Abstract

We predict the existence of vortex solitons supported by the surface between two optical lattices imprinted in Kerr-type nonlinear media. We find that such surface vortex solitons can exhibit strongly noncanonical profiles, and that their salient properties are dictated by the location of the vortex core relative to the surface. A refractive index modulation forming the optical lattices at both sides of the interface yields complete stability of the vortex solitons in wide domains of their existence, thus introducing the first known example of stable topological solitons supported by a surface.

© 2006 Optical Society of America

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    [CrossRef]

2006

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

2005

R. Carretero-Gonzalez, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, "Three-dimensional nonlinear lattices: from oblique vortices and octupoles to discrete diamonds and vortex cubes," Phys. Rev. Lett. 94, 203901 (2005).
[CrossRef] [PubMed]

T. J. Alexander, E. A. Ostrovskaya, A. A. Sukhorukov, and Y. S. Kivshar, "Three-dimensional matter-wave vortices in optical lattices," Phys. Rev. A 72, 043603 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable ring-profile vortex solitons in Bessel optical lattices," Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton topology versus discrete symmetry in optical lattices," Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

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

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, "Composite vortex-ring solitons in Bessel photonic lattices," J. Opt. Soc. Am. B 22, 1366 (2005).
[CrossRef]

K. G. Makris, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, "Discrete surface solitons," Opt. Lett. 30, 2466 (2005).
[CrossRef] [PubMed]

J. Hudock, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, "Vector discrete nonlinear surface waves," Opt. Express 13, 7720 (2005).
[CrossRef] [PubMed]

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

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

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, "Multicolor vortex solitons in two-dimensional photonic lattices," Phys. Rev. E 71, 016616 (2005).
[CrossRef]

A. Ferrando, M. Zacares, and M. A. Garcia-March, "Vorticity cutoff in nonlinear photonic crystals," Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef] [PubMed]

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonzalez, B. A. Malomed, and A. R. Bishop, "Discrete solitons and vortices on anisotropic lattices," Phys. Rev. E 72, 046613 (2005).
[CrossRef]

2004

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, "Asymmetric vortex solitons in nonlinear periodic lattices," Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

A. Ferrando, M. Zacares, P. Fernandez de Cordoba, D. Binosi, J. A. Monsoriu, "Vortex solitons in photonic crystal fibers," Opt. Express. 12, 817 (2004).
[CrossRef] [PubMed]

P. G. Kevrekidis, B. A. Malomed, Z. Chen, and D. J. Frantzeskakis, "Stable higher-order vortices and quasi-vortices in the discrete nonlinear Schrödinger equation," Phys. Rev. E 70, 056612 (2004).
[CrossRef]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Obser-vation 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]

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]

E. A. Ostrovskaya and Y. S. Kivshar, "Matter-wave gap vortices in optical lattices," Phys. Rev. Lett. 93, 160405 (2004).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

2003

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

J. Yang and Z. Musslimani, "Fundamental and vortex solitons in a two-dimensional optical lattice" Opt. Lett. 28, 2094 (2003).
[CrossRef] [PubMed]

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

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[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]

2002

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

2001

B. A. Malomed and P. G. Kevrekidis, "Discrete vortex solitons," Phys. Rev. E 64, 026601 (2001).
[CrossRef]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, "Observation of the dynamical inversion of the topological charge of an optical vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

G. Molina-Terriza, E. M. Wright, L. Torner "Propagation and control of noncanonical optical vortices", Opt. Lett. 26, 163 (2001).
[CrossRef]

1998

M. Johansson, S. Aubry, Y. B. Gaididei, P. L. Christiansen, and K. O. Rasmussen, "Dynamics of breathers in discrete nonlinear Schrödinger models," Physica D 119, 115 (1998).
[CrossRef]

1997

S. Aubry, "Breathers in nonlinear lattices: existence, linear stability and quantization," Physica D 103, 201 (1997).
[CrossRef]

1995

1989

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).

1988

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953 (1988).
[CrossRef]

1979

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, "Optical bistability at a nonlinear interface," Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

1978

P. Yeh, A, Yariv, and A. Y. Cho, "Optical surface waves in periodic layered media," Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

1976

A. E. Kaplan, "Hysteresis reflection and refraction at the nonlinear interface-a new class of effects in nonlinear optics," JETP Lett. 24, 114 (1976).

