Abstract

We predict theoretically that surface of an optical lattice imprinted in defocusing nonlinear media can support shock, or kink waves. Such new surface waves contain a modulationally stable pedestal and are strongly localized at the edge of the optical lattice due to Bragg-type reflection. The kink steepness and localization degree can be controlled by the lattice depth. We found two types of kinks, which exhibit distinct stability properties for each finite gap in the lattice spectrum. Our findings open the way to experimental observation of optical surface kink waves.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
  26. E. Smirnov, M. Stepic, C. E. Ruter, D. Kip, and V. Shandarov, "Observation of staggered surface solitary waves in one-dimensional waveguide arrays," Opt. Lett. 31, 2338 (2006).
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  30. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  31. F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffrac-tion and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express. 13, 4314 (2005).
    [CrossRef] [PubMed]

2006

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]

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

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

E. Smirnov, M. Stepic, C. E. Ruter, D. Kip, and V. Shandarov, "Observation of staggered surface solitary waves in one-dimensional waveguide arrays," Opt. Lett. 31, 2338 (2006).
[CrossRef] [PubMed]

2005

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

F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffrac-tion and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express. 13, 4314 (2005).
[CrossRef] [PubMed]

2004

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch-wave filtering and Bragg scattering in optically induced lattices," Phys. Rev. Lett. 92, 093901 (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]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton trains in photonic lattices," Opt. Express 12, 2831 (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. 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]

B. Freedman, T. Carmon, M. I. Carvalho, M. Segev, and D. N. Christodoulides, "Observation of locked optical kink-antikink spatial shock waves," Phys. Rev. Lett. 91, 133902 (2003).
[CrossRef] [PubMed]

2000

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

M. I. Carvalho, A. G. Grandpierre, D. N. Christodoulides, and M. Segev, "Optical spatial shock waves in photo-refractive media," Phys. Rev. E 62, 8657 (2000).
[CrossRef]

1999

1998

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

1997

V. A. Vysloukh, V. Kutuzov, V. M. Petnikova, and V. V. Shuvalov, "Formation of spatial solitons and spatial shock waves in photorefractive crystals," Sov. Phys. JETP 84, 388 (1997).
[CrossRef]

1994

Y. Chen and J. Atai, "Asymmetric dark modes in symmetric nonlinear waveguides," J. Lightwave Tech. 12, 855 (1994).
[CrossRef]

1993

Y. S. Kivshar and S. K. Turitsyn, "Optical double layers," Phys. Rev. A 47, R3502 (1993).
[CrossRef] [PubMed]

1992

G. P. Agrawal and C. HeadleyIII, "Kink solitons and optical shocks in dispersive nonlinear media," Phys. Rev. A 46, 1573 (1992).
[CrossRef] [PubMed]

1991

1989

D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," Prog. Opt. 27, 229 (1989).

1985

Agrawal, G. P.

G. P. Agrawal and C. HeadleyIII, "Kink solitons and optical shocks in dispersive nonlinear media," Phys. Rev. A 46, 1573 (1992).
[CrossRef] [PubMed]

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Andersen, D. R.

Atai, J.

Y. Chen and J. Atai, "Asymmetric dark modes in symmetric nonlinear waveguides," J. Lightwave Tech. 12, 855 (1994).
[CrossRef]

Bertolotti, M.

D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," 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]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Carmon, T.

B. Freedman, T. Carmon, M. I. Carvalho, M. Segev, and D. N. Christodoulides, "Observation of locked optical kink-antikink spatial shock waves," Phys. Rev. Lett. 91, 133902 (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]

Carvalho, M. I.

B. Freedman, T. Carmon, M. I. Carvalho, M. Segev, and D. N. Christodoulides, "Observation of locked optical kink-antikink spatial shock waves," Phys. Rev. Lett. 91, 133902 (2003).
[CrossRef] [PubMed]

M. I. Carvalho, A. G. Grandpierre, D. N. Christodoulides, and M. Segev, "Optical spatial shock waves in photo-refractive media," Phys. Rev. E 62, 8657 (2000).
[CrossRef]

Chen, F.

F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffrac-tion and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express. 13, 4314 (2005).
[CrossRef] [PubMed]

Chen, Y.

Y. Chen and J. Atai, "Asymmetric dark modes in symmetric nonlinear waveguides," J. Lightwave Tech. 12, 855 (1994).
[CrossRef]

Chen, Z.

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]

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]

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

B. Freedman, T. Carmon, M. I. Carvalho, M. Segev, and D. N. Christodoulides, "Observation of locked optical kink-antikink spatial shock waves," Phys. Rev. Lett. 91, 133902 (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]

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]

M. I. Carvalho, A. G. Grandpierre, D. N. Christodoulides, and M. Segev, "Optical spatial shock waves in photo-refractive media," Phys. Rev. E 62, 8657 (2000).
[CrossRef]

Darmanyan, S.

Efremidis, N. K.

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]

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

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]

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]

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]

Freedman, B.

