Abstract

We experimentally investigate the interaction of counterpropagating discrete solitons in a one-dimensional waveguide array in photorefractive lithium niobate. While for low input powers only weak interaction and formation of counterpropagating vector solitons are observed, for higher input powers a growing instability results in discrete lateral shifting of the formed discrete solitons. Numerical modeling shows the existence of three different regimes: stable propagation of vector solitons at low power, instability for intermediate power levels leading to discrete shifting of the two discrete solitons, and an irregular temporal dynamic behavior of the two beams for high input power.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]

2006 (3)

2005 (4)

2004 (2)

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

M. Belic, Ph. Jander, K. Motzek, A. Desyatnikov, D. Jovic, A. Strinic, M. Petrovic, C. Denz, and F. Kaiser, J. Opt. B: Quantum Semiclassical Opt. 6, 190 (2004).
[CrossRef]

2003 (2)

M. Belic, Ph. Jander, A. Strinic, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, R025601 (2003).
[CrossRef]

K. Motzek, Ph. Jander, A. Desyatnikov, M. Belic, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[CrossRef]

2002 (1)

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

1999 (2)

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

D. Kip, M. Wesner, C. Herden, and V. Shandarov, Appl. Phys. B 68, 971 (1999).
[CrossRef]

1998 (1)

H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

1997 (1)

1993 (1)

1988 (1)

1983 (1)

Agrawal, G. P.

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

Aitchison, J. S.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Opt. Lett. 30, 1027 (2005).
[CrossRef] [PubMed]

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

H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Arsenovic, D.

Bartal, G.

Belic, M.

M. Belic, D. Jovic, S. Prvanovic, D. Arsenovic, and M. Petrovic, Opt. Express 14, 794 (2006).
[CrossRef] [PubMed]

M. Petrovic, D. Jovic, M. Belic, J. Schröder, Ph. Jander, and C. Denz, Phys. Rev. Lett. 95, 053901 (2005).
[CrossRef] [PubMed]

M. Belic, Ph. Jander, K. Motzek, A. Desyatnikov, D. Jovic, A. Strinic, M. Petrovic, C. Denz, and F. Kaiser, J. Opt. B: Quantum Semiclassical Opt. 6, 190 (2004).
[CrossRef]

K. Motzek, Ph. Jander, A. Desyatnikov, M. Belic, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[CrossRef]

M. Belic, Ph. Jander, A. Strinic, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, R025601 (2003).
[CrossRef]

Boyd, A. R.

H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Buljan, H.

Carmon, T.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

Chen, F.

Christodoulides, D. N.

Cohen, O.

Denz, C.

M. Petrovic, D. Jovic, M. Belic, J. Schröder, Ph. Jander, and C. Denz, Phys. Rev. Lett. 95, 053901 (2005).
[CrossRef] [PubMed]

M. Belic, Ph. Jander, K. Motzek, A. Desyatnikov, D. Jovic, A. Strinic, M. Petrovic, C. Denz, and F. Kaiser, J. Opt. B: Quantum Semiclassical Opt. 6, 190 (2004).
[CrossRef]

K. Motzek, Ph. Jander, A. Desyatnikov, M. Belic, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[CrossRef]

M. Belic, Ph. Jander, A. Strinic, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, R025601 (2003).
[CrossRef]

Desyatnikov, A.

M. Belic, Ph. Jander, K. Motzek, A. Desyatnikov, D. Jovic, A. Strinic, M. Petrovic, C. Denz, and F. Kaiser, J. Opt. B: Quantum Semiclassical Opt. 6, 190 (2004).
[CrossRef]

K. Motzek, Ph. Jander, A. Desyatnikov, M. Belic, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[CrossRef]

M. Belic, Ph. Jander, A. Strinic, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, R025601 (2003).
[CrossRef]

Efremidis, N. K.

Eisenberg, H.

H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Fleischer, J. W.

Freedman, B.

Gordon, J. P.

Herden, C.

D. Kip, M. Wesner, C. Herden, and V. Shandarov, Appl. Phys. B 68, 971 (1999).
[CrossRef]

Jander, Ph.

