Abstract

We experimentally demonstrate the interaction of an optical probe beam with both bright and dark blocker solitons formed with low optical light power in a saturable defocusing waveguide array in photorefractive lithium niobate. A phase insensitive interaction of the beams is achieved by means of counterpropagating light waves. Partial and full reflection (blocking) of the probe beam on the positive or negative light-induced defect is obtained, respectively, in good agreement with numerical simulations.

© 2006 Optical Society of America

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  1. D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled wave-guides," Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  2. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
    [CrossRef]
  3. D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  4. S. G. Johnson and J. D. Joannopoulos, Photonic Crystals: The Road from Theory to Practice, (Kluwer, Boston, 2002).
  5. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Experimental observation of linear and nonlinear optical Bloch oscillations," Phys. Rev. Lett. 83, 4756 (1999).
    [CrossRef]
  6. J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically-induced real time waveguide arrays," Phys. Rev. Lett. 90, 23902 (2003).
    [CrossRef]
  7. F. Chen, M. Stepić, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express 13, 4314 (2005).
    [CrossRef] [PubMed]
  8. H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
    [CrossRef] [PubMed]
  9. D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti and J. S. Aitchison, "Band structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 53902 (2003).
    [CrossRef]
  10. J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Express 13, 1780 (2005).
    [CrossRef] [PubMed]
  11. D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, "Gap solitons in waveguide arrays," Phys. Rev. Lett. 92, 93904 (2004).
    [CrossRef]
  12. J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically-induced nonlinear photonic lattices," Nature 422, 147 (2003).
    [CrossRef] [PubMed]
  13. Lj. Hadžievski, A. Maluckov, M. Stepić, and D. Kip, "Power controlled soliton stability and steering in lattices with saturable nonlinearity," Phys. Rev. Lett. 93, 33901 (2004).
    [CrossRef]
  14. H. Meng, G. Salamo, M. Shih, and M. Segev, "Coherent collisions of photorefractive solitons," Opt. Lett. 22, 448 (1997).
    [CrossRef] [PubMed]
  15. M. Shih, M. Segev, and G. Salamo, "Three dimensional spiraling of interacting spatial solitons," Phys. Rev. Lett. 78, 2551 (1997).
    [CrossRef]
  16. G. I. Stegeman and M. Segev, "Optical spatial solitons and their interactions: universality and diversity," Science 286, 1518 (1999).
    [CrossRef] [PubMed]
  17. D. N. Christodoulides and E. D. Eugenieva, "Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays," Phys. Rev. Lett. 87, 233901 (2001).
    [CrossRef] [PubMed]
  18. A. B. Aceves, C. DeAngelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, S. Wabnitz, "Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays," Phys. Rev. E 53, 1172 (1996).
    [CrossRef]
  19. I. E. Papacharalampous, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, "Soliton collisions in the discrete nonlinear Schrodinger equation," Phys. Rev. E 68, 046604 (2003).
    [CrossRef]
  20. J. Meier, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, M. Sorel, H. Yang, G. Salamo, J. S. Aitchison, and Y. Silberberg, "Nonlinear beam interactions in 1D discrete Kerr systems," Opt. Express 13, 1797 (2005).
    [CrossRef] [PubMed]
  21. J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Nonlinear optical beam interactions in waveguide arrays," Phys. Rev. Lett. 93, 093903 (2004).
    [CrossRef] [PubMed]
  22. J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Beam interactions with a blocker soliton in one-dimensional arrays," Opt. Lett. 30, 1027 (2005).
    [CrossRef] [PubMed]
  23. J. Meier, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, G. Salamo, H. Yang, M. Sorel, Y. Silberberg, and J. S. Aitchison, "Incoherent blocker soliton interaction in Kerr waveguide arrays," Opt. Lett. 30, 3174 (2005).
    [CrossRef] [PubMed]
  24. D. Kip, M. Wesner, C. Herden, and V. Shandarov, "Interaction of spatial photorefractive solitons in a planar waveguide," Appl. Phys. B 68, 971 (1999).
    [CrossRef]
  25. W. Królikowski, B. Luther-Davies, C. Denz, and T. Tschudi, "Annihilation of photorefractive solitons," Opt. Lett. 23, 97 (1998).
    [CrossRef]
  26. D. Kip, M. Soljačić, M. Segev, S. M. Sears, and D. N. Christodoulides, "(1+1) Dimensional modulation instability of spatially-incoherent light," J. Opt. Soc. Am. B 19, 502 (2002).
    [CrossRef]
  27. E. Smirnov, C. E. Rüter, M. Stepić, V. Shandarov, and D. Kip, "Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays," arXiv:nlin.PS/0607030 (2006).
  28. M. Stepić, E. Smirnov, C. E. Rüter, V. Shandarov, and D. Kip, "Beam interactions in one-dimensional saturable waveguide arrays," will appear in PRE, arXiv:physics/0607028 (2006).
  29. M. Matuszewski, C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, A. Mitchell, M. Trippenbach, M. W. Austin, W. Królikowski, and Yu. S. Kivshar, "Crossover from self-defocusing to discrete trapping in nonlinear waveguide arrays," Opt. Express 14, 254 (2006).
    [CrossRef] [PubMed]
  30. For r < 1.1 only partial focusing of the narrow input beam is achieved. Nevertheless for such small intensity ratios (i.e. in the Kerr regime) bright solitons may still be obtained using larger soliton (input) widths.

