Abstract

We predict theoretically and generate experimentally in pho-torefractive crystal two-dimensional self-trapped periodic waves of different symmetries, including vortex lattices – patterns of phase dislocations with internal energy flows. We demonstrate that these nonlinear waves exist with nonlocal nonlinearity even when the optically-induced periodic refractive index becomes highly anisotropic, and it depends on the orientation of the two-dimensional lattice relative to the crystallographic c-axis.

© 2006 Optical Society of America

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  1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, 2003), 540 pp., and references therein.
  2. S. F. Mingaleev, Yu. S. Kivshar, and R. Sammut, in: Soliton-driven Photonics, A. D. Boardman and A. P. Sukhorukov, Eds. (Kluwer, Dordrecht, Netherlands, 2001), pp. 487-504.
    [CrossRef]
  3. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
    [CrossRef]
  4. J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  5. D. Neshev, E. Ostrovskaya, Yu. S. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710-712 (2003).
    [CrossRef] [PubMed]
  6. A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, "Composite band-gap solitons in nonlinear optically induced lattices, " Phys. Rev. Lett. 91, 153902 (2003).
    [CrossRef] [PubMed]
  7. D. Neshev, Yu. S. Kivshar, H. Martin, and Z. G. Chen, "Soliton stripes in two-dimensional nonlinear photonic lattices," Opt. Lett. 29, 486 (2004).
    [CrossRef] [PubMed]
  8. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
    [CrossRef] [PubMed]
  9. S. Minardi, S. Sapone, W. Chinaglia, P. Di Trapani, and A. Berzanskis, "Pixellike parametric generator based on controlled spatial-soliton formation," Opt. Lett. 25, 326 (2000).
    [CrossRef]
  10. Z. Chen, and K. McCarthy, "Spatial soliton pixels from partially incoherent light," Opt. Lett. 27, 2019 (2002).
    [CrossRef]
  11. J. Petter, J. Schröder, D. Träger, and C. Denz, "Optical control of arrays of photorefractive screening solitons," Opt. Lett. 28, 438 (2003).
    [CrossRef] [PubMed]
  12. M. Petrović, D. Träger, A. Strinić, M. Belić, J. Schröder, and C. Denz, "Solitonic lattices in photorefractive crystals," Phys. Rev. E 68, 055601R (2003).
    [CrossRef]
  13. Ya. V. Kartashov, V. A. Visloukh, and L. Torner, "Two-dimensional cnoidal waves in Kerr-type saturable nonlinear media," Phys. Rev. E 68, 015603 (2003).
    [CrossRef]
  14. A. S. Desyatnikov, D. N. Neshev, Y. S. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. V. Kartashov, "Nonlinear photonic lattices in anisotropic nonlocal self-focusing media," Opt. Lett. 30, 869 (2005).
    [CrossRef] [PubMed]
  15. Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
    [CrossRef] [PubMed]
  16. A. Sukhorukov, "Soliton dynamics in deformable nonlinear lattices," arXiv:nlin.PS/0507050 (2005).
  17. A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, "Optical vortices and vortex solitons," in Progress in Optics, Vol. 47, Ed. E. Wolf (Elsevier, Amstredam, 2005), pp. 219-319.
  18. J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21 (2001).
    [CrossRef]
  19. D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, "Motion control of ensembles of ordered optical vortices generated on finite extent background," Opt. Commun. 151, 413 (1998).
    [CrossRef]
  20. A. Dreischuh, S. Chervenkov, D. Neshev, G. G. Paulus, and H. Walther, "Generation of lattice structures of optical vortices," J. Opt. Soc. Am. B 19, 550-556 (2002).
    [CrossRef]
  21. A. Desyatnikov, D. Neshev, and Yu. Kivshar, "Vortex solitons, soliton clusters, and vortex lattices," Ukr. J. Phys. Optics 6, 71 (2005).
    [CrossRef]
  22. D. Jovic, D. Arsenovic, A. Strinić, M. Belić, and M. Petrović, "Counterpropagating optical vortices in photorefractive crystals," Opt. Express 13, 4379-4389 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4379
    [CrossRef] [PubMed]
  23. N. R. Cooper, E. H. Rezayi, and S. H. Simon, "Vortex lattices in rotating atomic Bose gases with dipolar interactions," Phys. Rev. Lett. 95, 200402 (2005), and references therein.
    [CrossRef] [PubMed]
  24. 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 (1997).
    [CrossRef]
  25. G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
    [CrossRef] [PubMed]
  26. A. A. Sukhorukov, D. Neshev,W. Krolikowski, and Yu. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices, " Phys. Rev. Lett. 92, 093901 (2004).
    [CrossRef] [PubMed]
  27. A. S. Desyatnikov and Yu. S. Kivshar, "Rotating optical soliton clusters," Phys. Rev. Lett. 88, 053901 (2002).
    [CrossRef] [PubMed]
  28. A. S. Desyatnikov, A. A. Sukhorukov, and Yu. S. Kivshar, "Azimuthons: spatially modulated vortex solitons," Phys. Rev. Lett. 95, 203904 (2005).
    [CrossRef] [PubMed]
  29. D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
    [CrossRef] [PubMed]
  30. J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
    [CrossRef] [PubMed]

