Abstract

We analyze spatiotemporal light localization at the interface separating two different periodic photonic lattices. We demonstrate the existence of a novel class of continuous–discrete spatiotemporal solitons propagating along the interface, including hybrid staggered–unstaggered discrete light bullets with tails belonging to spectral gaps of different types.

© 2007 Optical Society of America

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References

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  1. G. Borstel and H. J. Falge, in Electromagnetic Surface Modes, A.D.Boardmann, ed. (Wiley, 1982), pp. 219-248.
  2. P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
    [CrossRef]
  3. See, e.g., D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989), and references therein.
  4. A. D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, in Nonlinear Surface Electromagnetic Phenomena, V.M.Agranovich, A.A.Maradudin, H.-E.Ponath, and G.I.Stegeman, eds. (Elsevier, 1991), pp. 73-287.
  5. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Haché, Opt. Lett. 30, 2466 (2005).
    [CrossRef] [PubMed]
  6. S. Suntsov, K. G. Makris, D. N. Christodoulides, G. I. Stegeman, A. Haché, R. Morandotti, H. Yang, G. Salamo, and M. Sorel, Phys. Rev. Lett. 96, 063901 (2006).
    [CrossRef] [PubMed]
  7. Ya. V. Kartashov, V. V. Vysloukh, and L. Torner, Phys. Rev. Lett. 96, 073901 (2006).
    [CrossRef] [PubMed]
  8. C. R. Rosberg, D. N. Neshev, W. Krolikowski, A. Mitchell, R. A. Vicencio, M. I. Molina, and Yu. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
    [CrossRef] [PubMed]
  9. K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (2006).
    [CrossRef] [PubMed]
  10. K. Motzek, A. A. Sukhorukov, and Yu. S. Kivshar, Opt. Express 14, 9873 (2006).
    [CrossRef] [PubMed]
  11. M. I. Molina, and Yu. S. Kivshar, Phys. Lett. A 362, 280 (2007).
    [CrossRef]
  12. D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, Opt. Express 15, 589 (2007).
    [CrossRef] [PubMed]
  13. B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B 7, R53 (2005).
    [CrossRef]
  14. A. B. Aceves, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, Opt. Lett. 19, 329 (1994).
    [CrossRef] [PubMed]
  15. E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn, Phys. Rev. Lett. 73, 1055 (1994).
    [CrossRef] [PubMed]
  16. E. W. Laedke, K. H. Spatschek, S. K. Turitsyn, and V. K. Mezentsev, Phys. Rev. E 52, 5549 (1995).
    [CrossRef]
  17. A. B. Aceves, G. G. Luther, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, Phys. Rev. Lett. 75, 73 (1995).
    [CrossRef] [PubMed]
  18. Z. Xu, Ya. V. Kartashov, L. C. Crasovan, D. Mihalache, and L. Torner, Phys. Rev. E 70, 066618 (2004).
    [CrossRef]
  19. N. C. Panoiu, R. M. Osgood, Jr., and B. A. Malomed, Opt. Lett. 31, 1097 (2006).
    [CrossRef] [PubMed]
  20. A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 97, 233901 (2006).
    [CrossRef]
  21. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).
  22. G. Dahlquist and Å. Björk, Numerical Methods (Prentice-Hall, 1974).

2007 (2)

2006 (7)

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

Ya. V. Kartashov, V. V. Vysloukh, and L. Torner, 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, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. I. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (2006).
[CrossRef] [PubMed]

K. Motzek, A. A. Sukhorukov, and Yu. S. Kivshar, Opt. Express 14, 9873 (2006).
[CrossRef] [PubMed]

N. C. Panoiu, R. M. Osgood, Jr., and B. A. Malomed, Opt. Lett. 31, 1097 (2006).
[CrossRef] [PubMed]

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 97, 233901 (2006).
[CrossRef]

2005 (2)

2004 (1)

Z. Xu, Ya. V. Kartashov, L. C. Crasovan, D. Mihalache, and L. Torner, Phys. Rev. E 70, 066618 (2004).
[CrossRef]

1995 (2)

E. W. Laedke, K. H. Spatschek, S. K. Turitsyn, and V. K. Mezentsev, Phys. Rev. E 52, 5549 (1995).
[CrossRef]

A. B. Aceves, G. G. Luther, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, Phys. Rev. Lett. 75, 73 (1995).
[CrossRef] [PubMed]

1994 (2)

1989 (1)

See, e.g., D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989), and references therein.

