Abstract

We address the properties of surface solitons supported by optical lattices imprinted in photorefractive media with asymmetrical diffusion nonlinearity. Such solitons exist only in finite gaps of the lattice spectrum. In contrast to latticeless geometries, where surface waves exist only when nonlinearity deflects light toward the material surface, the surface lattice solitons exist in settings where diffusion would cause beam bending against the surface.

© 2008 Optical Society of America

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2007 (2)

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]

2006 (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]

Y. V. Kartashov, V. A. 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 Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

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

Z. Xu, Y. V. Kartashov, and L. Torner, Opt. Lett. 31, 2027 (2006).
[CrossRef] [PubMed]

E. Smirnov, M. Stepic, C. E. Rüter, D. Kip, and V. Shandarov, Opt. Lett. 31, 2338 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (1)

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 153903 (2004).
[CrossRef] [PubMed]

2001 (1)

V. Aleshkevich, Y. Kartashov, A. Egorov, and V. Vysloukh, Phys. Rev. E 64, 056610 (2001).
[CrossRef]

1998 (1)

1996 (4)

1995 (3)

G. Garcia-Quirino, J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

M. Cronin-Golomb, Opt. Lett. 20, 2075 (1995).
[CrossRef] [PubMed]

1994 (2)

A. A. Zozulya, M. Saffman, and D. Z. Anderson, Phys. Rev. Lett. 73, 818 (1994).
[CrossRef] [PubMed]

M. Segev, J. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

1993 (1)

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

M. I. Carvalho, S. R. Singh, and D. N. Christodoulides, Opt. Commun. 120, 311 (1995).
[CrossRef]

Opt. Lett. (8)

Phys. Rev. A (1)

G. Garcia-Quirino, J. Sanchez-Mondragon, and S. Stepanov, Phys. Rev. A 51, 1571 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (2)

V. Aleshkevich, Y. Kartashov, A. Egorov, and V. Vysloukh, Phys. Rev. E 64, 056610 (2001).
[CrossRef]

W. Krolikowski, N. Akhmediev, B. Luther-Davies, and M. Cronin-Golomb, Phys. Rev. E 54, 5761 (1996).
[CrossRef]

Phys. Rev. Lett. (9)

G. C. Duree, J. L. Shultz, G. J. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. J. Sharp, and R. R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993).
[CrossRef] [PubMed]

A. A. Zozulya, M. Saffman, and D. Z. Anderson, Phys. Rev. Lett. 73, 818 (1994).
[CrossRef] [PubMed]

M. Segev, J. C. Valley, B. Crosignani, P. Di Porto, and A. Yariv, Phys. Rev. Lett. 73, 3211 (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]

Y. V. Kartashov, V. A. 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 Y. S. Kivshar, Phys. Rev. Lett. 97, 083901 (2006).
[CrossRef] [PubMed]

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]

Y. V. Kartashov, V. A. Vysloukh, and L. Torner, Phys. Rev. Lett. 93, 153903 (2004).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

(a) Floquet–Bloch spectrum of infinite lattice. Gray regions show bands and white regions correspond to gaps. (b) Energy flow versus propagation constant for μ = 1 [gray curve (red online)] and μ = 1 (black curve) at p = 6 . (c) Domain of existence of surface solitons on the ( p , b ) plane for μ = 1 [gray curve (red online)] and μ = 1 (black curve). (d) Real part of perturbation growth rate versus propagation constant at p = 6 , μ = 1 . In all cases Ω = 2 .

Fig. 2
Fig. 2

Profiles of surface solitons at (a) b = 1.9 , p = 3.5 , μ = 1 (black curve) and μ = 1 [gray curve (red online)]; (b) b = 0.62 , p = 3.5 , and μ = 1 ; (c) b = 2.27 , p = 3.5 , μ = 1 ; (d) b = 0.1 , p = 1.5 , and μ = 1 ; (e) b = 3.53 , p = 5 , and μ = 1 ; and (f) b = 2.4 , p = 5 , and μ = 1 . In gray regions R ( η ) 1 2 , while in white regions R ( η ) < 1 2 . In all cases Ω = 2 .

Fig. 3
Fig. 3

Stable propagation of perturbed surface solitons corresponding to (a) b = 1.9 , p = 3.5 , and μ = 1 , and (b) b = 2.23 , p = 3.5 , μ = 1 . Broadband white noise was added into input field distributions. Dynamics of propagation of a Gaussian beam launched into the first channel of the lattice with p = 3 at (c) μ = 1 and (d) μ = 1 . In all cases field modulus distributions are shown, white dashed lines indicate interface position, and lattice frequency Ω = 2 .

Equations (1)

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i q ξ = 1 2 2 q η 2 + μ q 1 + S q 2 q 2 η p R ( η ) q ,

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