2005

A. Desyatnikov, D. Neshev, and Yu. Kivshar, "Vortex solitons, soliton clusters, and vortex lattices," Ukr. J. Phys. Optics 6, 71 (2005).
[CrossRef]

N. R. Cooper, E. H. Rezayi, and S. H. Simon, "Vortex lattices in rotating atomic Bose gases with dipolar interactions," Phys. Rev. Lett. 95, 200402 (2005), and references therein.
[CrossRef] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[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. S. Desyatnikov, D. N. Neshev, Y. S. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. V. Kartashov, "Nonlinear photonic lattices in anisotropic nonlocal self-focusing media," Opt. Lett. 30, 869 (2005).
[CrossRef] [PubMed]

D. Jovic, D. Arsenovic, A. Strinić, M. Belić, and M. Petrović, "Counterpropagating optical vortices in photorefractive crystals," Opt. Express 13, 4379-4389 (2005), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-12-4379
[CrossRef] [PubMed]

2004

D. Neshev, Yu. S. Kivshar, H. Martin, and Z. G. Chen, "Soliton stripes in two-dimensional nonlinear photonic lattices," Opt. Lett. 29, 486 (2004).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. Neshev,W. Krolikowski, and Yu. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices, " Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

2003

J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, "Composite band-gap solitons in nonlinear optically induced lattices, " Phys. Rev. Lett. 91, 153902 (2003).
[CrossRef] [PubMed]

M. Petrović, D. Träger, A. Strinić, M. Belić, J. Schröder, and C. Denz, "Solitonic lattices in photorefractive crystals," Phys. Rev. E 68, 055601R (2003).
[CrossRef]

Ya. V. Kartashov, V. A. Visloukh, and L. Torner, "Two-dimensional cnoidal waves in Kerr-type saturable nonlinear media," Phys. Rev. E 68, 015603 (2003).
[CrossRef]

J. Petter, J. Schröder, D. Träger, and C. Denz, "Optical control of arrays of photorefractive screening solitons," Opt. Lett. 28, 438 (2003).
[CrossRef] [PubMed]

D. Neshev, E. Ostrovskaya, Yu. S. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710-712 (2003).
[CrossRef] [PubMed]

2002

A. Dreischuh, S. Chervenkov, D. Neshev, G. G. Paulus, and H. Walther, "Generation of lattice structures of optical vortices," J. Opt. Soc. Am. B 19, 550-556 (2002).
[CrossRef]

Z. Chen, and K. McCarthy, "Spatial soliton pixels from partially incoherent light," Opt. Lett. 27, 2019 (2002).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

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

2001

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21 (2001).
[CrossRef]

2000

1998

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, "Motion control of ensembles of ordered optical vortices generated on finite extent background," Opt. Commun. 151, 413 (1998).
[CrossRef]

1997

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 (1997).
[CrossRef]

Alexander, T. J.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

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 (1997).
[CrossRef]

Arsenovic, D.

