Abstract

Abstract

We study spatiotemporal solitons at the edge of a semi-infinite binary array of optical waveguides and, in particular, predict theoretically the existence of a novel type of surface soliton, the surface gap light bullets. We analyze the stability properties of these solitons in the framework of the continuous-discrete model of an array of two types of optical waveguides.

©2007 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Stable discrete surface light bullets

Dumitru Mihalache, Dumitru Mazilu, Falk Lederer, and Yuri S. Kivshar
Opt. Express 15(2) 589-595 (2007)

Observation of discrete gap solitons in binary waveguide arrays

Roberto Morandotti, Daniel Mandelik, Yaron Silberberg, J. Stewart Aitchison, Marc Sorel, Demetrios N. Christodoulides, Andrey A. Sukhorukov, and Yuri S. Kivshar
Opt. Lett. 29(24) 2890-2892 (2004)

Discrete surface solitons in semi-infinite binary waveguide arrays

Mario I. Molina, Ivan L. Garanovich, Andrey A. Sukhorukov, and Yuri S. Kivshar
Opt. Lett. 31(15) 2332-2334 (2006)

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. S. Suntsov, K.G. Makris, D.N. Christodoulides, G.I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
    [Crossref] [PubMed]
  3. Ya.V. Kartashov, V.V. Vysloukh, and L. Torner, “Surface gap solitons,” Phys. Rev. Lett. 96, 073901 (2006).
    [Crossref] [PubMed]
  4. 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]
  5. D. Mihalache, D. Mazilu, F. Lederer, and Yu.S. Kivshar, “Stable discrete surface light bullets,” Opt. Express 15, 589–595 (2007); http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-2-589
    [Crossref] [PubMed]
  6. Yu. S. Kivshar and G. P. Agrawal, “Optical Solitons: From Fibers to Photonic Crystals” (Academic Press, San Diego, 2003), 540 pp.
  7. B.A. Malomed, D. Mihalache, F. Wise, and L. Torner, “Spatiotemporal optical solitons,” J. Opt. B: Quantum Semiclass. Opt. 7, R53–R72 (2005).
    [Crossref]
  8. 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]
  9. 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]
  10. 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]
  11. 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).
  12. Z. Xu, Ya.V. Kartashov, L.C. Crasovan, D. Mihalache, and L. Torner, “Spatiotemporal discrete multicolor solitons,” Phys. Rev. E 70, 066618 (2004).
  13. 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]
  14. A.A. Sukhorukov and Yu.S. Kivshar, “Discrete gap solitons in modulated waveguide arrays,” Opt. Lett. 27, 2112–2114 (2002).
    [Crossref]
  15. A.A. Sukhorukov and Yu.S. Kivshar, “Generation and stability of discrete gap solitons,” Opt. Lett. 28, 2345–2347 (2003).
    [Crossref] [PubMed]
  16. Y.J. He, W.H. Chen, H.Z. Wang, and B.A. Malomed, “Surface superlattice gap solitons,” Opt. Lett. 32, 1390–1392 (2007).
    [Crossref] [PubMed]
  17. R. Morandotti, D. Mandelik, Y. Silberberg, J.S. Aitchison, M. Sorel, D.N. Christodoulides, A.A. Sukhorukov, and Yu.S. Kivshar, “Observation of discrete gap solitons in binary waveguide arrays,” Opt. Lett. 29, 2890–2892 (2004).
    [Crossref]
  18. G. Dahlquist and Å. Björk, “Numerical Methods,” (Prentice Hall, Englewood Cliffs, 1974).
  19. J. M. Ortega and W. C. Rheinboldt, “Iterative Solution of Nonlinear Equations in Several Variables,” (Academic Press, New York, 1970), p. 182.

2007 (2)

2006 (4)

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]

S. Suntsov, K.G. Makris, D.N. Christodoulides, G.I. Stegeman, A. Haché, 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]

2005 (2)

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

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]

2004 (2)

2003 (1)

2002 (1)

1997 (1)

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).

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)

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]

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]

Aceves, A.B.

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).

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]

Agrawal, G. P.

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

Aitchison, J.S.

Björk, Å.

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

Chen, W.H.

Christodoulides, D.N.

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).

Dahlquist, G.