Alexander, T. J.

T. J. Alexander, E. A. Ostrovskaya, A. A. Sukhorukov, and Y. S. Kivshar, "Three-dimensional matter-wave vortices in optical lattices," Phys. Rev. A 72, 043603 (2005).
[CrossRef]

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, "Asymmetric vortex solitons in nonlinear periodic lattices," Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

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

Aubry, S.

M. Johansson, S. Aubry, Y. B. Gaididei, P. L. Christiansen, and K. O. Rasmussen, "Dynamics of breathers in discrete nonlinear Schrödinger models," Physica D 119, 115 (1998).
[CrossRef]

S. Aubry, "Breathers in nonlinear lattices: existence, linear stability and quantization," Physica D 103, 201 (1997).
[CrossRef]

Baizakov, B. B.

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

Bang, O.

Bartal, G.

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29, 2049 (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]

Bertolotti, M.

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).

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]

Binosi, D.

A. Ferrando, M. Zacares, P. Fernandez de Cordoba, D. Binosi, J. A. Monsoriu, "Vortex solitons in photonic crystal fibers," Opt. Express. 12, 817 (2004).
[CrossRef] [PubMed]

Bishop, A. R.

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonzalez, B. A. Malomed, and A. R. Bishop, "Discrete solitons and vortices on anisotropic lattices," Phys. Rev. E 72, 046613 (2005).
[CrossRef]

Briedis, D.

Carmon, T.

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

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

Carretero-Gonzalez, R.

R. Carretero-Gonzalez, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, "Three-dimensional nonlinear lattices: from oblique vortices and octupoles to discrete diamonds and vortex cubes," Phys. Rev. Lett. 94, 203901 (2005).
[CrossRef] [PubMed]

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonzalez, B. A. Malomed, and A. R. Bishop, "Discrete solitons and vortices on anisotropic lattices," Phys. Rev. E 72, 046613 (2005).
[CrossRef]

Chen, Z.

P. G. Kevrekidis, B. A. Malomed, Z. Chen, and D. J. Frantzeskakis, "Stable higher-order vortices and quasi-vortices in the discrete nonlinear Schrödinger equation," Phys. Rev. E 70, 056612 (2004).
[CrossRef]

D. N. Neshev, T. J. Alexander, E. A. Ostrovskaya, Y. S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, "Obser-vation of discrete vortex solitons in optically induced photonic lattices," Phys. Rev. Lett. 92, 123903 (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]

Christiansen, P. L.

M. Johansson, S. Aubry, Y. B. Gaididei, P. L. Christiansen, and K. O. Rasmussen, "Dynamics of breathers in discrete nonlinear Schrödinger models," Physica D 119, 115 (1998).
[CrossRef]

Christodoulides, D. N.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

J. Hudock, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, "Vector discrete nonlinear surface waves," Opt. Express 13, 7720 (2005).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, "Discrete surface solitons," Opt. Lett. 30, 2466 (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, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[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 lattices," Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Cohen, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and T. Carmon, "Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (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]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

Crasovan, L.-C.

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, "Multicolor vortex solitons in two-dimensional photonic lattices," Phys. Rev. E 71, 016616 (2005).
[CrossRef]

Cronin Golomb, M.

Edmundson, D.

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]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

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

Egorov, A. A.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton topology versus discrete symmetry in optical lattices," Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

Eugenieva, E. D.

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]

Fernandez de Cordoba, P.

A. Ferrando, M. Zacares, P. Fernandez de Cordoba, D. Binosi, J. A. Monsoriu, "Vortex solitons in photonic crystal fibers," Opt. Express. 12, 817 (2004).
[CrossRef] [PubMed]

Ferrando, A.

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton topology versus discrete symmetry in optical lattices," Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

A. Ferrando, M. Zacares, and M. A. Garcia-March, "Vorticity cutoff in nonlinear photonic crystals," Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef] [PubMed]

A. Ferrando, M. Zacares, P. Fernandez de Cordoba, D. Binosi, J. A. Monsoriu, "Vortex solitons in photonic crystal fibers," Opt. Express. 12, 817 (2004).
[CrossRef] [PubMed]

Finlayson, N.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953 (1988).
[CrossRef]

Fleischer, J. W.

