Abstract

We analyze spatiotemporal light localization near the edge of a semi-infinite array of weakly coupled nonlinear optical waveguides and demonstrate the existence of a novel class of continuous-discrete spatiotemporal solitons, the so-called discrete surface light bullets. We show that their properties are strongly affected by the presence of the surface. To this end the crossover between surface and quasi-bulk bullets is studied by analyzing the families of solitons propagating at different distances from the edge of the waveguide array.

©2007 Optical Society of America

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  1. G. Borstel and H. J. Falge, in: Electromagnetic SurfaceModes (ed. A. D. Boardman)219–248 (Wiley, Chichester, 1982).
  2. P. Yeh, A. Yariv, and A.Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32,104–105 (1978).(1978).
    [Crossref]
  3. D. Mihalache, M. Bertolotti, and C. Sibilia, “Nonlinear wave propagation in planar structures,” Prog. Opt. 27,229–313 (1989).
  4. A.D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, “Third-order nonlinear electromagnetic TE and TM guided waves,” in: Nonlinear Surface Electromagnetic Phenomena,V.M. Agranovich, A.A. Maradudin, H.-E. Ponath, and G.I. Stegeman, eds. (Elsevier Science Publishers B.V., New York, 1991), pp.73–287.
  5. W.J. Tomlinson, “Surface wave at a nonlinear interface,” Opt. Lett. 5,323–325 (1980)
    [Crossref] [PubMed]
  6. V.K. Fedyanin and D. Mihalache, “P-polarized nonlinear surface polaritons in layered structures,” Z. Phys. B 47,167 (1982).
    [Crossref]
  7. G.I. Stegeman, C.T. Seaton, J. Chilwell, and S.D. Smith, “Nonlinear waves guided by thin films,” Appl. Phys. Lett. 44,830–832 (1984).
    [Crossref]
  8. N.N. Akhmediev, V.I. Korneyev, and Y.V. Kuzmenko, “Excitation of nonlinear surface-waves by Gaussian light beams,” Zh. Eksp. Teor. Fiz. 88,107 (1985).
  9. F. Lederer and D. Mihalache, “An additional kind of nonlinear s-polarized surface plasmon-polaritons,” Solid State Commun. 59,151 (1986).
    [Crossref]
  10. K.G. Makris, S. Suntsov, D.N. Christodoulides, G.I. stegeman, and A. Hache, “Discrete surface solitons,” Opt. Lett. 30,2466–2668 (2005).
    [Crossref] [PubMed]
  11. S. Suntsov, K.G. Makris, D.N. Christodoulides, G.I. Stegeman, A. Naché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96,063901 (2006).
    [Crossref] [PubMed]
  12. Ya.V. Kartashov, V.V. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96,073901 (2006).
    [Crossref] [PubMed]
  13. C.R. Rosberg, D.N. Neshev, W. Krolikowski, A. Mitchell, R.A. Vicencio, M.I. Molina, and Yu.S. Kivshar, “Observation of surface gap solitons,” Phys. Rev. Lett. 97,083901 (2006).
    [Crossref] [PubMed]
  14. I.E. Tamm, “A possible kind of electron binding on crystal surfaces,” Z. Phys. 76,849–850 (1932).
    [Crossref]
  15. Y. Silberberg, “Collapse of optical pulses,” Opt. Lett. 15,1282–1284 (1990).
    [Crossref] [PubMed]
  16. B.A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons”, J. Opt. B: Quantum Semiclass. Opt. 7, R53-R72 (2005).
    [Crossref]
  17. A.B. Aceves, C. De Angelis, A.M. Rubenchik, and S.K. Turitsyn, “Multidimensional solitons in fiber arrays,” Opt. Lett. 19,329–331 (1994).
    [Crossref] [PubMed]
  18. E.W. Laedke, K.H. Spatschek, and S.K. Turitsyn, “Stability of discrete solitons and quasicollapse to intrinsically localized modes,”Phys. Rev. Lett. 73,1055–1058 (1994).
    [Crossref] [PubMed]
  19. A.B. Aceves, G.G. Luther, C. De Angelis, A.M. Rubenchik, and S.K. Turitsyn, “Energy localization in nonlinear fiber arrays: Collapse-effect compresor,” Phys. Rev. Lett. 75,73–76 (1995).
    [Crossref] [PubMed]
  20. A.B. Aceves, M. Santagiustina, and C. De Angelis, “Analytical study of nonlinear-optical pulse dynamics in arrays of linearly coupled waveguides”, J. Opt. Soc. Am. B 14,1807–1815 (1997).
    [Crossref]
  21. Z. Xu, Ya.V. Kartashov, L.C. Crasovan, D. Mihalache, and L. Torner, “Spatiotemporal discrete multicolor solitons,” Phys. Rev. E 70,066618 (2004).
    [Crossref]
  22. N.C. Panoiu, R.M. Osgood, and B.A. Malomed, “Semidiscrete composite solitons in arrays of quadratically nonlinear waveguides,” Opt. Lett. 31,1097–1099 (2006).
    [Crossref] [PubMed]
  23. Yu. S. Kivshar and G. P. Agrawal, “Optical Solitons: From Fibers to Photonic Crystals” (Academic Press, San Diego, 2003).
  24. G. Dahlquist and Å. Björk, “Numerical Methods,” (Prentice Hall, Englewood Cliffs, 1974).
  25. M.I. Molina, R.A. Vicencio, and Yu.S. Kivshar, “Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays,” Opt. Lett. 31,1693–1695 (2006).
    [Crossref] [PubMed]
  26. J. M. Ortega and W. C. Rheinboldt, “Iterative Solution of Nonlinear Equations in Several Variables,” (Academic Press, New York, 1970), p. 182.

