Abstract

We experimentally study light self-trapping in triangular photonic lattices induced optically in nonlinear photorefractive crystals. We observe the formation of two-dimensional discrete and gap spatial solitons originating from the first and second bands of the linear transmission spectrum.

© 2007 Optical Society of America

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References

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  1. P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, in Confined Electrons and Photons, E.Burstein and C.Weisbuch, eds. (Plenum, 1995), pp. 585-633.
    [CrossRef]
  2. A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres (Kluwer/Springer, 2003).
    [CrossRef]
  3. H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903-4 (2005).
  4. B. S. Song, S. Noda, T. Asano, and Y. Akahane, Astrophys. J., Suppl. Ser. 4, 207 (2005).
  5. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Phootnic Crystals (Academic, 2003).
  6. R. Fischer, D. Trager, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905-4 (2006).
    [CrossRef]
  7. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  8. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902-4 (2004).
  9. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  10. N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
    [CrossRef]
  11. E. DelRe, B. Crosignani, and P. Di Porto, in Spatial Solitons, Vol. 82 of Springer Series in Optical Sciences, S. Trillo and W.E. Torruellas, eds. (Springer-Verlag, 2001), pp. 61-85.
  12. G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902-4 (2005).
    [CrossRef]
  13. P. G. Kevrekidis, B. A. Malomed, and Y. B. Gaididei, Phys. Rev. E 66, 016609-10 (2002).
  14. N. Akozbek and S. John, Phys. Rev. E 57, 2287 (1998).
    [CrossRef]
  15. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [CrossRef] [PubMed]

2006 (1)

R. Fischer, D. Trager, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905-4 (2006).
[CrossRef]

2005 (3)

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903-4 (2005).

B. S. Song, S. Noda, T. Asano, and Y. Akahane, Astrophys. J., Suppl. Ser. 4, 207 (2005).

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902-4 (2005).
[CrossRef]

2004 (1)

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902-4 (2004).

2003 (3)

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

2002 (2)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

P. G. Kevrekidis, B. A. Malomed, and Y. B. Gaididei, Phys. Rev. E 66, 016609-10 (2002).

1998 (1)

N. Akozbek and S. John, Phys. Rev. E 57, 2287 (1998).
[CrossRef]

Agrawal, G. P.

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

Akahane, Y.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, Astrophys. J., Suppl. Ser. 4, 207 (2005).

Akozbek, N.

N. Akozbek and S. John, Phys. Rev. E 57, 2287 (1998).
[CrossRef]

Asano, T.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, Astrophys. J., Suppl. Ser. 4, 207 (2005).

Bartal, G.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902-4 (2005).
[CrossRef]

Birks, T. A.

P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, in Confined Electrons and Photons, E.Burstein and C.Weisbuch, eds. (Plenum, 1995), pp. 585-633.
[CrossRef]

Bjarklev, A.

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres (Kluwer/Springer, 2003).
[CrossRef]

Bjarklev, A. S.

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres (Kluwer/Springer, 2003).
[CrossRef]

Bogaerts, W.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903-4 (2005).

Broeng, J.

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres (Kluwer/Springer, 2003).
[CrossRef]

Buljan, H.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902-4 (2005).
[CrossRef]

Chen, Z.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902-4 (2004).

Christodoulides, D. N.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902-4 (2004).

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

Cohen, O.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902-4 (2005).
[CrossRef]

Crosignani, B.

E. DelRe, B. Crosignani, and P. Di Porto, in Spatial Solitons, Vol. 82 of Springer Series in Optical Sciences, S. Trillo and W.E. Torruellas, eds. (Springer-Verlag, 2001), pp. 61-85.

DelRe, E.

E. DelRe, B. Crosignani, and P. Di Porto, in Spatial Solitons, Vol. 82 of Springer Series in Optical Sciences, S. Trillo and W.E. Torruellas, eds. (Springer-Verlag, 2001), pp. 61-85.

Denz, C.

R. Fischer, D. Trager, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905-4 (2006).
[CrossRef]

Di Porto, P.

E. DelRe, B. Crosignani, and P. Di Porto, in Spatial Solitons, Vol. 82 of Springer Series in Optical Sciences, S. Trillo and W.E. Torruellas, eds. (Springer-Verlag, 2001), pp. 61-85.

Efremidis, N. K.

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

Engelen, R. J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903-4 (2005).

Eugenieva, E. D.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902-4 (2004).

Fischer, R.

R. Fischer, D. Trager, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905-4 (2006).
[CrossRef]

Fleischer, J. W.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902-4 (2005).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

Gaididei, Y. B.

P. G. Kevrekidis, B. A. Malomed, and Y. B. Gaididei, Phys. Rev. E 66, 016609-10 (2002).

Gersen, H.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903-4 (2005).

John, S.

N. Akozbek and S. John, Phys. Rev. E 57, 2287 (1998).
[CrossRef]

Karle, T. J.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903-4 (2005).

Kevrekidis, P. G.

P. G. Kevrekidis, B. A. Malomed, and Y. B. Gaididei, Phys. Rev. E 66, 016609-10 (2002).

Kivshar, Y.

Kivshar, Yu. S.

R. Fischer, D. Trager, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905-4 (2006).
[CrossRef]

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

Korterik, J. P.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903-4 (2005).

Krauss, T. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903-4 (2005).

Krolikowski, W.