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29, 2049 (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]

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]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

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

Frantzeskakis, D. J.

R. Carretero-Gonzalez, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, "Three-dimensional nonlinear lattices: from oblique vortices and octupoles to discrete diamonds and vortex cubes," Phys. Rev. Lett. 94, 203901 (2005).
[CrossRef] [PubMed]

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonzalez, B. A. Malomed, and A. R. Bishop, "Discrete solitons and vortices on anisotropic lattices," Phys. Rev. E 72, 046613 (2005).
[CrossRef]

P. G. Kevrekidis, B. A. Malomed, Z. Chen, and D. J. Frantzeskakis, "Stable higher-order vortices and quasi-vortices in the discrete nonlinear Schrödinger equation," Phys. Rev. E 70, 056612 (2004).
[CrossRef]

Gaididei, Y. B.

M. Johansson, S. Aubry, Y. B. Gaididei, P. L. Christiansen, and K. O. Rasmussen, "Dynamics of breathers in discrete nonlinear Schrödinger models," Physica D 119, 115 (1998).
[CrossRef]

Garcia-March, M. A.

A. Ferrando, M. Zacares, and M. A. Garcia-March, "Vorticity cutoff in nonlinear photonic crystals," Phys. Rev. Lett. 95, 043901 (2005).
[CrossRef] [PubMed]

Hache, A.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Hermann, J. P.

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, "Optical bistability at a nonlinear interface," Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

Hudock, J.

J. Hudock, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, "Vector discrete nonlinear surface waves," Opt. Express 13, 7720 (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]

Johansson, M.

M. Johansson, S. Aubry, Y. B. Gaididei, P. L. Christiansen, and K. O. Rasmussen, "Dynamics of breathers in discrete nonlinear Schrödinger models," Physica D 119, 115 (1998).
[CrossRef]

Kaplan, A. E.

A. E. Kaplan, "Hysteresis reflection and refraction at the nonlinear interface-a new class of effects in nonlinear optics," JETP Lett. 24, 114 (1976).

Kartashov, Y. V.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, "Composite vortex-ring solitons in Bessel photonic lattices," J. Opt. Soc. Am. B 22, 1366 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable ring-profile vortex solitons in Bessel optical lattices," Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, "Multicolor vortex solitons in two-dimensional photonic lattices," Phys. Rev. E 71, 016616 (2005).
[CrossRef]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton topology versus discrete symmetry in optical lattices," Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

Kevrekidis, P. G.

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonzalez, B. A. Malomed, and A. R. Bishop, "Discrete solitons and vortices on anisotropic lattices," Phys. Rev. E 72, 046613 (2005).
[CrossRef]

R. Carretero-Gonzalez, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, "Three-dimensional nonlinear lattices: from oblique vortices and octupoles to discrete diamonds and vortex cubes," Phys. Rev. Lett. 94, 203901 (2005).
[CrossRef] [PubMed]

P. G. Kevrekidis, B. A. Malomed, Z. Chen, and D. J. Frantzeskakis, "Stable higher-order vortices and quasi-vortices in the discrete nonlinear Schrödinger equation," Phys. Rev. E 70, 056612 (2004).
[CrossRef]

B. A. Malomed and P. G. Kevrekidis, "Discrete vortex solitons," Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Kivshar, Y.

Kivshar, Y. S.

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

T. J. Alexander, E. A. Ostrovskaya, A. A. Sukhorukov, and Y. S. Kivshar, "Three-dimensional matter-wave vortices in optical lattices," Phys. Rev. A 72, 043603 (2005).
[CrossRef]

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, "Asymmetric vortex solitons in nonlinear periodic lattices," Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

E. A. Ostrovskaya and Y. S. Kivshar, "Matter-wave gap vortices in optical lattices," Phys. Rev. Lett. 93, 160405 (2004).
[CrossRef] [PubMed]

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

Krolikowski, W.

Makasyuk, I.

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

Makris, K. G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, "Discrete surface solitons," Opt. Lett. 30, 2466 (2005).
[CrossRef] [PubMed]

Malomed, B. A.