M. Petrovic, D. Jovic, M. Belic, J. Schröder, Ph. Jander, and C. Denz, Phys. Rev. Lett. 95, 053901 (2005).
[CrossRef] [PubMed]

M. Belic, Ph. Jander, K. Motzek, A. Desyatnikov, D. Jovic, A. Strinic, M. Petrovic, C. Denz, and F. Kaiser, J. Opt. B: Quantum Semiclassical Opt. 6, 190 (2004).
[CrossRef]

K. Motzek, Ph. Jander, A. Desyatnikov, M. Belic, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[CrossRef]

M. Belic, Ph. Jander, A. Strinic, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, R025601 (2003).
[CrossRef]

Joseph, R. I.

Jovic, D.

M. Belic, D. Jovic, S. Prvanovic, D. Arsenovic, and M. Petrovic, Opt. Express 14, 794 (2006).
[CrossRef] [PubMed]

M. Petrovic, D. Jovic, M. Belic, J. Schröder, Ph. Jander, and C. Denz, Phys. Rev. Lett. 95, 053901 (2005).
[CrossRef] [PubMed]

M. Belic, Ph. Jander, K. Motzek, A. Desyatnikov, D. Jovic, A. Strinic, M. Petrovic, C. Denz, and F. Kaiser, J. Opt. B: Quantum Semiclassical Opt. 6, 190 (2004).
[CrossRef]

Kaiser, F.

M. Belic, Ph. Jander, K. Motzek, A. Desyatnikov, D. Jovic, A. Strinic, M. Petrovic, C. Denz, and F. Kaiser, J. Opt. B: Quantum Semiclassical Opt. 6, 190 (2004).
[CrossRef]

K. Motzek, Ph. Jander, A. Desyatnikov, M. Belic, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[CrossRef]

Kip, D.

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

E. Smirnov, C. E. Rüter, M. Stepic, V. Shandarov, and D. Kip, Opt. Express 14, 11248 (2006).
[CrossRef] [PubMed]

F. Chen, M. Stepic, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, Opt. Express 13, 4314 (2005).
[CrossRef] [PubMed]

D. Kip, M. Wesner, C. Herden, and V. Shandarov, Appl. Phys. B 68, 971 (1999).
[CrossRef]

Kivshar, Yu. S.

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

Manela, O.

Meier, J.

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]

H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Motzek, K.

M. Belic, Ph. Jander, K. Motzek, A. Desyatnikov, D. Jovic, A. Strinic, M. Petrovic, C. Denz, and F. Kaiser, J. Opt. B: Quantum Semiclassical Opt. 6, 190 (2004).
[CrossRef]

K. Motzek, Ph. Jander, A. Desyatnikov, M. Belic, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[CrossRef]

Odoulov, S.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

Petrovic, M.

M. Belic, D. Jovic, S. Prvanovic, D. Arsenovic, and M. Petrovic, Opt. Express 14, 794 (2006).
[CrossRef] [PubMed]

M. Petrovic, D. Jovic, M. Belic, J. Schröder, Ph. Jander, and C. Denz, Phys. Rev. Lett. 95, 053901 (2005).
[CrossRef] [PubMed]

M. Belic, Ph. Jander, K. Motzek, A. Desyatnikov, D. Jovic, A. Strinic, M. Petrovic, C. Denz, and F. Kaiser, J. Opt. B: Quantum Semiclassical Opt. 6, 190 (2004).
[CrossRef]

Prönneke, L.

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

Prvanovic, S.

Runde, D.

Rüter, C. E.

Salamo, G.

Schröder, J.

M. Petrovic, D. Jovic, M. Belic, J. Schröder, Ph. Jander, and C. Denz, Phys. Rev. Lett. 95, 053901 (2005).
[CrossRef] [PubMed]

Schwartz, T.

Segev, M.

Shandarov, V.

