Abstract

We demonstrate the formation of fundamental and dipolelike vector solitons in an optically induced two-dimensional photonic lattice. Such vector solitons are realized by mutual trapping of two beams in the lattice. Our theoretical results are in good agreement with experimental observations.

© 2004 Optical Society of America

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  1. D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  2. D. Campbell, S. Flach, and Y. S. Kivshar, Phys. Today 57(1), 43 (2004).
    [CrossRef]
  3. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  4. R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
    [CrossRef] [PubMed]
  5. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
    [CrossRef]
  6. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 150 (2003).
    [CrossRef]
  7. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  8. H. Martin, E. D. Eugenieva, Z. Chen, and D. N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004).
    [CrossRef]
  9. Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
    [CrossRef]
  10. B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
    [CrossRef]
  11. J. Yang and Z. H. Musslimani, Opt. Lett. 28, 2094 (2003).
    [CrossRef] [PubMed]
  12. F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Optical Solitons, S. Trillo and W. E. Torruellas, eds. (Springer-Verlag, New York, 2001).
  13. M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. E 65, 056618 (2002).
    [CrossRef]
  14. J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
    [CrossRef]
  15. J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
    [CrossRef]
  16. Z. Chen and K. McCarthy, Opt. Lett. 27, 2019 (2002).
    [CrossRef]
  17. Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
    [CrossRef] [PubMed]
  18. N. G. Vakhitov and A. A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
    [CrossRef]
  19. J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Opt. Lett. 29, 1662 (2004).
    [CrossRef] [PubMed]

2004 (4)

D. Campbell, S. Flach, and Y. S. Kivshar, Phys. Today 57(1), 43 (2004).
[CrossRef]

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

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

2003 (7)

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

J. Yang and Z. H. Musslimani, Opt. Lett. 28, 2094 (2003).
[CrossRef] [PubMed]

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[CrossRef]

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 150 (2003).
[CrossRef]

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

2002 (2)

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. E 65, 056618 (2002).
[CrossRef]

Z. Chen and K. McCarthy, Opt. Lett. 27, 2019 (2002).
[CrossRef]

2001 (2)

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

1998 (1)

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

1996 (1)

1973 (1)

N. G. Vakhitov and A. A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
[CrossRef]

Ablowitz, M. J.

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. E 65, 056618 (2002).
[CrossRef]

Aitchison, J. S.

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

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

Bezryadina, A.

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

Boyd, A. R.

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

Campbell, D.

D. Campbell, S. Flach, and Y. S. Kivshar, Phys. Today 57(1), 43 (2004).
[CrossRef]

Carmon, T.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 150 (2003).
[CrossRef]

Chen, Z.

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, Opt. Lett. 29, 1662 (2004).
[CrossRef] [PubMed]

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

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

Z. Chen and K. McCarthy, Opt. Lett. 27, 2019 (2002).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
[CrossRef] [PubMed]

Christodoulides, D. N.

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

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

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

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 150 (2003).
[CrossRef]

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
[CrossRef] [PubMed]

Coskun, T. H.

Darmanyan, S.

F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Optical Solitons, S. Trillo and W. E. Torruellas, eds. (Springer-Verlag, New York, 2001).

Efremidis, N. K.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 150 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

Eisenberg, H. S.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

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

Eugenieva, E. D.

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

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

Flach, S.

D. Campbell, S. Flach, and Y. S. Kivshar, Phys. Today 57(1), 43 (2004).
[CrossRef]

Fleischer, J. W.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 150 (2003).
[CrossRef]

Hudock, J.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[CrossRef]

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

Kevrekidis, P. G.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[CrossRef]

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Kivshar, Y.

Kivshar, Y. S.

D. Campbell, S. Flach, and Y. S. Kivshar, Phys. Today 57(1), 43 (2004).
[CrossRef]

Kobyakov, A.

F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Optical Solitons, S. Trillo and W. E. Torruellas, eds. (Springer-Verlag, New York, 2001).

Kolokolov, A. A.

N. G. Vakhitov and A. A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
[CrossRef]

Krolikowski, W.

