Abstract

We demonstrate coherent interactions between spatial gap solitons in optically induced photonic lattices. Because of the “staggered” phase structures, two in-phase (out-of-phase) bright gap solitons can repel (attract) each other at close proximity, in contrast to soliton interaction in homogeneous media. A reversal of energy transfer direction and a transition between attractive and repulsive interaction forces can be obtained solely by changing the initial soliton separation relative to the lattice spacing.

© 2011 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2010

2007

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

C. Lou, X. Wang, J. Xu, and Z. Chen, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

F. Xiao, P. Zhang, S. Liu, and J. Zhao, Chin. Phys. Lett. 24, 3435 (2007).
[CrossRef]

2006

M. Stepić, E. Smirnov, C. E. Rüter, L. Prönneke, and D. Kip, Phys. Rev. E 74, 046614 (2006).
[CrossRef]

2004

J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 93, 093903 (2004).
[CrossRef] [PubMed]

2003

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

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

1999

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

1997

1991

Aitchison, J. S.

J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 93, 093903 (2004).
[CrossRef] [PubMed]

J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. Smith, Opt. Lett. 16, 15 (1991).
[CrossRef] [PubMed]

Chen, Z.

S. Huang, P. Zhang, Z. Wang, and Z. Chen, Opt. Lett. 35, 2284 (2010).
[CrossRef] [PubMed]

C. Lou, X. Wang, J. Xu, and Z. Chen, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

Christodoulides, D. N.

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]

Dreisow, F.

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

Efremidis, N. K.

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

Fleischer, J. W.

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

Hartung, H.

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

Huang, S.

Jackel, J. L.

Kip, D.

M. Stepić, E. Smirnov, C. E. Rüter, L. Prönneke, and D. Kip, Phys. Rev. E 74, 046614 (2006).
[CrossRef]

Leaird, D. E.

Lederer, F.

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

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

Liu, S.

F. Xiao, P. Zhang, S. Liu, and J. Zhao, Chin. Phys. Lett. 24, 3435 (2007).
[CrossRef]

Lou, C.

C. Lou, X. Wang, J. Xu, and Z. Chen, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

Meier, J.

J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 93, 093903 (2004).
[CrossRef] [PubMed]

Meng, H.

Morandotti, R.

J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 93, 093903 (2004).
[CrossRef] [PubMed]

Nolte, S.

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

Oliver, M. K.

Prönneke, L.

M. Stepić, E. Smirnov, C. E. Rüter, L. Prönneke, and D. Kip, Phys. Rev. E 74, 046614 (2006).
[CrossRef]

Rüter, C. E.

M. Stepić, E. Smirnov, C. E. Rüter, L. Prönneke, and D. Kip, Phys. Rev. E 74, 046614 (2006).
[CrossRef]

Salamo, G.

Segev, M.

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

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

H. Meng, G. Salamo, M. Shih, and M. Segev, Opt. Lett. 22, 448 (1997).
[CrossRef] [PubMed]

Shih, M.

Silberberg, Y.

J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 93, 093903 (2004).
[CrossRef] [PubMed]

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

J. S. Aitchison, A. M. Weiner, Y. Silberberg, D. E. Leaird, M. K. Oliver, J. L. Jackel, and P. W. Smith, Opt. Lett. 16, 15 (1991).
[CrossRef] [PubMed]

Smirnov, E.

M. Stepić, E. Smirnov, C. E. Rüter, L. Prönneke, and D. Kip, Phys. Rev. E 74, 046614 (2006).
[CrossRef]

Smith, P. W.

Stegeman, G. I.

J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 93, 093903 (2004).
[CrossRef] [PubMed]

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

Stepic, M.

M. Stepić, E. Smirnov, C. E. Rüter, L. Prönneke, and D. Kip, Phys. Rev. E 74, 046614 (2006).
[CrossRef]

Szameit, A.

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

Tünnermann, A.

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

Wang, X.

C. Lou, X. Wang, J. Xu, and Z. Chen, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

Wang, Z.

Weiner, A. M.

Xiao, F.

F. Xiao, P. Zhang, S. Liu, and J. Zhao, Chin. Phys. Lett. 24, 3435 (2007).
[CrossRef]

Xu, J.

C. Lou, X. Wang, J. Xu, and Z. Chen, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

Zhang, P.

S. Huang, P. Zhang, Z. Wang, and Z. Chen, Opt. Lett. 35, 2284 (2010).
[CrossRef] [PubMed]

F. Xiao, P. Zhang, S. Liu, and J. Zhao, Chin. Phys. Lett. 24, 3435 (2007).
[CrossRef]

Zhao, J.

F. Xiao, P. Zhang, S. Liu, and J. Zhao, Chin. Phys. Lett. 24, 3435 (2007).
[CrossRef]

Appl. Phys. Lett.

A. Szameit, F. Dreisow, H. Hartung, S. Nolte, A. Tünnermann, and F. Lederer, Appl. Phys. Lett. 90, 241113 (2007).
[CrossRef]

Chin. Phys. Lett.

F. Xiao, P. Zhang, S. Liu, and J. Zhao, Chin. Phys. Lett. 24, 3435 (2007).
[CrossRef]

Nature

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

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

Opt. Lett.

Phys. Rev. E

M. Stepić, E. Smirnov, C. E. Rüter, L. Prönneke, and D. Kip, Phys. Rev. E 74, 046614 (2006).
[CrossRef]

Phys. Rev. Lett.

C. Lou, X. Wang, J. Xu, and Z. Chen, Phys. Rev. Lett. 98, 213903 (2007).
[CrossRef] [PubMed]

J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 93, 093903 (2004).
[CrossRef] [PubMed]

Science

G. I. Stegeman and M. Segev, Science 286, 1518 (1999).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of gap soliton interactions in an optically induced photonic lattice. (b) Bandgap structure and (c) first- and second-band gap solitons with the low-index regions shaded. (d) Overlapping of two second-band gap solitons at different separations.

Fig. 2
Fig. 2

BPM simulations of coherent interactions of gap solitons at different separations D and phase differences Δ φ . (a)–(d)  D = 3 d , 4 d , 5 d , and 6 d . Left to right, Δ φ = 0 , π / 2 , and π.

Fig. 3
Fig. 3

Experimental setup for observing coherent interactions between gap solitons: SBN, strontium barium niobate; BS, beam splitter; λ / 2 , half-wave plate; RT, reversed telescope; RD, rotating diffuser; L, lens; MS, amplitude mask; M, mirror; F, Fourier-plane filter; CL, cylindrical lens; and FP, focal plane.

Fig. 4
Fig. 4

Experimental observation (top panels, input; bottom panels, output) and numerical simulation (middle panels) of in-phase gap solitons interacting in an optically induced photonic lattice. The initial beam separation in (a)–(d) is D = d , 2 d , 3 d , and 4 d , respectively.

Equations (1)

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( z i 2 2 x 2 ) B i ( x , z ) = i E 0 ( I l + I p 1 + I l + I p ) B i ( x , z ) , i = 1 , 2 ,

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