Spec. Top. 173, 281-288 (2009).
[CrossRef]

Europhys. Lett.

B. B. Baizakov, B. A. Malomed, and M. Salerno, “Multidimensional solitons in periodic potentials,” Europhys. Lett. 63, 642-648 (2003).
[CrossRef]

J. Opt. B: Quantum Semiclassical Opt.

A. Desyatnikov and Yu. Kivshar, “Spatial optical solitons and soliton clusters carrying an angular momentum,” J. Opt. B: Quantum Semiclassical Opt. 4, S58-S64 (2002).
[CrossRef]

J. Opt. Soc. Am. A Opt. Image Sci. Vis.

A. Ferrando, E. Silvestre, J. J. Miret, and P. Andrés, “Vector description of higher-order modes in photonic crystal fibers,” J. Opt. Soc. Am. A Opt. Image Sci. Vis. 17, 1333-1340 (2000).
[CrossRef] [PubMed]

Nature

J. C. Knight, “Photonic crystals fibers,” Nature 424, 847-851 (2003).
[CrossRef] [PubMed]

Opt. Commun.

W. N. MacPherson, J. D. C. Jones, B. J. Mangan, J. C. Knight, and P. D. J. Russell, “Two-core photonic crystal fibre for Doppler difference velocimetry,” Opt. Commun. 223, 375-380 (2003).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

J. R. Salgueiro, D. Olivieri, and H. Michinel, “Computation of linear and nonlinear stationary states of photonic structures using modern iterative solvers,” Opt. Quantum Electron. 39, 239-260 (2007).
[CrossRef]

Phys. Lett. A

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

Phys. Rev. A

A. Gubeskys and B. A. Malomed, “Spontaneous soliton symmetry breaking in two-dimensional coupled Bose-Einstein condensates supported by optical lattices,” Phys. Rev. A 76, 043623 (2007).
[CrossRef]

A. A. Minzoni, N. F. Smyth, A. L. Worthy, and Yu. S. Kivshar, “Stabilization of vortex solitons in nonlocal nonlinear media,” Phys. Rev. A 76, 063803 (2007).
[CrossRef]

Phys. Rev. E

J. Yang and D. E. Pelinovsky, “Stable vortex and dipole vector solitons in a saturable nonlinear medium,” Phys. Rev. E 67, 016608 (2003).
[CrossRef]

J. R. Salgueiro and Yu. S. Kivshar, “Single- and double-vortex vector solitons in self-focusing nonlinear media,” Phys. Rev. E 70, 056613 (2004).
[CrossRef]

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

P. Xie, Z. Zhang, and X. Zhang, “Gap solitons and soliton trains in finite-sized two-dimensional periodic and quasi-periodic photonic crystals,” Phys. Rev. E 67, 026607 (2003).
[CrossRef]

D. Mihalache, D. Mazilu, L. C. Crasovan, B. A. Malomed, F. Lederer, and L. Torner, “Robust soliton clusters in media with competing cubic and quintic nonlinearities,” Phys. Rev. E 68, 046612 (2003).
[CrossRef]

Phys. Rev. Lett.

A. S. Desyatnikov and Yu. S. Kivshar, “Rotating optical soliton clusters,” Phys. Rev. Lett. 88, 053901 (2002).
[CrossRef] [PubMed]

Y. V. Kartashov, L. C. Crasovan, D. Mihalache, and L. Torner, “Robust propagation of two-color soliton clusters supported by competing nonlinearities,” Phys. Rev. Lett. 89, 273902 (2002).
[CrossRef]

A. Ferrando, M. Zacarés, and M. A. García-March, “Vorticity cutoff in nonlinear photonic crystals,” Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef] [PubMed]

Physica B

D. Buccoliero, S. López-Aguayo, S. Skupin, A. S. Desyatnikov, O. Bang, W. Krolikowski, and Yu. S. Kivshar, “Spiraling solitons and multipole localized modes in nonlocal nonlinear media,” Physica B 394, 351-356 (2007).
[CrossRef]

Science

Ph. Russell, “Photonic crystals fibers,” Science 299, 358-562 (2003).
[CrossRef] [PubMed]

Stud. Appl. Math.

J. R. Salgueiro, Yu. S. Kivshar, D. E. Pelinovski, V. Simón, and H. Michinel, “Spatial vector solitons in nonlinear photonic crystal fibers,” Stud. Appl. Math. 115, 157-171 (2005).
[CrossRef]

Other

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

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, in Progress in Optics, E.Wolf, ed. (North-Holland, 2005), Vol. 47.
[CrossRef]

N. N. Akhmediev and A. Ankiewicz, Solitons (Chapman and Hall, 1997).

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Figures (11)

Fig. 1
Fig. 1

Sketch of the central part of the PCF with triangular structure and two close defects (double solid core) showing the basic parameters.

