Abstract

We analyze spatiotemporal light localization in truncated two-dimensional photonic lattices and demonstrate the existence of two-dimensional surface light bullets localized in the lattice corners or the edges. We study the families of the spatiotemporal surface solitons and their properties such as bistability and compare them with the modes located deep inside the photonic lattice.

© 2007 Optical Society of America

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  1. K. G. Makris, J. Hudock, D. N. Christodoulides, G. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (2006).
    [CrossRef] [PubMed]
  2. R. A. Vicencio, S. Flach, M. I. Molina, and Yu. S. Kivshar, Phys. Lett. A 364, 274 (2007).
    [CrossRef]
  3. H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Franzeskakis, Phys. Rev. E 75, 056605 (2007).
    [CrossRef]
  4. X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
    [CrossRef] [PubMed]
  5. A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
    [CrossRef]
  6. K. G. Makris, S. Suntsov, D. N. Christodoulides, G. I. Stegeman, and A. Haché, Opt. Lett. 30, 2466 (2005).
    [CrossRef] [PubMed]
  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]
  8. M. Molina, R. Vicencio, and Yu. S. Kivshar, Opt. Lett. 31, 1693 (2006).
    [CrossRef] [PubMed]
  9. D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, Opt. Express 15, 589 (2007).
    [CrossRef] [PubMed]
  10. See the review paper: B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005).
    [CrossRef]
  11. E. W. Laedke, K. H. Spatschek, S. K. Turitsyn, and V. K. Mezentsev, Phys. Rev. E 52, 5549 (1995).
    [CrossRef]

2007 (5)

R. A. Vicencio, S. Flach, M. I. Molina, and Yu. S. Kivshar, Phys. Lett. A 364, 274 (2007).
[CrossRef]

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Franzeskakis, Phys. Rev. E 75, 056605 (2007).
[CrossRef]

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, Opt. Express 15, 589 (2007).
[CrossRef] [PubMed]

2006 (3)

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]

M. Molina, R. Vicencio, and Yu. S. Kivshar, Opt. Lett. 31, 1693 (2006).
[CrossRef] [PubMed]

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

2005 (2)

See the review paper: B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005).
[CrossRef]

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

1995 (1)

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

Bezryadina, A.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Carretero-González, R.

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Franzeskakis, Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Chen, Z.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Christodoulides, D. N.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[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]

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

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

Dreisow, F.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Flach, S.

R. A. Vicencio, S. Flach, M. I. Molina, and Yu. S. Kivshar, Phys. Lett. A 364, 274 (2007).
[CrossRef]

Franzeskakis, D. J.

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Franzeskakis, Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Haché, A.

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]

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

Hudock, J.

Kartashov, Y. V.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Kevrekidis, P. G.

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Franzeskakis, Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Kivshar, Yu. S.

Laedke, E. W.

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

Lederer, F.

Makris, K. G.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

K. G. Makris, J. Hudock, D. N. Christodoulides, G. Stegeman, O. Manela, and M. Segev, Opt. Lett. 31, 2774 (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, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

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

Malomed, B. A.

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Franzeskakis, Phys. Rev. E 75, 056605 (2007).
[CrossRef]

See the review paper: B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005).
[CrossRef]

Manela, O.

Mazilu, D.

Mezentsev, V. K.

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

Mihalache, D.

D. Mihalache, D. Mazilu, F. Lederer, and Yu. S. Kivshar, Opt. Express 15, 589 (2007).
[CrossRef] [PubMed]

See the review paper: B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005).
[CrossRef]

Molina, M.

Molina, M. I.

R. A. Vicencio, S. Flach, M. I. Molina, and Yu. S. Kivshar, Phys. Lett. A 364, 274 (2007).
[CrossRef]

Morandotti, R.

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]

Nolte, S.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Pertsch, T.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Salamo, G.

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]

Segev, M.

Sorel, M.

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]

Spatschek, K. H.

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

Stegeman, G.

Stegeman, G. I.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[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]

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

Suntsov, S.