Assa, M.

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, "Motion control of ensembles of ordered optical vortices generated on finite extent background," Opt. Commun. 151, 413 (1998).
[CrossRef]

Bartal, G.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Belic, M.

Berzanskis, A.

Bezryadina, A.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Buljan, H.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

Chen, Z.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Z. Chen, and K. McCarthy, "Spatial soliton pixels from partially incoherent light," Opt. Lett. 27, 2019 (2002).
[CrossRef]

Chen, Z. G.

Chervenkov, S.

Chinaglia, W.

Christodoulides, D. N.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Cohen, O.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Cooper, N. R.

N. R. Cooper, E. H. Rezayi, and S. H. Simon, "Vortex lattices in rotating atomic Bose gases with dipolar interactions," Phys. Rev. Lett. 95, 200402 (2005), and references therein.
[CrossRef] [PubMed]

Denz, C.

A. S. Desyatnikov, D. N. Neshev, Y. S. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. V. Kartashov, "Nonlinear photonic lattices in anisotropic nonlocal self-focusing media," Opt. Lett. 30, 869 (2005).
[CrossRef] [PubMed]

M. Petrović, D. Träger, A. Strinić, M. Belić, J. Schröder, and C. Denz, "Solitonic lattices in photorefractive crystals," Phys. Rev. E 68, 055601R (2003).
[CrossRef]

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, "Composite band-gap solitons in nonlinear optically induced lattices, " Phys. Rev. Lett. 91, 153902 (2003).
[CrossRef] [PubMed]

J. Petter, J. Schröder, D. Träger, and C. Denz, "Optical control of arrays of photorefractive screening solitons," Opt. Lett. 28, 438 (2003).
[CrossRef] [PubMed]

Desyatnikov, A.

A. Desyatnikov, D. Neshev, and Yu. Kivshar, "Vortex solitons, soliton clusters, and vortex lattices," Ukr. J. Phys. Optics 6, 71 (2005).
[CrossRef]

Desyatnikov, A. S.

A. S. Desyatnikov, D. N. Neshev, Y. S. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. V. Kartashov, "Nonlinear photonic lattices in anisotropic nonlocal self-focusing media," Opt. Lett. 30, 869 (2005).
[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. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, "Composite band-gap solitons in nonlinear optically induced lattices, " Phys. Rev. Lett. 91, 153902 (2003).
[CrossRef] [PubMed]

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

Di Trapani, P.

Dinev, S.

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, "Motion control of ensembles of ordered optical vortices generated on finite extent background," Opt. Commun. 151, 413 (1998).
[CrossRef]

Dreischuh, A.

A. Dreischuh, S. Chervenkov, D. Neshev, G. G. Paulus, and H. Walther, "Generation of lattice structures of optical vortices," J. Opt. Soc. Am. B 19, 550-556 (2002).
[CrossRef]

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, "Motion control of ensembles of ordered optical vortices generated on finite extent background," Opt. Commun. 151, 413 (1998).
[CrossRef]

Dubik, B.

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21 (2001).
[CrossRef]

Efremidis, N. K.

J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Eugenieva, E. D.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

Fleischer, J. W.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Fleischer, J.W.

J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

Hudock, J.

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Jägers, J.

Jovic, D.

Kartashov, Y. V.

Kartashov, Ya. V.

Ya. V. Kartashov, V. A. Visloukh, and L. Torner, "Two-dimensional cnoidal waves in Kerr-type saturable nonlinear media," Phys. Rev. E 68, 015603 (2003).
[CrossRef]

Kivshar, Y. S.

Kivshar, Yu.

A. Desyatnikov, D. Neshev, and Yu. Kivshar, "Vortex solitons, soliton clusters, and vortex lattices," Ukr. J. Phys. Optics 6, 71 (2005).
[CrossRef]

Kivshar, Yu. S.