Other (30)

D. N. Christodoulides and R. I. Joseph, "Discrete self-focusing in nonlinear arrays of coupled wave-guides," Opt. Lett. 13, 794 (1988).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, "Discrete spatial optical solitons in waveguide arrays," Phys. Rev. Lett. 81, 3383 (1998).
[CrossRef]

D. N. Christodoulides, F. Lederer, and Y. Silberberg, "Discretizing light behaviour in linear and nonlinear waveguide lattices," Nature 424, 817 (2003).
[CrossRef] [PubMed]

S. G. Johnson and J. D. Joannopoulos, Photonic Crystals: The Road from Theory to Practice, (Kluwer, Boston, 2002).

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, "Experimental observation of linear and nonlinear optical Bloch oscillations," Phys. Rev. Lett. 83, 4756 (1999).
[CrossRef]

J. W. Fleischer, T. Carmon, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of discrete solitons in optically-induced real time waveguide arrays," Phys. Rev. Lett. 90, 23902 (2003).
[CrossRef]

F. Chen, M. Stepić, C. E. Rüter, D. Runde, D. Kip, V. Shandarov, O. Manela, and M. Segev, "Discrete diffraction and spatial gap solitons in photovoltaic LiNbO3 waveguide arrays," Opt. Express 13, 4314 (2005).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Diffraction management," Phys. Rev. Lett. 85, 1863 (2000).
[CrossRef] [PubMed]

D. Mandelik, H. S. Eisenberg, Y. Silberberg, R. Morandotti and J. S. Aitchison, "Band structure of waveguide arrays and excitation of Floquet-Bloch solitons," Phys. Rev. Lett. 90, 53902 (2003).
[CrossRef]

J. W. Fleischer, G. Bartal, O. Cohen, T. Schwartz, O. Manela, B. Freedman, M. Segev, H. Buljan, and N. K. Efremidis, "Spatial photonics in nonlinear waveguide arrays," Opt. Express 13, 1780 (2005).
[CrossRef] [PubMed]

D. Mandelik, R. Morandotti, J. S. Aitchison, and Y. Silberberg, "Gap solitons in waveguide arrays," Phys. Rev. Lett. 92, 93904 (2004).
[CrossRef]

J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, "Observation of two-dimensional discrete solitons in optically-induced nonlinear photonic lattices," Nature 422, 147 (2003).
[CrossRef] [PubMed]

Lj. Hadžievski, A. Maluckov, M. Stepić, and D. Kip, "Power controlled soliton stability and steering in lattices with saturable nonlinearity," Phys. Rev. Lett. 93, 33901 (2004).
[CrossRef]

H. Meng, G. Salamo, M. Shih, and M. Segev, "Coherent collisions of photorefractive solitons," Opt. Lett. 22, 448 (1997).
[CrossRef] [PubMed]

M. Shih, M. Segev, and G. Salamo, "Three dimensional spiraling of interacting spatial solitons," Phys. Rev. Lett. 78, 2551 (1997).
[CrossRef]

G. I. Stegeman and M. Segev, "Optical spatial solitons and their interactions: universality and diversity," Science 286, 1518 (1999).
[CrossRef] [PubMed]

D. N. Christodoulides and E. D. Eugenieva, "Blocking and routing discrete solitons in two-dimensional networks of nonlinear waveguide arrays," Phys. Rev. Lett. 87, 233901 (2001).
[CrossRef] [PubMed]

A. B. Aceves, C. DeAngelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, S. Wabnitz, "Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays," Phys. Rev. E 53, 1172 (1996).
[CrossRef]

I. E. Papacharalampous, P. G. Kevrekidis, B. A. Malomed, and D. J. Frantzeskakis, "Soliton collisions in the discrete nonlinear Schrodinger equation," Phys. Rev. E 68, 046604 (2003).
[CrossRef]

J. Meier, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, M. Sorel, H. Yang, G. Salamo, J. S. Aitchison, and Y. Silberberg, "Nonlinear beam interactions in 1D discrete Kerr systems," Opt. Express 13, 1797 (2005).
[CrossRef] [PubMed]