R. Carretero-Gonzalez, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, "Three-dimensional nonlinear lattices: from oblique vortices and octupoles to discrete diamonds and vortex cubes," Phys. Rev. Lett. 94, 203901 (2005).
[CrossRef] [PubMed]

P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-Gonzalez, B. A. Malomed, and A. R. Bishop, "Discrete solitons and vortices on anisotropic lattices," Phys. Rev. E 72, 046613 (2005).
[CrossRef]

P. G. Kevrekidis, B. A. Malomed, Z. Chen, and D. J. Frantzeskakis, "Stable higher-order vortices and quasi-vortices in the discrete nonlinear Schrödinger equation," Phys. Rev. E 70, 056612 (2004).
[CrossRef]

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

B. A. Malomed and P. G. Kevrekidis, "Discrete vortex solitons," Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Maloney, P. J.

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, "Optical bistability at a nonlinear interface," Appl. Phys. Lett. 35, 846 (1979).
[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 observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29, 2049 (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]

Martin, H.

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]

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

Mihalache, D.

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, "Multicolor vortex solitons in two-dimensional photonic lattices," Phys. Rev. E 71, 016616 (2005).
[CrossRef]

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).

Molina-Terriza, G.

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, "Observation of the dynamical inversion of the topological charge of an optical vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

G. Molina-Terriza, E. M. Wright, L. Torner "Propagation and control of noncanonical optical vortices", Opt. Lett. 26, 163 (2001).
[CrossRef]

Monsoriu, J. A.

A. Ferrando, M. Zacares, P. Fernandez de Cordoba, D. Binosi, J. A. Monsoriu, "Vortex solitons in photonic crystal fibers," Opt. Express. 12, 817 (2004).
[CrossRef] [PubMed]

Morandotti, R.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Musslimani, Z.

Neshev, D.

Neshev, D. N.

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

Ostrovskaya, E.

Ostrovskaya, E. A.

T. J. Alexander, E. A. Ostrovskaya, A. A. Sukhorukov, and Y. S. Kivshar, "Three-dimensional matter-wave vortices in optical lattices," Phys. Rev. A 72, 043603 (2005).
[CrossRef]

E. A. Ostrovskaya and Y. S. Kivshar, "Matter-wave gap vortices in optical lattices," Phys. Rev. Lett. 93, 160405 (2004).
[CrossRef] [PubMed]

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

Petersen, D. E.

Rasmussen, K. O.

M. Johansson, S. Aubry, Y. B. Gaididei, P. L. Christiansen, and K. O. Rasmussen, "Dynamics of breathers in discrete nonlinear Schrödinger models," Physica D 119, 115 (1998).
[CrossRef]

Recolons, J.

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, "Observation of the dynamical inversion of the topological charge of an optical vortex," Phys. Rev. Lett. 87, 023902 (2001).
[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 observation of coherent elliptic solitons and of vortex-ring solitons," Phys. Rev. Lett. 95, 213904 (2005).
[CrossRef] [PubMed]

Salamo, G.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Salerno, M.

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

Sears, S.

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

Seaton, C. T.

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953 (1988).
[CrossRef]

Segev, M.

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

O. Manela, O. Cohen, G. Bartal, J. W. Fleischer, and M. Segev, "Two-dimensional higher-band vortex lattice solitons," Opt. Lett. 29, 2049 (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]

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]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically induced real time waveguide arrays," Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef] [PubMed]

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

Sibilia, C.

D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989).

Smith, P. W.

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, "Optical bistability at a nonlinear interface," Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

Sorel, M.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Stegeman, G. I.

S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Hache, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, "Observation of discrete surface solitons," Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

J. Hudock, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, "Vector discrete nonlinear surface waves," Opt. Express 13, 7720 (2005).
[CrossRef] [PubMed]

K. G. Makris, S. Suntsov, D. N. Christodoulides, and G. I. Stegeman, "Discrete surface solitons," Opt. Lett. 30, 2466 (2005).
[CrossRef] [PubMed]

G. I. Stegeman, E. M. Wright, N. Finlayson, R. Zanoni, C. T. Seaton, "Third order nonlinear integrated optics," J. Lightwave Technol. 6, 953 (1988).
[CrossRef]

Sukhorukov, A. A.

T. J. Alexander, E. A. Ostrovskaya, A. A. Sukhorukov, and Y. S. Kivshar, "Three-dimensional matter-wave vortices in optical lattices," Phys. Rev. A 72, 043603 (2005).
[CrossRef]

T. J. Alexander, A. A. Sukhorukov, and Y. S. Kivshar, "Asymmetric vortex solitons in nonlinear periodic lattices," Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

Suntsov, S.