2006 (5)

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

Ya.V. Kartashov, V.V. 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 Yu.S. Kivshar, “Observation of surface gap solitons,” Phys. Rev. Lett. 97,083901 (2006).
[Crossref] [PubMed]

N.C. Panoiu, R.M. Osgood, and B.A. Malomed, “Semidiscrete composite solitons in arrays of quadratically nonlinear waveguides,” Opt. Lett. 31,1097–1099 (2006).
[Crossref] [PubMed]

M.I. Molina, R.A. Vicencio, and Yu.S. Kivshar, “Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays,” Opt. Lett. 31,1693–1695 (2006).
[Crossref] [PubMed]

2005 (2)

K.G. Makris, S. Suntsov, D.N. Christodoulides, G.I. stegeman, and A. Hache, “Discrete surface solitons,” Opt. Lett. 30,2466–2668 (2005).
[Crossref] [PubMed]

B.A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons”, J. Opt. B: Quantum Semiclass. Opt. 7, R53-R72 (2005).
[Crossref]

2004 (1)

Z. Xu, Ya.V. Kartashov, L.C. Crasovan, D. Mihalache, and L. Torner, “Spatiotemporal discrete multicolor solitons,” Phys. Rev. E 70,066618 (2004).
[Crossref]

1997 (1)

1995 (1)

A.B. Aceves, G.G. Luther, C. De Angelis, A.M. Rubenchik, and S.K. Turitsyn, “Energy localization in nonlinear fiber arrays: Collapse-effect compresor,” Phys. Rev. Lett. 75,73–76 (1995).
[Crossref] [PubMed]

1994 (2)

E.W. Laedke, K.H. Spatschek, and S.K. Turitsyn, “Stability of discrete solitons and quasicollapse to intrinsically localized modes,”Phys. Rev. Lett. 73,1055–1058 (1994).
[Crossref] [PubMed]

A.B. Aceves, C. De Angelis, A.M. Rubenchik, and S.K. Turitsyn, “Multidimensional solitons in fiber arrays,” Opt. Lett. 19,329–331 (1994).
[Crossref] [PubMed]

1990 (1)

1989 (1)

D. Mihalache, M. Bertolotti, and C. Sibilia, “Nonlinear wave propagation in planar structures,” Prog. Opt. 27,229–313 (1989).

1986 (1)

F. Lederer and D. Mihalache, “An additional kind of nonlinear s-polarized surface plasmon-polaritons,” Solid State Commun. 59,151 (1986).
[Crossref]

1985 (1)

N.N. Akhmediev, V.I. Korneyev, and Y.V. Kuzmenko, “Excitation of nonlinear surface-waves by Gaussian light beams,” Zh. Eksp. Teor. Fiz. 88,107 (1985).