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

D. Neshev, Yu. S. Kivshar, H. Martin, and Z. G. Chen, "Soliton stripes in two-dimensional nonlinear photonic lattices," Opt. Lett. 29, 486 (2004).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. Neshev,W. Krolikowski, and Yu. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices, " Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, "Composite band-gap solitons in nonlinear optically induced lattices, " Phys. Rev. Lett. 91, 153902 (2003).
[CrossRef] [PubMed]

D. Neshev, E. Ostrovskaya, Yu. S. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710-712 (2003).
[CrossRef] [PubMed]

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

Krolikowski, W.

A. A. Sukhorukov, D. Neshev,W. Krolikowski, and Yu. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices, " Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

D. Neshev, E. Ostrovskaya, Yu. S. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710-712 (2003).
[CrossRef] [PubMed]

Makasyuk, I.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

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 (1997).
[CrossRef]

Manela, O.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Martin, H.

D. Neshev, Yu. S. Kivshar, H. Martin, and Z. G. Chen, "Soliton stripes in two-dimensional nonlinear photonic lattices," Opt. Lett. 29, 486 (2004).
[CrossRef] [PubMed]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Masajada, J.

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21 (2001).
[CrossRef]

McCarthy, K.

Minardi, S.

Neshev, D.

A. Desyatnikov, D. Neshev, and Yu. Kivshar, "Vortex solitons, soliton clusters, and vortex lattices," Ukr. J. Phys. Optics 6, 71 (2005).
[CrossRef]

D. Neshev, Yu. S. Kivshar, H. Martin, and Z. G. Chen, "Soliton stripes in two-dimensional nonlinear photonic lattices," Opt. Lett. 29, 486 (2004).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. Neshev,W. Krolikowski, and Yu. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices, " Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

D. Neshev, E. Ostrovskaya, Yu. S. Kivshar, and W. Krolikowski, "Spatial solitons in optically induced gratings," Opt. Lett. 28, 710-712 (2003).
[CrossRef] [PubMed]

A. Dreischuh, S. Chervenkov, D. Neshev, G. G. Paulus, and H. Walther, "Generation of lattice structures of optical vortices," J. Opt. Soc. Am. B 19, 550-556 (2002).
[CrossRef]

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, "Motion control of ensembles of ordered optical vortices generated on finite extent background," Opt. Commun. 151, 413 (1998).
[CrossRef]

Neshev, D. N.

A. S. Desyatnikov, D. N. Neshev, Y. S. Kivshar, N. Sagemerten, D. Träger, J. Jägers, C. Denz, and Y. V. Kartashov, "Nonlinear photonic lattices in anisotropic nonlocal self-focusing media," Opt. Lett. 30, 869 (2005).
[CrossRef] [PubMed]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

Ostrovskaya, E.

Ostrovskaya, E. A.

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, "Composite band-gap solitons in nonlinear optically induced lattices, " Phys. Rev. Lett. 91, 153902 (2003).
[CrossRef] [PubMed]

Paulus, G. G.

Petrovic, M.

Petter, J.

Rezayi, E. H.

N. R. Cooper, E. H. Rezayi, and S. H. Simon, "Vortex lattices in rotating atomic Bose gases with dipolar interactions," Phys. Rev. Lett. 95, 200402 (2005), and references therein.
[CrossRef] [PubMed]

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 (1997).
[CrossRef]

Sagemerten, N.

Sapone, S.

Schröder, J.

J. Petter, J. Schröder, D. Träger, and C. Denz, "Optical control of arrays of photorefractive screening solitons," Opt. Lett. 28, 438 (2003).
[CrossRef] [PubMed]

M. Petrović, D. Träger, A. Strinić, M. Belić, J. Schröder, and C. Denz, "Solitonic lattices in photorefractive crystals," Phys. Rev. E 68, 055601R (2003).
[CrossRef]

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Segev, M.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Simon, S. H.