J. Meier, G. I. Stegeman, Y. Silberberg, R. Morandotti, and J. S. Aitchison, "Nonlinear optical beam interactions in waveguide arrays," Phys. Rev. Lett. 93, 093903 (2004).
[CrossRef] [PubMed]

J. Meier, G. I. Stegeman, D. N. Christodoulides, Y. Silberberg, H. Yang, G. Salamo, M. Sorel, and J. S. Aitchison, "Beam interactions with a blocker soliton in one-dimensional arrays," Opt. Lett. 30, 1027 (2005).
[CrossRef] [PubMed]

J. Meier, G. I. Stegeman, D. N. Christodoulides, R. Morandotti, G. Salamo, H. Yang, M. Sorel, Y. Silberberg, and J. S. Aitchison, "Incoherent blocker soliton interaction in Kerr waveguide arrays," Opt. Lett. 30, 3174 (2005).
[CrossRef] [PubMed]

D. Kip, M. Wesner, C. Herden, and V. Shandarov, "Interaction of spatial photorefractive solitons in a planar waveguide," Appl. Phys. B 68, 971 (1999).
[CrossRef]

W. Królikowski, B. Luther-Davies, C. Denz, and T. Tschudi, "Annihilation of photorefractive solitons," Opt. Lett. 23, 97 (1998).
[CrossRef]

D. Kip, M. Soljačić, M. Segev, S. M. Sears, and D. N. Christodoulides, "(1+1) Dimensional modulation instability of spatially-incoherent light," J. Opt. Soc. Am. B 19, 502 (2002).
[CrossRef]

E. Smirnov, C. E. Rüter, M. Stepić, V. Shandarov, and D. Kip, "Formation and light guiding properties of dark solitons in one-dimensional waveguide arrays," arXiv:nlin.PS/0607030 (2006).

M. Stepić, E. Smirnov, C. E. Rüter, V. Shandarov, and D. Kip, "Beam interactions in one-dimensional saturable waveguide arrays," will appear in PRE, arXiv:physics/0607028 (2006).

M. Matuszewski, C. R. Rosberg, D. N. Neshev, A. A. Sukhorukov, A. Mitchell, M. Trippenbach, M. W. Austin, W. Królikowski, and Yu. S. Kivshar, "Crossover from self-defocusing to discrete trapping in nonlinear waveguide arrays," Opt. Express 14, 254 (2006).
[CrossRef] [PubMed]

For r < 1.1 only partial focusing of the narrow input beam is achieved. Nevertheless for such small intensity ratios (i.e. in the Kerr regime) bright solitons may still be obtained using larger soliton (input) widths.

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Figures (6)

Fig. 1.
Fig. 1.

Scheme of the experimental setup: M’s, mirrors; BS’s, beam splitters; CL, cylindrical lens; ML’s, 20× microscope lenses; WA, waveguide array; CCD’s, CCD cameras.

Fig. 2.
Fig. 2.

Linear propagation of blocker and probe beams: comparison of simulation (left hand side) and experiment (right hand side). a) Discrete diffraction for (bright) singlechannel excitation; b) discrete diffraction of a dark notch covering about 3 channels; and c) propagation of a broader probe beam in the array.

Fig. 3.
Fig. 3.

Reflection of the probe beam by a bright blocker soliton. a), b) Temporal evolution of the intensity on the output facet for probe (Pin =10nW) and bright soliton beam (Pin =6µW), respectively; c), d) Simulation of propagation of probe beam (r=0.01, propagation from top to bottom) and bright soliton (r=6, propagation from bottom to top), respectively, in steady-state.

Fig. 4.
Fig. 4.

Reflection of the probe beam by a dark blocker soliton. a) and b): Linear output (t=0) and nonlinear steady-state (t=15 min) intensity distribution on the output face for probe and dark soliton beam, respectively; c) and d): Simulation of propagation of probe beam (r=0.01, propagation from top to bottom) and dark soliton (r=0.4, propagation from bottom to top), respectively, in steady-state.

Fig. 5.
Fig. 5.

Linear and nonlinear refractive index profiles of the waveguide array: permanent periodic refractive index modulation (blue solid line, left hand scale) and nonlinear lightinduced refractive index changes (green solid line, right hand scale) for a) bright blocker soliton (r=6) and b) dark blocker soliton (r=2).

Fig. 6.
Fig. 6.

Ratio Ir /(Ir +It ) of reflected and total transmitted intensity as a function of intensity ratio r for bright blocker soliton (solid line) and dark blocker soliton (dotted line), respectively. A bright soliton only exists for input power ratios r>1.1 (vertical dotted line).

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