B. Freedman, T. Carmon, M. I. Carvalho, M. Segev, and D. N. Christodoulides, "Observation of locked optical kink-antikink spatial shock waves," Phys. Rev. Lett. 91, 133902 (2003).
[CrossRef] [PubMed]

Grandpierre, A. G.

M. I. Carvalho, A. G. Grandpierre, D. N. Christodoulides, and M. Segev, "Optical spatial shock waves in photo-refractive media," Phys. Rev. E 62, 8657 (2000).
[CrossRef]

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]

Headley, C.

G. P. Agrawal and C. HeadleyIII, "Kink solitons and optical shocks in dispersive nonlinear media," Phys. Rev. A 46, 1573 (1992).
[CrossRef] [PubMed]

Johnson, A. M.

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, V. A. Vysloukh, and L. Torner, "Soliton trains in photonic lattices," Opt. Express 12, 2831 (2004).
[CrossRef] [PubMed]

Kip, D.

E. Smirnov, M. Stepic, C. E. Ruter, D. Kip, and V. Shandarov, "Observation of staggered surface solitary waves in one-dimensional waveguide arrays," Opt. Lett. 31, 2338 (2006).
[CrossRef] [PubMed]

F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffrac-tion and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express. 13, 4314 (2005).
[CrossRef] [PubMed]

Kivshar, Y.

Kivshar, Y. S.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

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

Y. S. Kivshar and S. K. Turitsyn, "Optical double layers," Phys. Rev. A 47, R3502 (1993).
[CrossRef] [PubMed]

Kobyakov, A.

Krolikowski, W.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

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

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

Kutuzov, V.

V. A. Vysloukh, V. Kutuzov, V. M. Petnikova, and V. V. Shuvalov, "Formation of spatial solitons and spatial shock waves in photorefractive crystals," Sov. Phys. JETP 84, 388 (1997).
[CrossRef]

Lederer, F.

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]

Manela, O.

F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffrac-tion and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express. 13, 4314 (2005).
[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]

Mihalache, D.

D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," Prog. Opt. 27, 229 (1989).

Mitchell, A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Molina, M. I.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
[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]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Neshev, D.

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

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

Neshev, D. N.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Ostrovskaya, E.

Pertsch, T.

Petnikova, V. M.

V. A. Vysloukh, V. Kutuzov, V. M. Petnikova, and V. V. Shuvalov, "Formation of spatial solitons and spatial shock waves in photorefractive crystals," Sov. Phys. JETP 84, 388 (1997).
[CrossRef]

Rosberg, C. R.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Runde, D.

F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffrac-tion and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express. 13, 4314 (2005).
[CrossRef] [PubMed]

Ruter, C. E.

E. Smirnov, M. Stepic, C. E. Ruter, D. Kip, and V. Shandarov, "Observation of staggered surface solitary waves in one-dimensional waveguide arrays," Opt. Lett. 31, 2338 (2006).
[CrossRef] [PubMed]

F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffrac-tion and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express. 13, 4314 (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]

Segev, M.

F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffrac-tion and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express. 13, 4314 (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]

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]

B. Freedman, T. Carmon, M. I. Carvalho, M. Segev, and D. N. Christodoulides, "Observation of locked optical kink-antikink spatial shock waves," Phys. Rev. Lett. 91, 133902 (2003).
[CrossRef] [PubMed]

M. I. Carvalho, A. G. Grandpierre, D. N. Christodoulides, and M. Segev, "Optical spatial shock waves in photo-refractive media," Phys. Rev. E 62, 8657 (2000).
[CrossRef]

Shandarov, V.

E. Smirnov, M. Stepic, C. E. Ruter, D. Kip, and V. Shandarov, "Observation of staggered surface solitary waves in one-dimensional waveguide arrays," Opt. Lett. 31, 2338 (2006).
[CrossRef] [PubMed]

F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffrac-tion and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express. 13, 4314 (2005).
[CrossRef] [PubMed]

Shuvalov, V. V.

V. A. Vysloukh, V. Kutuzov, V. M. Petnikova, and V. V. Shuvalov, "Formation of spatial solitons and spatial shock waves in photorefractive crystals," Sov. Phys. JETP 84, 388 (1997).
[CrossRef]

Sibilia, C.

D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," Prog. Opt. 27, 229 (1989).

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Skinner, S. R.

Smirnov, E.

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]

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

Stepic, M.

E. Smirnov, M. Stepic, C. E. Ruter, D. Kip, and V. Shandarov, "Observation of staggered surface solitary waves in one-dimensional waveguide arrays," Opt. Lett. 31, 2338 (2006).
[CrossRef] [PubMed]

F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffrac-tion and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express. 13, 4314 (2005).
[CrossRef] [PubMed]

Stolen, R. H.

Sukhorukov, A. A.

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

Suntsov, S.

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]

Tomlinson, W. J.