N. R. Cooper, E. H. Rezayi, and S. H. Simon, "Vortex lattices in rotating atomic Bose gases with dipolar interactions," Phys. Rev. Lett. 95, 200402 (2005), and references therein.
[CrossRef] [PubMed]

Strinic, A.

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]

A. A. Sukhorukov, D. Neshev,W. Krolikowski, and Yu. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices, " Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

Torner, L.

Ya. V. Kartashov, V. A. Visloukh, and L. Torner, "Two-dimensional cnoidal waves in Kerr-type saturable nonlinear media," Phys. Rev. E 68, 015603 (2003).
[CrossRef]

Träger, D.

Visloukh, V. A.

Ya. V. Kartashov, V. A. Visloukh, and L. Torner, "Two-dimensional cnoidal waves in Kerr-type saturable nonlinear media," Phys. Rev. E 68, 015603 (2003).
[CrossRef]

Walther, H.

Xu, J.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

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 (1997).
[CrossRef]

J. Opt. Soc. Am. B

Nature

J.W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

Opt. Commun.

J. Masajada and B. Dubik, "Optical vortex generation by three plane wave interference," Opt. Commun. 198, 21 (2001).
[CrossRef]

D. Neshev, A. Dreischuh, M. Assa, and S. Dinev, "Motion control of ensembles of ordered optical vortices generated on finite extent background," Opt. Commun. 151, 413 (1998).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. 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 (1997).
[CrossRef]

Phys. Rev. E

M. Petrović, D. Träger, A. Strinić, M. Belić, J. Schröder, and C. Denz, "Solitonic lattices in photorefractive crystals," Phys. Rev. E 68, 055601R (2003).
[CrossRef]

Ya. V. Kartashov, V. A. Visloukh, and L. Torner, "Two-dimensional cnoidal waves in Kerr-type saturable nonlinear media," Phys. Rev. E 68, 015603 (2003).
[CrossRef]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, "Discrete solitons in photorefractive optically induced photonic lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Phys. Rev. Lett.

N. R. Cooper, E. H. Rezayi, and S. H. Simon, "Vortex lattices in rotating atomic Bose gases with dipolar interactions," Phys. Rev. Lett. 95, 200402 (2005), and references therein.
[CrossRef] [PubMed]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, "Anisotropic enhancement of discrete diffraction and formation of two-dimensional discrete-soliton trains," Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef] [PubMed]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, "Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices," Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

A. S. Desyatnikov, E. A. Ostrovskaya, Yu. S. Kivshar, and C. Denz, "Composite band-gap solitons in nonlinear optically induced lattices, " Phys. Rev. Lett. 91, 153902 (2003).
[CrossRef] [PubMed]

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, "Brillouin zone spectroscopy of nonlinear photonic lattices," Phys. Rev. Lett. 94, 163902 (2005).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. Neshev,W. Krolikowski, and Yu. S. Kivshar, "Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices, " Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

A. S. Desyatnikov and Yu. S. Kivshar, "Rotating optical soliton clusters," Phys. Rev. Lett. 88, 053901 (2002).
[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. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Yu. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Observation of discrete vortex solitons in optically-induced photonic lattices," Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

J. W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D. N. Christodoulides, "Observation of vortex-ring discrete solitons in 2D photonic lattices," Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

Ukr. J. Phys. Optics

A. Desyatnikov, D. Neshev, and Yu. Kivshar, "Vortex solitons, soliton clusters, and vortex lattices," Ukr. J. Phys. Optics 6, 71 (2005).
[CrossRef]

Other

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, 2003), 540 pp., and references therein.

S. F. Mingaleev, Yu. S. Kivshar, and R. Sammut, in: Soliton-driven Photonics, A. D. Boardman and A. P. Sukhorukov, Eds. (Kluwer, Dordrecht, Netherlands, 2001), pp. 487-504.
[CrossRef]

A. Sukhorukov, "Soliton dynamics in deformable nonlinear lattices," arXiv:nlin.PS/0507050 (2005).

A. S. Desyatnikov, Yu. S. Kivshar, and L. Torner, "Optical vortices and vortex solitons," in Progress in Optics, Vol. 47, Ed. E. Wolf (Elsevier, Amstredam, 2005), pp. 219-319.