1984 (1)

G.I. Stegeman, C.T. Seaton, J. Chilwell, and S.D. Smith, “Nonlinear waves guided by thin films,” Appl. Phys. Lett. 44,830–832 (1984).
[Crossref]

1982 (1)

V.K. Fedyanin and D. Mihalache, “P-polarized nonlinear surface polaritons in layered structures,” Z. Phys. B 47,167 (1982).
[Crossref]

1980 (1)

1978 (1)

P. Yeh, A. Yariv, and A.Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32,104–105 (1978).(1978).
[Crossref]

1974 (1)

G. Dahlquist and Å. Björk, “Numerical Methods,” (Prentice Hall, Englewood Cliffs, 1974).

1970 (1)

J. M. Ortega and W. C. Rheinboldt, “Iterative Solution of Nonlinear Equations in Several Variables,” (Academic Press, New York, 1970), p. 182.

1932 (1)

I.E. Tamm, “A possible kind of electron binding on crystal surfaces,” Z. Phys. 76,849–850 (1932).
[Crossref]

Aceves, A.B.

Agrawal, G. P.

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

Akhmediev, N.N.

N.N. Akhmediev, V.I. Korneyev, and Y.V. Kuzmenko, “Excitation of nonlinear surface-waves by Gaussian light beams,” Zh. Eksp. Teor. Fiz. 88,107 (1985).

Angelis, C. De

Bertolotti, M.

D. Mihalache, M. Bertolotti, and C. Sibilia, “Nonlinear wave propagation in planar structures,” Prog. Opt. 27,229–313 (1989).

Björk, Å.

G. Dahlquist and Å. Björk, “Numerical Methods,” (Prentice Hall, Englewood Cliffs, 1974).

Boardman, A.D.

A.D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, “Third-order nonlinear electromagnetic TE and TM guided waves,” in: Nonlinear Surface Electromagnetic Phenomena,V.M. Agranovich, A.A. Maradudin, H.-E. Ponath, and G.I. Stegeman, eds. (Elsevier Science Publishers B.V., New York, 1991), pp.73–287.

Borstel, G.

G. Borstel and H. J. Falge, in: Electromagnetic SurfaceModes (ed. A. D. Boardman)219–248 (Wiley, Chichester, 1982).

Chilwell, J.

G.I. Stegeman, C.T. Seaton, J. Chilwell, and S.D. Smith, “Nonlinear waves guided by thin films,” Appl. Phys. Lett. 44,830–832 (1984).
[Crossref]

Cho, A.Y.

P. Yeh, A. Yariv, and A.Y. Cho, “Optical surface waves in periodic layered media,” Appl. Phys. Lett. 32,104–105 (1978).(1978).
[Crossref]

Christodoulides, D.N.

S. Suntsov, K.G. Makris, D.N. Christodoulides, G.I. Stegeman, A. Naché, 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, G.I. stegeman, and A. Hache, “Discrete surface solitons,” Opt. Lett. 30,2466–2668 (2005).
[Crossref] [PubMed]

Crasovan, L.C.

Z. Xu, Ya.V. Kartashov, L.C. Crasovan, D. Mihalache, and L. Torner, “Spatiotemporal discrete multicolor solitons,” Phys. Rev. E 70,066618 (2004).
[Crossref]

Dahlquist, G.

G. Dahlquist and Å. Björk, “Numerical Methods,” (Prentice Hall, Englewood Cliffs, 1974).

Egan, P.

A.D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, “Third-order nonlinear electromagnetic TE and TM guided waves,” in: Nonlinear Surface Electromagnetic Phenomena,V.M. Agranovich, A.A. Maradudin, H.-E. Ponath, and G.I. Stegeman, eds. (Elsevier Science Publishers B.V., New York, 1991), pp.73–287.

Falge, H. J.

G. Borstel and H. J. Falge, in: Electromagnetic SurfaceModes (ed. A. D. Boardman)219–248 (Wiley, Chichester, 1982).

Fedyanin, V.K.

V.K. Fedyanin and D. Mihalache, “P-polarized nonlinear surface polaritons in layered structures,” Z. Phys. B 47,167 (1982).
[Crossref]

Hache, A.

Kartashov, Ya.V.

Ya.V. Kartashov, V.V. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96,073901 (2006).
[Crossref] [PubMed]

Z. Xu, Ya.V. Kartashov, L.C. Crasovan, D. Mihalache, and L. Torner, “Spatiotemporal discrete multicolor solitons,” Phys. Rev. E 70,066618 (2004).
[Crossref]

Kivshar, Yu. S.