Tomlinson, W. J.

P. W. Smith, J. P. Hermann, W. J. Tomlinson, and P. J. Maloney, "Optical bistability at a nonlinear interface," Appl. Phys. Lett. 35, 846 (1979).
[CrossRef]

Torner, L.

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Surface gap solitons," Phys. Rev. Lett. 96, 073901 (2006).
[CrossRef] [PubMed]

Y. V. Kartashov, L. Torner, and V. A. Vysloukh, "Composite vortex-ring solitons in Bessel photonic lattices," J. Opt. Soc. Am. B 22, 1366 (2005).
[CrossRef]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Stable ring-profile vortex solitons in Bessel optical lattices," Phys. Rev. Lett. 94, 043902 (2005).
[CrossRef] [PubMed]

Z. Xu, Y. V. Kartashov, L.-C. Crasovan, D. Mihalache, and L. Torner, "Multicolor vortex solitons in two-dimensional photonic lattices," Phys. Rev. E 71, 016616 (2005).
[CrossRef]

Y. V. Kartashov, A. Ferrando, A. A. Egorov, and L. Torner, "Soliton topology versus discrete symmetry in optical lattices," Phys. Rev. Lett. 95, 123902 (2005).
[CrossRef] [PubMed]

G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. M. Wright, "Observation of the dynamical inversion of the topological charge of an optical vortex," Phys. Rev. Lett. 87, 023902 (2001).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Field modulus distributions for vortex surface solitons at b = 8, p = 4.5, S = 0.05, and (a) δp = 1, (b) δp = 4. (c) Lattice profile at p = 4.5 and δp = 1. Field modulus distributions for the highly asymmetric vortex solitons at b = 3, p = 4, S = 0.2, and (d) δp = 0.8, (e) δp = 1.3, (f) δp = 0.6. In all cases Ω = 4. Vertical dashed lines indicate the location of the interface.

Fig. 2.
Fig. 2.

(a) Phase distribution for surface vortex soliton depicted in Fig. 1(b). (b) Same but for a similar canonical vortex soliton supported by a uniform medium.

Fig. 3.
Fig. 3.

(a) Domains of existence of surface vortex solitons at the (δp,b) plane. (b) Energy flow versus propagation constant at p = 4.5. Points marked by circles correspond to solitons shown in Figs. 1(a) and 1(b). (c) Critical value of δp versus lattice depth. In all cases Ω = 4, S = 0.05.

Fig. 4.
Fig. 4.

Real part of perturbation growth rate versus propagation constant for p = 4.5 at δp = 0.5 (a) and δp = 1 (b). (c) Stability and instability domains for surface vortex solitons on (δp, b) plane at p = 4.5. Vortex solitons exist in the region between upper and lower solid lines. They are stable in the region above dashed line and oscillatory unstable in the region between dashed and lower solid lines. In all cases Ω = 4, S = 0.05.

Fig. 5.
Fig. 5.

Propagation dynamics of surface vortex solitons with b = 8 (a) and b = 6.65 (b) at p = 4.5 and δp = 4 in the presence of white input noise with the variance σnoise2 = 0.01. Vertical dashed lines indicate interface position. In all cases Ω = 4, S = 0.05.

Equations (5)

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

i q ξ = 1 2 ( 2 q η 2 + 2 q ζ 2 ) q q 2 1 + S q 2 R ( η , ζ ) q .
U = q 2 dηdζ .
1 2 ( 2 η 2 + 2 ζ 2 ) w r , i b w r , i + w r , i ( w r 2 + w i 2 ) 1 + S ( w r 2 + w i 2 ) + R w r , i = 0 ,
U r , i = w r , i 2 dηdζ
( 3 w r , i 2 + w i , r 2 + S ( w r 2 + w i 2 ) 2 [ 1 + S ( w r 2 + w i 2 ) ] 2 u r , i + 2 w r w i [ 1 + S ( w r 2 + w i 2 ) ] 2 u i , r ) + 1 2 ( 2 η 2 + 2 ζ 2 ) u r , i b u r , i + R u r , i = ± ξ u i , r

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