Abstract

We experimentally study light localization at phase-slip waveguides and at the intersection of phase slips in a two-dimensional (2D) square photonic lattice. Such systems allow for the observation of a variety of effects, including the existence of spatially localized modes for low powers, the generation of strongly localized states in the form of discrete bulk and surface solitons, as well as a crossover between one-dimensional and 2D localization.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]

2009 (2)

2008 (1)

2006 (5)

K. Itoh, W. Watanabe, S. Nolte, and C. Schaffer, MRS Bull. 31, 620 (2006).
[CrossRef]

A. Szameit, J. Burghoff, T. Pertsch, S. Nolte, A. Tünnermann, and F. Lederer, Opt. Express 14, 6055(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]

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]

X. Wang, J. Young, Z. Chen, D. Weinstein, and J. Yang, Opt. Express 14, 7362 (2006).
[CrossRef] [PubMed]

2005 (1)

2003 (5)

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

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, Opt. Lett. 28, 834 (2003).
[CrossRef] [PubMed]

H. Trompeter, U. Peschel, T. Pertsch, F. Lederer, U. Streppel, D. Michaelis, and A. Bräuer, Opt. Express 11, 3404 (2003).
[CrossRef] [PubMed]

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

V. M. Apalkov and M. E. Raikh, Phys. Rev. Lett. 90, 253901 (2003).
[CrossRef] [PubMed]

2001 (1)

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 083901 (2001).
[CrossRef] [PubMed]

1996 (1)

1993 (1)

Yu. S. Kivshar, Phys. Rev. B 47, 11167 (1993).
[CrossRef]

1988 (1)

Aitchison, J. S.

Apalkov, V. M.

V. M. Apalkov and M. E. Raikh, Phys. Rev. Lett. 90, 253901 (2003).
[CrossRef] [PubMed]

Bräuer, A.

Burghoff, J.

Chen, Z.

Christodoulides, D.

Christodoulides, D. N.

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

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

Dreisow, F.

Efremidis, N. K.

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

Eisenberg, H. S.

Fedele, F.

Fleischer, J. W.

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

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]

Heinrich, M.

Itoh, K.

K. Itoh, W. Watanabe, S. Nolte, and C. Schaffer, MRS Bull. 31, 620 (2006).
[CrossRef]

Joseph, R.

Kartashov, Y. V.

Kivshar, Yu. S.

M. I. Molina and Yu. S. Kivshar, Phys. Rev. A 80, 063812 (2009).
[CrossRef]

M. I. Molina and Yu. S. Kivshar, Opt. Lett. 33, 917 (2008).
[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. 87, 083901 (2001).
[CrossRef] [PubMed]

W. Krolikowski and Yu. S. Kivshar, J. Opt. Soc. Am. B 13, 876 (1996).
[CrossRef]

Yu. S. Kivshar, Phys. Rev. B 47, 11167 (1993).
[CrossRef]

Krolikowski, W.

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]

W. Krolikowski and Yu. S. Kivshar, J. Opt. Soc. Am. B 13, 876 (1996).
[CrossRef]

Lederer, F.

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, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Mandelik, D.

Michaelis, D.

Mitchell, A.

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]

Modotto, D.

Molina, M. I.

M. I. Molina and Yu. S. Kivshar, Phys. Rev. A 80, 063812 (2009).
[CrossRef]

M. I. Molina and Yu. S. Kivshar, Opt. Lett. 33, 917 (2008).
[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]

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]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, Opt. Lett. 28, 834 (2003).
[CrossRef] [PubMed]

Neshev, D. N.

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]

Nolte, S.

Pertsch, T.

Peschel, U.

Raikh, M. E.

V. M. Apalkov and M. E. Raikh, Phys. Rev. Lett. 90, 253901 (2003).
[CrossRef] [PubMed]

Rosberg, C. R.

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]

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]

Schaffer, C.

K. Itoh, W. Watanabe, S. Nolte, and C. Schaffer, MRS Bull. 31, 620 (2006).
[CrossRef]

Segev, M.

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

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, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

R. Morandotti, H. S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C. R. Stanley, and J. S. Aitchison, Opt. Lett. 28, 834 (2003).
[CrossRef] [PubMed]

Stanley, C. R.

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, Phys. Rev. Lett. 96, 063901 (2006).
[CrossRef] [PubMed]

Streppel, U.

Sukhorukov, A. A.

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 083901 (2001).
[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]

Szameit, A.

Torner, L.

Trompeter, H.

Tünnermann, A.

Vicencio, R. A.

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]

Vysloukh, V. A.

Wang, X.

Watanabe, W.

K. Itoh, W. Watanabe, S. Nolte, and C. Schaffer, MRS Bull. 31, 620 (2006).
[CrossRef]

Weinstein, D.

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]

Yang, J.

Young, J.

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

MRS Bull. (1)

K. Itoh, W. Watanabe, S. Nolte, and C. Schaffer, MRS Bull. 31, 620 (2006).
[CrossRef]

Nature (2)

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

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

Opt. Express (3)

Opt. Lett. (5)

Phys. Rev. A (1)

M. I. Molina and Yu. S. Kivshar, Phys. Rev. A 80, 063812 (2009).
[CrossRef]

Phys. Rev. B (1)

Yu. S. Kivshar, Phys. Rev. B 47, 11167 (1993).
[CrossRef]

Phys. Rev. Lett. (4)

A. A. Sukhorukov and Yu. S. Kivshar, Phys. Rev. Lett. 87, 083901 (2001).
[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]

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]

V. M. Apalkov and M. E. Raikh, Phys. Rev. Lett. 90, 253901 (2003).
[CrossRef] [PubMed]

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Figures (6)

Fig. 1
Fig. 1

Schematics of an intersection of two different phase slips (H, V a ). The case of a single phase slip corresponds to either H a or V a . Marked waveguides show the excitation points.

Fig. 2
Fig. 2

Power diagrams for the cases: (a) mode localized at a cross intersection of two phase slips with V = H = 29 μm and (b) surface mode localized at a single phase slip with V = 25 μm , H = a = 40 μm . Solid curves refer to stable states, while dashed branches refer to the unstable modes.

Fig. 3
Fig. 3

Light diffraction and localization in a perfect square lattice, for different input powers: (a) 75 kW , (b) 1600 kW , and (c) 2000 kW . Excited waveguides are marked with white circles.

Fig. 4
Fig. 4

(a) Experimental and (b) theoretical results for the generation of a linear localized mode at an intersection of two phase-slip waveguides for V = H = 22 μm and an input power 75 kW [cf. Figure 3a]. Excited waveguides are marked with white circles; phase slips are marked by dashed lines.

Fig. 5
Fig. 5

Experimental images of the light intensity at the output facet showing the generation of (a) 1D stripe surface soliton for an input power 1700 kW and (b) its transformation into a 2D soliton at 2000 kW . The waveguide parameters are H = 29 μm and V = a = 40 μm . Excited waveguides are marked with white circles; phase slips are marked by dashed lines.

Fig. 6
Fig. 6

Experimental images of the output light intensity showing the generation of (a), (b) 2D soliton ( H = V = 29 μm ), and (c), (d) generation of a surface soliton at a phase slip ( H = 40 μm and V = 25 μm ). Input powers: (a) 1400 kW , (b) 2500 kW , (c) 75 kW , and (d) 2800 kW . Excited waveguides are marked with white circles; phase slips are marked by dashed lines.

Equations (2)

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i d E n d z + m C n , m E m + γ | E n | 2 E n = 0 ,
β = C V + 1 C V + C H + 1 C H ,

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