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

Kivshar, Yu.S.

C.R. Rosberg, D.N. Neshev, W. Krolikowski, A. Mitchell, R.A. Vicencio, M.I. Molina, and Yu.S. Kivshar, “Observation of surface gap solitons,” Phys. Rev. Lett. 97,083901 (2006).
[Crossref] [PubMed]

M.I. Molina, R.A. Vicencio, and Yu.S. Kivshar, “Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays,” Opt. Lett. 31,1693–1695 (2006).
[Crossref] [PubMed]

Korneyev, V.I.

N.N. Akhmediev, V.I. Korneyev, and Y.V. Kuzmenko, “Excitation of nonlinear surface-waves by Gaussian light beams,” Zh. Eksp. Teor. Fiz. 88,107 (1985).

Krolikowski, W.

C.R. Rosberg, D.N. Neshev, W. Krolikowski, A. Mitchell, R.A. Vicencio, M.I. Molina, and Yu.S. Kivshar, “Observation of surface gap solitons,” Phys. Rev. Lett. 97,083901 (2006).
[Crossref] [PubMed]

Kuzmenko, Y.V.

N.N. Akhmediev, V.I. Korneyev, and Y.V. Kuzmenko, “Excitation of nonlinear surface-waves by Gaussian light beams,” Zh. Eksp. Teor. Fiz. 88,107 (1985).

Laedke, E.W.

E.W. Laedke, K.H. Spatschek, and S.K. Turitsyn, “Stability of discrete solitons and quasicollapse to intrinsically localized modes,”Phys. Rev. Lett. 73,1055–1058 (1994).
[Crossref] [PubMed]

Langbein, U.

A.D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, “Third-order nonlinear electromagnetic TE and TM guided waves,” in: Nonlinear Surface Electromagnetic Phenomena,V.M. Agranovich, A.A. Maradudin, H.-E. Ponath, and G.I. Stegeman, eds. (Elsevier Science Publishers B.V., New York, 1991), pp.73–287.

Lederer, F.

F. Lederer and D. Mihalache, “An additional kind of nonlinear s-polarized surface plasmon-polaritons,” Solid State Commun. 59,151 (1986).
[Crossref]

A.D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, “Third-order nonlinear electromagnetic TE and TM guided waves,” in: Nonlinear Surface Electromagnetic Phenomena,V.M. Agranovich, A.A. Maradudin, H.-E. Ponath, and G.I. Stegeman, eds. (Elsevier Science Publishers B.V., New York, 1991), pp.73–287.

Luther, G.G.

A.B. Aceves, G.G. Luther, C. De Angelis, A.M. Rubenchik, and S.K. Turitsyn, “Energy localization in nonlinear fiber arrays: Collapse-effect compresor,” Phys. Rev. Lett. 75,73–76 (1995).
[Crossref] [PubMed]

Makris, K.G.

S. Suntsov, K.G. Makris, D.N. Christodoulides, G.I. Stegeman, A. Naché, 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, G.I. stegeman, and A. Hache, “Discrete surface solitons,” Opt. Lett. 30,2466–2668 (2005).
[Crossref] [PubMed]

Malomed, B.A.

N.C. Panoiu, R.M. Osgood, and B.A. Malomed, “Semidiscrete composite solitons in arrays of quadratically nonlinear waveguides,” Opt. Lett. 31,1097–1099 (2006).
[Crossref] [PubMed]

B.A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons”, J. Opt. B: Quantum Semiclass. Opt. 7, R53-R72 (2005).
[Crossref]

Mihalache, D.

B.A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons”, J. Opt. B: Quantum Semiclass. Opt. 7, R53-R72 (2005).
[Crossref]

Z. Xu, Ya.V. Kartashov, L.C. Crasovan, D. Mihalache, and L. Torner, “Spatiotemporal discrete multicolor solitons,” Phys. Rev. E 70,066618 (2004).
[Crossref]

D. Mihalache, M. Bertolotti, and C. Sibilia, “Nonlinear wave propagation in planar structures,” Prog. Opt. 27,229–313 (1989).