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, V. A. Vysloukh, and L. Torner, "Soliton trains in photonic lattices," Opt. Express 12, 2831 (2004).
[CrossRef] [PubMed]

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Y. S. Kivshar and S. K. Turitsyn, "Optical double layers," Phys. Rev. A 47, R3502 (1993).
[CrossRef] [PubMed]

Vicencio, R. A.

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

Vysloukh, V. A.

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

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, "Soliton trains in photonic lattices," Opt. Express 12, 2831 (2004).
[CrossRef] [PubMed]

V. A. Vysloukh, V. Kutuzov, V. M. Petnikova, and V. V. Shuvalov, "Formation of spatial solitons and spatial shock waves in photorefractive crystals," Sov. Phys. JETP 84, 388 (1997).
[CrossRef]

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]

Yang, H.

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. Lightwave Tech.

Y. Chen and J. Atai, "Asymmetric dark modes in symmetric nonlinear waveguides," J. Lightwave Tech. 12, 855 (1994).
[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. Express

Opt. Express.

F. Chen, M. Stepic, C. E. Ruter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffrac-tion and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express. 13, 4314 (2005).
[CrossRef] [PubMed]

Opt. Lett.

Phys. Rev. A

G. P. Agrawal and C. HeadleyIII, "Kink solitons and optical shocks in dispersive nonlinear media," Phys. Rev. A 46, 1573 (1992).
[CrossRef] [PubMed]

Y. S. Kivshar and S. K. Turitsyn, "Optical double layers," Phys. Rev. A 47, R3502 (1993).
[CrossRef] [PubMed]

Phys. Rev. E

M. I. Carvalho, A. G. Grandpierre, D. N. Christodoulides, and M. Segev, "Optical spatial shock waves in photo-refractive media," Phys. Rev. E 62, 8657 (2000).
[CrossRef]

Phys. Rev. Lett.

B. Freedman, T. Carmon, M. I. Carvalho, M. Segev, and D. N. Christodoulides, "Observation of locked optical kink-antikink spatial shock waves," Phys. Rev. Lett. 91, 133902 (2003).
[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]

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]

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

C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Y. S. Kivshar, "Observation of surface gap solitons in semi-infinite waveguide arrays," Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

A. A. Sukhorukov, D. Neshev, W. Krolikowski, and Y. S. Kivshar, "Nonlinear Bloch-wave filtering and Bragg scattering in optically induced lattices," Phys. Rev. Lett. 92, 093901 (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]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Prog. Opt.

D. Mihalache, M. Bertolotti, and C. Sibilia, "Nonlinear wave propagation in planar structures," Prog. Opt. 27, 229 (1989).

Sov. Phys. JETP

V. A. Vysloukh, V. Kutuzov, V. M. Petnikova, and V. V. Shuvalov, "Formation of spatial solitons and spatial shock waves in photorefractive crystals," Sov. Phys. JETP 84, 388 (1997).
[CrossRef]

Other

H. E. Ponath and G. I. Stegeman Eds., Nonlinear surface electromagnetic phenomena, (North Holland, Amster-dam, 1991).

A. A. Maradudin, in Optical and Acoustic Waves in Solids - Modern Topics, M. Borissov Ed., (World Scientific, Singapore, 1983).

F. V. Shugaev and L. S. Shtemenko, Propagation and reflection of shock waves (World Scientific, Singapore, 1998).
[CrossRef]

M. A. Liberman and A. L. Velikovich, Physics of shock waves in gases and plasmas (Springer-Verlag, Heidel-berg, 1986).

G. P. Agrawal, Nonlinear fiber optics (Academic Press, New York, 1995).

S. A. Akhmanov, V. A. Vysloukh, and A. S. Chirkin, Optics of femtosecond laser pulses (American Institute of Physics, New York, 1992).

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Figures (3)

Fig. 1.
Fig. 1.

(a) Bang-gap structure of periodic lattice. Bands are shown gray, gaps are shown white. Domains of existence of “out-of-phase” (b) and “in-phase” (c) shock surface waves. (d) Reduced energy versus propagation constant for “out-of-phase” shock waves. In all cases Ω=4.

Fig. 2.
Fig. 2.

Profiles of surface shock waves at (a) b=-0.85, (b) b=-0.45, (c) b=-0.1, (d) b=-0.5, (e) b=-0.05, and (f) b =-0.8. Lattice depth p=9 for panel (f), while in all other panels p=2. White regions correspond to R(η)≤1, while in gray regions R(η)>1. In all cases Ω=4.

Fig. 3.
Fig. 3.

Propagation of perturbed (a) “out-of-phase” shock surface wave at b=-0.2, p=3, and (b) “in-phase” wave at b=-0.1, p=3. In all cases Ω=4.

Equations (3)

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

i q ξ = 1 2 2 q η 2 + q q 2 p R ( η ) q .
b w = 1 2 ( d 2 w d η 2 + 2 i k d w d η k 2 w ) + p R w
U r = [ w ( η ) b 1 2 H ( η ) ] 2 d η

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