1978 (1)

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

Appl. Phys. Lett. (1)

P. Yeh, A. Yariv, and A. Y. Cho, Appl. Phys. Lett. 32, 104 (1978).
[CrossRef]

J. Opt. B (1)

B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B 7, R53 (2005).
[CrossRef]

Opt. Express (2)

Opt. Lett. (4)

Phys. Lett. A (1)

M. I. Molina, and Yu. S. Kivshar, Phys. Lett. A 362, 280 (2007).
[CrossRef]

Phys. Rev. E (2)

Z. Xu, Ya. V. Kartashov, L. C. Crasovan, D. Mihalache, and L. Torner, Phys. Rev. E 70, 066618 (2004).
[CrossRef]

E. W. Laedke, K. H. Spatschek, S. K. Turitsyn, and V. K. Mezentsev, Phys. Rev. E 52, 5549 (1995).
[CrossRef]

Phys. Rev. Lett. (6)

A. B. Aceves, G. G. Luther, C. De Angelis, A. M. Rubenchik, and S. K. Turitsyn, Phys. Rev. Lett. 75, 73 (1995).
[CrossRef] [PubMed]

E. W. Laedke, K. H. Spatschek, and S. K. Turitsyn, Phys. Rev. Lett. 73, 1055 (1994).
[CrossRef] [PubMed]

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

Ya. V. Kartashov, V. V. Vysloukh, and L. Torner, 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, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 97, 233901 (2006).
[CrossRef]

Prog. Opt. (1)

See, e.g., D. Mihalache, M. Bertolotti, and C. Sibilia, Prog. Opt. 27, 229 (1989), and references therein.

Other (4)

A. D. Boardman, P. Egan, F. Lederer, U. Langbein, and D. Mihalache, in Nonlinear Surface Electromagnetic Phenomena, V.M.Agranovich, A.A.Maradudin, H.-E.Ponath, and G.I.Stegeman, eds. (Elsevier, 1991), pp. 73-287.

G. Borstel and H. J. Falge, in Electromagnetic Surface Modes, A.D.Boardmann, ed. (Wiley, 1982), pp. 219-248.

Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: from Fibers to Photonic Crystals (Academic, 2003).

G. Dahlquist and Å. Björk, Numerical Methods (Prentice-Hall, 1974).

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Figures (5)

Fig. 1
Fig. 1

Examples of (a) stable (at β = 3.7 ) and (b), (c) unstable (at β = 3.2 and β = 3.7 , respectively) unstaggered spatiotemporal interface light bullets.

Fig. 2
Fig. 2

Families of unstaggered spatiotemporal interface solitons. (a) Power versus propagation constant. Points a–c mark the modes shown in Figs. 1a, 1b, 1c, respectively. (b) Hamiltonian versus power.

Fig. 3
Fig. 3

Hopping of the unstable (at β = 3.2 ) soliton centered at n = 0 into the neighboring site n = 1 .

Fig. 4
Fig. 4

Examples of (a) stable (at β = 0.2 , P = 2.74 ) and (b)–(d) unstable [(b) β = 0.3 , P = 14.4 , (c) β = 0.6 , P = 16.66 , and (d) β = 0.3 , P = 6.75 ] hybrid staggered–unstaggered light bullets.

Fig. 5
Fig. 5

(a) Power versus propagation constant for the hybrid solitons. Points a–d correspond to the solitons shown in Figs. 4a, 4b, 4c, 4d, respectively. (b) Real part of the dominant instability eigenvalue versus propagation constant.

Equations (3)

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i d E n d z γ n 2 E n t 2 + ( E n + 1 + E n 1 ) + f n ( E n 2 ) E n = 0 ,
P ( β ) = n + E n ( β ) 2 d t
H = n + { E n E n 1 2 ( 2 + ϵ n ) E n 2 γ n E n τ 2 1 2 σ n E n 4 } d t .

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