F. Lederer and D. Mihalache, “An additional kind of nonlinear s-polarized surface plasmon-polaritons,” Solid State Commun. 59,151 (1986).
[Crossref]

V.K. Fedyanin and D. Mihalache, “P-polarized nonlinear surface polaritons in layered structures,” Z. Phys. B 47,167 (1982).
[Crossref]

A.D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, “Third-order nonlinear electromagnetic TE and TM guided waves,” in: Nonlinear Surface Electromagnetic Phenomena,V.M. Agranovich, A.A. Maradudin, H.-E. Ponath, and G.I. Stegeman, eds. (Elsevier Science Publishers B.V., New York, 1991), pp.73–287.

Mitchell, A.

C.R. Rosberg, D.N. Neshev, W. Krolikowski, A. Mitchell, R.A. Vicencio, M.I. Molina, and Yu.S. Kivshar, “Observation of surface gap solitons,” 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 Yu.S. Kivshar, “Observation of surface gap solitons,” Phys. Rev. Lett. 97,083901 (2006).
[Crossref] [PubMed]

M.I. Molina, R.A. Vicencio, and Yu.S. Kivshar, “Discrete solitons and nonlinear surface modes in semi-infinite waveguide arrays,” Opt. Lett. 31,1693–1695 (2006).
[Crossref] [PubMed]

Morandotti, R.

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

Naché, A.

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

Neshev, D.N.

C.R. Rosberg, D.N. Neshev, W. Krolikowski, A. Mitchell, R.A. Vicencio, M.I. Molina, and Yu.S. Kivshar, “Observation of surface gap solitons,” Phys. Rev. Lett. 97,083901 (2006).
[Crossref] [PubMed]

Ortega, J. M.

J. M. Ortega and W. C. Rheinboldt, “Iterative Solution of Nonlinear Equations in Several Variables,” (Academic Press, New York, 1970), p. 182.

Osgood, R.M.

Panoiu, N.C.

Rheinboldt, W. C.

J. M. Ortega and W. C. Rheinboldt, “Iterative Solution of Nonlinear Equations in Several Variables,” (Academic Press, New York, 1970), p. 182.

Rosberg, C.R.

C.R. Rosberg, D.N. Neshev, W. Krolikowski, A. Mitchell, R.A. Vicencio, M.I. Molina, and Yu.S. Kivshar, “Observation of surface gap solitons,” Phys. Rev. Lett. 97,083901 (2006).
[Crossref] [PubMed]

Rubenchik, A.M.

A.B. Aceves, G.G. Luther, C. De Angelis, A.M. Rubenchik, and S.K. Turitsyn, “Energy localization in nonlinear fiber arrays: Collapse-effect compresor,” Phys. Rev. Lett. 75,73–76 (1995).
[Crossref] [PubMed]

A.B. Aceves, C. De Angelis, A.M. Rubenchik, and S.K. Turitsyn, “Multidimensional solitons in fiber arrays,” Opt. Lett. 19,329–331 (1994).
[Crossref] [PubMed]

Salamo, G.

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

Santagiustina, M.

Seaton, C.T.

G.I. Stegeman, C.T. Seaton, J. Chilwell, and S.D. Smith, “Nonlinear waves guided by thin films,” Appl. Phys. Lett. 44,830–832 (1984).
[Crossref]

Sibilia, C.

D. Mihalache, M. Bertolotti, and C. Sibilia, “Nonlinear wave propagation in planar structures,” Prog. Opt. 27,229–313 (1989).

Silberberg, Y.

Smith, S.D.

G.I. Stegeman, C.T. Seaton, J. Chilwell, and S.D. Smith, “Nonlinear waves guided by thin films,” Appl. Phys. Lett. 44,830–832 (1984).
[Crossref]

Sorel, M.

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

Spatschek, K.H.

E.W. Laedke, K.H. Spatschek, and S.K. Turitsyn, “Stability of discrete solitons and quasicollapse to intrinsically localized modes,”Phys. Rev. Lett. 73,1055–1058 (1994).
[Crossref] [PubMed]

Stegeman, G.I.

S. Suntsov, K.G. Makris, D.N. Christodoulides, G.I. Stegeman, A. Naché, 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, G.I. stegeman, and A. Hache, “Discrete surface solitons,” Opt. Lett. 30,2466–2668 (2005).
[Crossref] [PubMed]

G.I. Stegeman, C.T. Seaton, J. Chilwell, and S.D. Smith, “Nonlinear waves guided by thin films,” Appl. Phys. Lett. 44,830–832 (1984).
[Crossref]

Suntsov, S.