Fig. 2
Fig. 2

Power versus propagation constant for the different families of vortexlike solutions (continuous curves), the double-dipole solutions (dashed curves), and the asymmetric dipoles (dashed-dotted curves). Big capital letters label points corresponding to the different examples shown in other figures below. The italic legends label the branches correspondent to the different types of solutions: double dipoles (DDs), asymmetric dipoles (ADs), DVs, and AVs. Beware that curves may actually constitute a bunch of close-together curves (not distinguished due to the scale of the figure) describing families of solutions with similar (though different) power. Inset: detail of the DV branch at higher power, where double-quadrupole solutions originate.

Fig. 3
Fig. 3

(a)–(d) Four DD states of a dual-core PCF for β = 0.8 : (a) bounding type ( b ) , (b) antibounding ( a ) , (c) parallel ( p ) , (d) crossed ( x ) . (e),(f) Two asymmetric dipoles (AD1 and AD2) that bifurcate from the DDs at points O 6 and O 7 (Fig. 4) and take the shape of single dipoles at high enough power.

Fig. 4
Fig. 4

Detail of the power curves for the low power regime. Dashed lines are the four DD families (b, a, p, and x stand for the bounding, antibounding, parallel, and crossed families, respectively). Points labeled O 1 O 4 are those from where the four DV families bifurcate [the four types bounding positive ( b + ) , bounding negative ( b ) , antibounding positive ( a + ) , and antibounding negative ( a ) are indicated]. O 5 and O 6 are the bifurcation points for the two asymmetric DD families (labeled as AD1 and AD2 and plotted as dashed-dotted lines). O 7 is the bifurcation point for the AV. Inset: zoom of the region close to point O 5 to show that branches AD1 and AD2 are noncoincident.

Fig. 5
Fig. 5

(a),(b) Intensity-level plots of two DV states for β = 0.85 (point B in Fig. 2), one of the bounding type (a) and another of the antibounding type (b). (c)–(f) Phase patterns for each of the DV states correspondent to that point. Images (c) and (e) show the phase of the same vorticity states ( + ) and images (d) and (f) the phase of those with opposite vorticity (−), so that images (c)–(f) correspond to the states b + , b , a + , and a , respectively.

Fig. 6
Fig. 6

Some examples of DV states plotted as intensity-level images and correspondent to different branches in the power diagram. Two double-doughnut states (A, D)—one close to the bifurcation point (A)—two double tripoles (C1, C2), and two double quadrupoles (E1, E2) are shown. Labels correspond to points (A, C, D, and E) in Fig. 2.

Fig. 7
Fig. 7

(a) Detail of the power diagram at the junction where double-tripole branches (labeled DT) originate from the DV ones. Different curves correspondent to families of different phase structure are shown: bounding positive ( b + ) , bounding negative ( b ) , antibounding positive ( a + ) , and antibounding negative ( a ) . For the low branch lines corresponding to the families a + and a are very close and not resolved at the scale of the plot. (b) Same for the junction point where double-quadrupole (DQ) solutions originate. Again curves corresponding to a + and a are too close to be resolved.

Fig. 8
Fig. 8

Some examples of single vortices and VF states with different shapes (shown as intensity plots): two types of STs (F1, F2), single doughnut (G), two types of TF states (H1, H2), and doughnut-fundamental state (I). Labels correspond to points in Fig. 2.

Fig. 9
Fig. 9

Detail of the power diagram at the junction where different branches of ST and TF solutions originate from the asymmetric-vortex family. The shape of the different solutions is indicated with labels: single (doughnut) vortex (SV), ST, TF, and (doughnut) VF. Additionally, the type of solution according to the phase structure is also indicated with labels: bounding ( b ) and antibounding ( a ) . The numbers in brackets indicate the type of solution according to symmetry criteria (cases F and H in Fig. 8).

Fig. 10
Fig. 10

Examples of single vortices and VF states correspondent to families of the doughnut and quadrupole types. The two types of single quadrupoles (J1, J2) originate from the SV branch in Fig. 9 at higher power. The two types of quadrupole-fundamental states (L1, L2) originate from the VF branch at higher power. The doughnut-shaped single-vortex (K) and VF (M) are also examples related to a higher power.

Fig. 11
Fig. 11

Maximum intensity versus propagation distance for different double vortices (continuous curves) and single vortices (dashed curves). DV curves correspond to P = 34.4 (a), P = 30.1 (b), P = 27.9 (c), and P = 5.8 (d). Single-vortex simulations are for P = 27.3 (e), P = 15.8 (f), P = 15.1 (g), and P = 2.76 (h).

Equations (5)

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

2 i k E Z + 2 E + 2 k 2 [ W ( X , Y ) + γ V ( X , Y ) | E | 2 ] E = 0 ,
i U z + 2 U + V ( x , y ) ( 1 + | U | 2 ) U = 0 ,
U ( x , y , z ) = u ( x , y ) exp ( i β z ) ,
β u + 2 u + V ( x , y ) ( 1 + | u | 2 ) u = 0.
β u i + Δ u i + V ( 1 + u 1 2 + u 2 2 ) u i = 0 ,     i = 1 , 2.

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