R. Fischer, D. Trager, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905-4 (2006).
[CrossRef]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

Kuipers, L.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903-4 (2005).

Lederer, F.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Lloyd Lucas, F. D.

P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, in Confined Electrons and Photons, E.Burstein and C.Weisbuch, eds. (Plenum, 1995), pp. 585-633.
[CrossRef]

Malomed, B. A.

P. G. Kevrekidis, B. A. Malomed, and Y. B. Gaididei, Phys. Rev. E 66, 016609-10 (2002).

Manela, O.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902-4 (2005).
[CrossRef]

Martin, H.

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902-4 (2004).

Neshev, D.

Neshev, D. N.

R. Fischer, D. Trager, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905-4 (2006).
[CrossRef]

Noda, S.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, Astrophys. J., Suppl. Ser. 4, 207 (2005).

Ostrovskaya, E.

Russell, P. St. J.

P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, in Confined Electrons and Photons, E.Burstein and C.Weisbuch, eds. (Plenum, 1995), pp. 585-633.
[CrossRef]

Sears, S.

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

Segev, M.

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902-4 (2005).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

Silberberg, Y.

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Song, B. S.

B. S. Song, S. Noda, T. Asano, and Y. Akahane, Astrophys. J., Suppl. Ser. 4, 207 (2005).

Sukhorukov, A. A.

R. Fischer, D. Trager, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905-4 (2006).
[CrossRef]

Trager, D.

R. Fischer, D. Trager, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905-4 (2006).
[CrossRef]

van Hulst, N. F.

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903-4 (2005).

Astrophys. J., Suppl. Ser. (1)

B. S. Song, S. Noda, T. Asano, and Y. Akahane, Astrophys. J., Suppl. Ser. 4, 207 (2005).

Nature (2)

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 147 (2003).
[CrossRef] [PubMed]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. E (3)

N. K. Efremidis, S. Sears, D. N. Christodoulides, J. W. Fleischer, and M. Segev, Phys. Rev. E 66, 046602-5 (2002).
[CrossRef]

P. G. Kevrekidis, B. A. Malomed, and Y. B. Gaididei, Phys. Rev. E 66, 016609-10 (2002).

N. Akozbek and S. John, Phys. Rev. E 57, 2287 (1998).
[CrossRef]

Phys. Rev. Lett. (4)

G. Bartal, O. Cohen, H. Buljan, J. W. Fleischer, O. Manela, and M. Segev, Phys. Rev. Lett. 94, 163902-4 (2005).
[CrossRef]

H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902-4 (2004).

H. Gersen, T. J. Karle, R. J. P. Engelen, W. Bogaerts, J. P. Korterik, N. F. van Hulst, T. F. Krauss, and L. Kuipers, Phys. Rev. Lett. 94, 073903-4 (2005).

R. Fischer, D. Trager, D. N. Neshev, A. A. Sukhorukov, W. Krolikowski, C. Denz, and Yu. S. Kivshar, Phys. Rev. Lett. 96, 023905-4 (2006).
[CrossRef]

Other (4)

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

P. St. J. Russell, T. A. Birks, and F. D. Lloyd Lucas, in Confined Electrons and Photons, E.Burstein and C.Weisbuch, eds. (Plenum, 1995), pp. 585-633.
[CrossRef]

A. Bjarklev, J. Broeng, and A. S. Bjarklev, Photonic Crystal Fibres (Kluwer/Springer, 2003).
[CrossRef]

E. DelRe, B. Crosignani, and P. Di Porto, in Spatial Solitons, Vol. 82 of Springer Series in Optical Sciences, S. Trillo and W.E. Torruellas, eds. (Springer-Verlag, 2001), pp. 61-85.

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Figures (3)

Fig. 1
Fig. 1

(a) Lattice unit cell in Fourier space; (b) Bloch-wave dispersion along the contour passing through the high-symmetry points marked in (a); (c) refractive index profile of the triangular lattice; (d), (e) Bloch waves corresponding to the Γ and Y points in (a) and (b); (d) intensity at the Γ point of the first band; (e), (f) intensity and phase at the Y point of the second band.

Fig. 2
Fig. 2

Experimental images of (a) triangular lattice (period 23 μ m ), (b) single-beam input intensity distribution, and (c) Fourier spectrum of input and lattice beams. In (a) and (b) the dashed hexagon indicates the lattice unit cell, and in (c) the edge of the first Brillouin zone as defined by the three lattice beams. (d), (e) Measured linear discrete diffraction and nonlinear self-trapping, respectively, from the top of the first band. The plot dimensions are 150 μ m along both x and y. (f) Numerically calculated intensity of discrete soliton.

Fig. 3
Fig. 3

Experimental images of (a) two-beam input intensity distribution, (b) Fourier spectrum of input and lattice beams, and (c) linear second band Bloch wave at the crystal output. In (b) the dashed hexagon indicates the edge of the first Brillouin zone, and in (c) the lattice unit cell. (d), (e) Measured linear diffraction [as in (c)] and nonlinear self-trapping, respectively, from the top of the second band. The plot dimensions are 150 μ m along x and 200 μ m along y. (f) Measured phase interferogram for the self-trapped beam in (e). (g), (h) Numerically calculated gap soliton intensity distribution and phase, respectively. The lattice period is 30 μ m .

Equations (1)

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i E z + D ( 2 E x 2 + 2 E y 2 ) + F ( x , y , E 2 ) E = 0 ,

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