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]

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

Susanto, H.

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Franzeskakis, Phys. Rev. E 75, 056605 (2007).
[CrossRef]

Szameit, A.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Torner, L.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

See the review paper: B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005).
[CrossRef]

Tünnermann, A.

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

Turitsyn, S. K.

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

Vicencio, R.

Vicencio, R. A.

R. A. Vicencio, S. Flach, M. I. Molina, and Yu. S. Kivshar, Phys. Lett. A 364, 274 (2007).
[CrossRef]

Wang, X.

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

Wise, F.

See the review paper: B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005).
[CrossRef]

Yang, H.

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]

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

See the review paper: B. A. Malomed, D. Mihalache, F. Wise, and L. Torner, J. Opt. B: Quantum Semiclassical Opt. 7, R53 (2005).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Lett. A (1)

R. A. Vicencio, S. Flach, M. I. Molina, and Yu. S. Kivshar, Phys. Lett. A 364, 274 (2007).
[CrossRef]

Phys. Rev. E (2)

H. Susanto, P. G. Kevrekidis, B. A. Malomed, R. Carretero-González, and D. J. Franzeskakis, Phys. Rev. E 75, 056605 (2007).
[CrossRef]

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

Phys. Rev. Lett. (3)

X. Wang, A. Bezryadina, Z. Chen, K. G. Makris, D. N. Christodoulides, and G. I. Stegeman, Phys. Rev. Lett. 98, 123903 (2007).
[CrossRef] [PubMed]

A. Szameit, Y. V. Kartashov, F. Dreisow, T. Pertsch, S. Nolte, A. Tünnermann, and L. Torner, Phys. Rev. Lett. 98, 173903 (2007).
[CrossRef]

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]

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Figures (5)

Fig. 1
Fig. 1

Top: (a)–(c) Examples of the modes localized in the lattice corner, at the edge, and in the center of the lattice. Bottom: Spatial cross sections of the corresponding stable spatiotemporal surface solitons. The modes correspond to points (a)–(c) in Fig. 3c for (a) β = 5 , P = 9.5 ; (b) β = 5.5 , P = 10.09 ; and (c) β = 6 , P = 10.66 .

Fig. 2
Fig. 2

Temporal cross sections of spatiotemporal surface solitons localized in the corner, at the edge, and in the center of the lattice, respectively. Shown are the profiles of stable (higher curves) and unstable (lower curves) spatiotemporal solitons corresponding to points (a)–(f) in Fig. 3c.

Fig. 3
Fig. 3

Families of spatiotemporal surface solitons in two-dimensional lattices for the modes localized in the corner (co), at the edge (ed), and in the center (ce), respectively. (a), (d) Power versus propagation constant for lower and higher powers, respectively, (b) Hamiltonian versus power, (c) peak amplitude versus power. Points (a)–(f) mark the examples shown in Figs. 1, 2.

Fig. 4
Fig. 4

Evolution of the soliton amplitude versus propagation distance for (a) stable corner (co) ( β = 5.0 ) , and edge (ed) ( β = 5.5 ) spatiotemporal surface solitons perturbed by a white input noise, and (b) unstable, unperturbed corner (co) ( β = 4.1 ) and edge (ed) ( β = 4.3 ) spatiotemporal surface solitons.

Fig. 5
Fig. 5

(a), (b) Evolution of the unstable flat-top corner soliton into a stable corner soliton. (c), (d) Reshaping of an unstable edge soliton into a stable edge soliton.

Equations (4)

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

i E n , m z γ 2 E n , m t 2 + ( V n + V m + σ E n , m 2 ) E n , m = 0 ,
γ d 2 E n , m d t 2 = ( β + V n + V m + σ E n , m 2 ) E n , m .
P ( β ) = n , m + E n , m ( β ) 2 d t ,
H = n , m + { [ E n , m ( E n + 1 , m * + E n , m + 1 * ) + c.c. ] + γ E n , m t 2 + 1 2 σ E n , m 4 } d t .

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