S. Suntsov, K.G. Makris, D.N. Christodoulides, G.I. Stegeman, A. Naché, 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, G.I. stegeman, and A. Hache, “Discrete surface solitons,” Opt. Lett. 30,2466–2668 (2005).
[Crossref] [PubMed]

Tamm, I.E.

I.E. Tamm, “A possible kind of electron binding on crystal surfaces,” Z. Phys. 76,849–850 (1932).
[Crossref]

Tomlinson, W.J.

Torner, L.

Ya.V. Kartashov, V.V. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96,073901 (2006).
[Crossref] [PubMed]

B.A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons”, J. Opt. B: Quantum Semiclass. Opt. 7, R53-R72 (2005).
[Crossref]

Z. Xu, Ya.V. Kartashov, L.C. Crasovan, D. Mihalache, and L. Torner, “Spatiotemporal discrete multicolor solitons,” Phys. Rev. E 70,066618 (2004).
[Crossref]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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B.A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons”, J. Opt. B: Quantum Semiclass. Opt. 7, R53-R72 (2005).
[Crossref]

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Z. Xu, Ya.V. Kartashov, L.C. Crasovan, D. Mihalache, and L. Torner, “Spatiotemporal discrete multicolor solitons,” Phys. Rev. E 70,066618 (2004).
[Crossref]

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[Crossref]

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[Crossref]

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[Crossref]

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[Crossref] [PubMed]

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[Crossref] [PubMed]

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

Ya.V. Kartashov, V.V. 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 Yu.S. Kivshar, “Observation of surface gap solitons,” Phys. Rev. Lett. 97,083901 (2006).
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Figures (4)

Fig. 1.
Fig. 1. Examples of stable spatiotemporal surface solitons localized at distances of (a) d=0, (b) d=1, and (c) d=2 from the edge of the waveguide array (at β=3.5), and unstable modes centered at distances of (d) d=0, (e) d=1, and (f) d=2 (at β= 2.5).

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Fig. 2.
Fig. 2. Families of the spatiotemporal surface solitons. (a) Normalized power vs. propagation constant β for the surface solitons located at the distances d=0, d=1, and d=2 from the edge of the array. (b) Hamiltonian vs. power for the localized surface modes. Stable branches are plotted by black lines whereas unstable branches- by red lines; the blue lines show the corresponding dependencies for the case of odd spatiotemporal solitons in the infinite waveguide array.

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Fig. 3.
Fig. 3. Instability-driven evolution of unstable solitons corresponding to the upper branches in Fig. 2 for β=3. (a,b) Reshaping of the unstable d=0 soliton after the propagation for z=1200 into a stable d=0 soliton. (c,d) Hopping of the unstable d=1 soliton (z=0) into the neighboring site and the generation of a stable d=2 soliton at z=1200.

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Fig. 4.
Fig. 4. Evolution of the soliton amplitude (a) and Hamiltonian (b) versus propagation distance for the tho instability scenarios shown in Fig. 3. Red lines: the reshaping of the unstable d=0 solitons into the stable d=0 soliton; blue lines: the flipping of the unstable d=1 soliton into a stable d=2 one.

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Equations (6)

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i ∂ E 1 ∂ z − γ ∂ 2 E 1 ∂ t 2 + E 2 + σ ∣ E 1 ∣ 2 E 1 = 0 ,
i d E n dz − γ ∂ 2 E n ∂ t 2 + ( E n + 1 + E n − 1 ) + σ ∣ E n ∣ 2 E n = 0 , n ≥ 2 ,
d 2 E 1 d τ 2 − β E 1 + E 2 + ∣ E 1 ∣ 2 E 1 = 0 ,
d 2 E n d τ 2 − β E n + ( E n + 1 + E n − 1 ) + ∣ E n ∣ 2 E n = 0 , n ≥ 2 .
P ( β ) = ∑ j = 1 ∞ ∫ ∞ + ∞ ∣ E j ( β ) ∣ 2 dτ ,
H = ∑ j = 1 ∞ ∫ − ∞ + ∞ ( ∣ E j − E j − 1 ∣ 2 − 2 ∣ E j ∣ 2 + ∣ ∂ E j ∂ τ ∣ 2 − 1 2 ∣ E j ∣ 4 ) dτ .

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