Lederer, F.

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

F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Optical Solitons, S. Trillo and W. E. Torruellas, eds. (Springer-Verlag, New York, 2001).

Makasyuk, I.

Malomed, B. A.

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[CrossRef]

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Martin, H.

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

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

McCarthy, K.

Meier, J.

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

Morandotti, R.

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

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

Musslimani, Z. H.

J. Yang and Z. H. Musslimani, Opt. Lett. 28, 2094 (2003).
[CrossRef] [PubMed]

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. E 65, 056618 (2002).
[CrossRef]

Neshev, D.

Ostrovskaya, E.

Segev, M.

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 150 (2003).
[CrossRef]

Z. Chen, M. Segev, T. H. Coskun, and D. N. Christodoulides, Opt. Lett. 21, 1436 (1996).
[CrossRef] [PubMed]

Silberberg, Y.

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

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

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

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

Sorel, M.

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

Stegeman, G.

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

Vakhitov, N. G.

N. G. Vakhitov and A. A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
[CrossRef]

Xu, J.

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

Yang, J.

Nature (2)

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

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature 422, 150 (2003).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. E (3)

M. J. Ablowitz and Z. H. Musslimani, Phys. Rev. E 65, 056618 (2002).
[CrossRef]

J. Hudock, P. G. Kevrekidis, B. A. Malomed, and D. N. Christodoulides, Phys. Rev. E 67, 056618 (2003).
[CrossRef]

B. A. Malomed and P. G. Kevrekidis, Phys. Rev. E 64, 026601 (2001).
[CrossRef]

Phys. Rev. Lett. (6)

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

Z. Chen, H. Martin, E. D. Eugenieva, J. Xu, and A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004).
[CrossRef]

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

R. Morandotti, H. S. Eisenberg, Y. Silberberg, M. Sorel, and J. S. Aitchison, Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003).
[CrossRef]

J. Meier, J. Hudock, D. N. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, Phys. Rev. Lett. 91, 143907 (2003).
[CrossRef]

Phys. Today (1)

D. Campbell, S. Flach, and Y. S. Kivshar, Phys. Today 57(1), 43 (2004).
[CrossRef]

Radiophys. Quantum Electron. (1)

N. G. Vakhitov and A. A. Kolokolov, Radiophys. Quantum Electron. 16, 783 (1973).
[CrossRef]

Other (1)

F. Lederer, S. Darmanyan, and A. Kobyakov, in Spatial Optical Solitons, S. Trillo and W. E. Torruellas, eds. (Springer-Verlag, New York, 2001).

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Figures (4)

Fig. 1
Fig. 1

Experimental setup: PBS, polarizing beam splitter; BS, beam splitter; PZT, piezoelectric transducer; SBN, strontium barium niobate; V, voltage. Inset, photonic lattice created by optical induction.

Fig. 2
Fig. 2

Experimental and numerical results of a 2D discrete vector soliton. (a) Input, (b) discrete diffraction at low bias field, (c) mutual trapping, (d) decoupled output at high bias field. Rows 1 and 2 show the two components of the vector soliton from the experiment. Since the two components from the simulations are the same, only the U component is shown (row 3).

Fig. 3
Fig. 3

Exact solutions of scalar lattice solitons at E0=140 V/mm and I0=3Id. (a) Lattice pattern, (b) more localized soliton (with peak intensity I=Id), (c) less localized soliton (with peak intensity I=Id/4, (d) normalized power and intensity diagram.

Fig. 4
Fig. 4

Demonstration of dipolelike vector solitons in a 2D lattice. Top, experimental results. Bottom, corresponding numerical results. (a) Combined input; (b) and (c) combined output at low- and high-bias fields, respectively; (d), (e) U and V components from (c).

Equations (3)

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

iUz+2Ux2+2Uy2-E01+Ix,y+U2+V2U=0,
iVz+2Vx2+2Vy2-E01+Ix,y+U2+V2V=0,
2ϕx2+2ϕy2+μϕ-E01+Ix,y+ϕ2ϕ=0,

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