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Figures (7)

Fig. 1.
Fig. 1.

Comparison between the nonlinear square lattices in self-focusing (b, σ = +1), and self-defocusing (c, σ = - 1) media. The field U(x,y) in (a) and refractive index ∂ x φ in (b,c) are shown for three distinct values of the mode amplitude max U(x,y), or the propagation constant k, from low (k= -1.9 and k = -2.1) to high (k= -1.2 and k = -2.8) saturation. Colors are scaled, and the information about the absolute values of the mode amplitude, power density, and the refractive index modulation is summarized in (d).

Fig. 2.
Fig. 2.

Same as in Fig. 1 but for the diamond lattices.

Fig. 3.
Fig. 3.

Experimental setup, QWP – quarter wave plate, SLM – spatial light modulator, P – polarizer, L – lens, ID – iris diaphragm, BGI – background illumination, HV – High voltage, CCD – CCD camera. The insets show the chessboard-like phase patterns for square (left) and diamond (right) lattices, phase values are σ (black) and 0 (white).

Fig. 4.
Fig. 4.

Experimentally generated light intensity patterns with chessboard-like phase: square (upper row) and diamond (lower row). (a) linear output without applied electric field, (b) nonlinear output with applied electric field, (d) guiding of a plane wave in photonic lattice. (c) and (e) demonstrate the far field structure of the lattice and guided waves in (b) and (d) respectively.

Fig. 5.
Fig. 5.

Theoretical (color) and experimental (grayscale) results for triangular lattices created by interference of six plane waves, see far field images in the top panel. Two distinct orientations of the triangular lattices are compared (top and middle panel) as well as low (left) and high (right) saturation regimes. LW, field U(x,y) (color) and intensity (grayscale) of the lattice wave. GW, calculated profiles of the refractive index (color) and measured intensity of the guided wave (grayscale).

Fig. 6.
Fig. 6.

Diagonally-oriented square vortex lattices in photorefractive self-focusing media. Numerically calculated stationary solutions are shown for Γ = 11.8 close to linear diffraction-free wave with k = -0.1 and I max ≃ 0.42 in (a), and in higher saturation regime with k = 1.2 and I max ≃ 1.24 in (b). (c) Experimentally observed vortex lattice with the period 57μm: left - nonlinear output for bias 1.3kV, middle - magnified top right part of the lattice interfering with a reference broad beam to monitor the position of the vortex dislocations (marked by arrows), right - intensity of the guided plane wave launched from the edge of the first Brillouin zone.

Fig. 7.
Fig. 7.

Self-trapped hexagonal pattern with nested honeycomb vortex lattice, stationary solutions in isotropic saturable medium. The soliton constant k = -0.8 and peak intensity I max ≃ 0.42 in (a), and k = -0.4 and I max ≃ 3.58 in high saturation regime in (b). (c) Experimentally observed hexagonal vortex lattice of a period 22μm: left - nonlinear output for bias 1.3kV, middle - magnified bottom right part of the lattice interfering with a reference beam to identify the position of the vortices (marked by arrows), right - plane wave launched at the edge of the Brillouin zone and modulated by the induced index lattice.

Equations (8)

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

i E z + 2 E x 2 + 2 E y 2 + n ( I ) E = 0 ,
n ( I ) = σΓ φ x ,
2 φ + φ In ( 1 + I ) = x In ( 1 + I ) ,
kU + 2 U x 2 + 2 U y 2 + ΓU φ x = 0 .
U lin X Y = A sin X sin Y .
U 3 X Y = A sin ( 2 Y 3 ) sin ( Y 3 + X ) sin ( Y 3 X ) ,
U vs x y = A ( sin x sin y + i cos x cos y ) .
U vh x y = A [ exp ( ix ) + exp ( ix 2 + i 3 y 2 ) + exp ( ix 2 i 3 y 2 ) ] .

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