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

E. Smirnov, C. E. Rüter, M. Stepic, V. Shandarov, and D. Kip, Opt. Express 14, 11248 (2006).
[CrossRef] [PubMed]

F. Chen, M. Stepic, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, Opt. Express 13, 4314 (2005).
[CrossRef] [PubMed]

D. Kip, M. Wesner, C. Herden, and V. Shandarov, Appl. Phys. B 68, 971 (1999).
[CrossRef]

Sheppard, A. P.

Shih, M.

Silberberg, Y.

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, Opt. Lett. 30, 1027 (2005).
[CrossRef] [PubMed]

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

H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

Smirnov, E.

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

E. Smirnov, C. E. Rüter, M. Stepic, V. Shandarov, and D. Kip, Opt. Express 14, 11248 (2006).
[CrossRef] [PubMed]

Snyder, A. W.

Sorel, M.

Stegeman, G.

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

Stegeman, G. I.

Stepic, M.

Strinic, A.

M. Belic, Ph. Jander, K. Motzek, A. Desyatnikov, D. Jovic, A. Strinic, M. Petrovic, C. Denz, and F. Kaiser, J. Opt. B: Quantum Semiclassical Opt. 6, 190 (2004).
[CrossRef]

M. Belic, Ph. Jander, A. Strinic, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, R025601 (2003).
[CrossRef]

Uzdin, R.

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

Wesner, M.

D. Kip, M. Wesner, C. Herden, and V. Shandarov, Appl. Phys. B 68, 971 (1999).
[CrossRef]

Yang, H.

Appl. Phys. B (1)

D. Kip, M. Wesner, C. Herden, and V. Shandarov, Appl. Phys. B 68, 971 (1999).
[CrossRef]

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

M. Belic, Ph. Jander, K. Motzek, A. Desyatnikov, D. Jovic, A. Strinic, M. Petrovic, C. Denz, and F. Kaiser, J. Opt. B: Quantum Semiclassical Opt. 6, 190 (2004).
[CrossRef]

Opt. Express (4)

Opt. Lett. (5)

Phys. Rev. E (3)

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

M. Belic, Ph. Jander, A. Strinic, A. Desyatnikov, and C. Denz, Phys. Rev. E 68, R025601 (2003).
[CrossRef]

K. Motzek, Ph. Jander, A. Desyatnikov, M. Belic, C. Denz, and F. Kaiser, Phys. Rev. E 68, 066611 (2003).
[CrossRef]

Phys. Rev. Lett. (4)

M. Petrovic, D. Jovic, M. Belic, J. Schröder, Ph. Jander, and C. Denz, Phys. Rev. Lett. 95, 053901 (2005).
[CrossRef] [PubMed]

O. Cohen, R. Uzdin, T. Carmon, J. W. Fleischer, M. Segev, and S. Odoulov, Phys. Rev. Lett. 89, 133901 (2002).
[CrossRef] [PubMed]

H. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

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

Science (1)

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

Other (1)

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

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: ML, microscope lenses; M, mirrors; BS, beam splitters; WA, waveguide array; CCD, CCD cameras. Inset, forward- (#1) and backward- (#2) propagating beams.

Fig. 2
Fig. 2

Temporal evolution of discrete soliton formation for two different input powers, (a) P in = 1.8 μ W , (b) P in = 20 μ W of beam #1.

Fig. 3
Fig. 3

Interaction of forward- (#1) and backward- (#2) propagating discrete solitons for input powers (a) P in = 2 μ W , (b) P in = 6 μ W , and (c) P in = 12 μ W .

Fig. 4
Fig. 4

Simulation of the interaction of counterpropagating discrete solitons (left-hand side, beam #1; right-hand side, beam #2) for three different intensity ratios, (a) r = 1 , (b) r = 2.5 , and (c) r = 5 in steady state ( t = 10 τ ) .

Equations (3)

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

i E 1 y + 1 2 k 2 E 1 z 2 + k n ( z ) + Δ n n e E 1 = 0 ,
i E 2 y + 1 2 k 2 E 2 z 2 + k n ( z ) + Δ n n e E 2 = 0 ,
Δ n = Δ n 0 I 1 + I 2 I 1 + I 2 + I d = Δ n 0 2 r 2 r + 1 .

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