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

De Angelis, C.

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).

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]

Hache, A.

Haché, A.

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

He, Y.J.

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).

Kivshar, Yu. S.

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

Kivshar, Yu.S.

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]

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]

Lederer, F.

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. Haché, 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.

Mandelik, D.

Mazilu, D.

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, and Yu.S. Kivshar, “Stable discrete surface light bullets,” Opt. Express 15, 589–595 (2007); http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-2-589
[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).

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]

Morandotti, R.

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

R. Morandotti, D. Mandelik, Y. Silberberg, J.S. Aitchison, M. Sorel, D.N. Christodoulides, A.A. Sukhorukov, and Yu.S. Kivshar, “Observation of discrete gap solitons in binary waveguide arrays,” Opt. Lett. 29, 2890–2892 (2004).
[Crossref]

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. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, “Observation of discrete surface solitons,” Phys. Rev. Lett. 96, 063901 (2006).
[Crossref] [PubMed]

Santagiustina, M.

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).

Silberberg, Y.

Sorel, M.

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

R. Morandotti, D. Mandelik, Y. Silberberg, J.S. Aitchison, M. Sorel, D.N. Christodoulides, A.A. Sukhorukov, and Yu.S. Kivshar, “Observation of discrete gap solitons in binary waveguide arrays,” Opt. Lett. 29, 2890–2892 (2004).
[Crossref]

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. Haché, 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]

Sukhorukov, A.A.

Suntsov, S.

S. Suntsov, K.G. Makris, D.N. Christodoulides, G.I. Stegeman, A. Haché, 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]

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).

Turitsyn, S.K.

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]

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]

Vicencio, R.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]

Vysloukh, V.V.

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

Wang, H.Z.

Wise, F.

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

Xu, Z.

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

Yang, H.

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

J. Opt. B: Quantum Semiclass. Opt. (1)

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

J. Opt. Soc. Am. (1)

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).

Opt. Express (1)

Opt. Lett. (7)

Phys. Rev. (1)

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

Phys. Rev. Lett. (5)

S. Suntsov, K.G. Makris, D.N. Christodoulides, G.I. Stegeman, A. Haché, 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]

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, 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]

Other (3)

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

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

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

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. Schematic structure of a binary array of weakly coupled optical waveguides truncated at (a) wide and (b) narrow waveguides, respectively.
Fig. 2.
Fig. 2. Examples of unstaggered spatiotemporal solitons corresponding to points a-d in Fig. 3, for β=4: (a) stable and (b) unstable discrete surface light bullets in the array truncated at the wide waveguide; (c) stable and (d) unstable surface solitons in the array truncated at the narrow waveguide.
Fig. 3.
Fig. 3. Families of discrete unstaggered surface light bullets in the binary array truncated at the wide waveguide (first curve from the left in both panels), and in the waveguide array truncated at the narrow waveguide (second curve from the left in both panels). (a) Power vs. propagation constant. Points (a)–(d) mark the modes shown in Figs. 2(a–d), respectively. (b) Hamiltonian vs. power.
Fig. 4.
Fig. 4. (a,c) Stable (for β=-0.45 and β=0.45, respectively) and (b.d) unstable (for β=-0.1 and β=0.1, respectively) nonlinear spatiotemporal surface gap solitons corresponding to the arrays truncated at the narrow and wide waveguides, respectively.
Fig. 5.
Fig. 5. Power vs. propagation constant diagram for the surface gap light bullets (spatiotemporal nonlinear Tamm states) corresponding to (a) an array truncated at a narrow waveguide, and (b) an array truncated at a wide waveguide. Points (a–d) correspond to the soliton profiles shown in Figs. 4(a–d), respectively. (c,d) Real part of the dominant instability eigenvalue vs. propagation constant for the corresponding case (a,b) shown above.

Equations (3)

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

i E n z γ n 2 E n t 2 + ( E n + 1 + E n 1 ) + ( ρ n + σ n E n 2 ) E n = 0 ,
P ( β ) = n = 0 + E n ( β ) 2 dt ,
H = n = 0 + { E n E n 1 2 ( 2 + ρ n ) E n 2 γ n E n t 2 1 2 σ n E n 4 } dt ,

Metrics