Abstract

We review theoretical and experimental results on spatial solitons in nematic liquid crystalline cells, including two-dimensional solitons in bulk and discrete solitons in one-dimensional waveguide arrays. In bulk we describe the propagation of continuous solitons in the presence of adjustable walk-off, their interaction with light-induced defects and refraction-reflection at a voltage-tunable interface. In optical lattices we address the transition from discrete diffraction to localization, as well as all-optical beam steering.

©2007 Optical Society of America

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  1. G. I. Stegeman, D. N. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” J. Sel. Top. Quantum Electron. 6, 1419–1426 (2000).
    [Crossref]
  2. S. Trillo and W. E. Torruellas,Spatial Solitons (Springer-Verlag, Berlin2001).
  3. Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic Press, San Diego, 2003).
  4. C. Conti and G. Assanto, “Nonlinear Optics Applications: Bright Spatial Solitons,” Encyclopedia of Modern Optics, Vol.5, 43–55, R. D. Guenther, D. G. Steel, and L. Bayvel, eds., (Elsevier, Oxford, 2004).
  5. M. Peccianti, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in Planar Nematic Liquid Crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
    [Crossref]
  6. C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
    [Crossref] [PubMed]
  7. C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
    [Crossref] [PubMed]
  8. M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of highly anisotropic spatial solitons and modulational instability in liquid crystals,” Nature (London) 432, 733M–737 (2004).
    [Crossref]
  9. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete propagation and spatial solitons in nematic liquid crystals,” Opt. Lett. 29, 1530–1532 (2004).
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  10. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford U. Press, London, 1993).
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    [PubMed]
  13. G. Assanto, M. Peccianti, and C. Conti, “Nematicons: optical spatial solitons in nematic liquid crystals,” Opt. Photon. News 14, 44–48 (2003).
    [Crossref]
  14. K. Kos, H. Meng, G. Salamo, M.-F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
    [Crossref]
  15. W. Królikowski, C. Denz, A. Stepkenz, M. Saffmanx, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclass. Opt. 10, 823–837 (1998).
    [Crossref]
  16. C. Rotschild, O. Cohen, O. Manela, M. Segev, and O. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality,” Phys. Rev. Lett. 95, 213904 (2005).
    [Crossref] [PubMed]
  17. A. Alberucci, M. Peccianti, G. Assanto, G. Coschignano, A.De Luca, and C. Umeton, “Self-healing generation of spatial solitons in liquid crystals,” Opt. Lett. 30, 1381–1383 (2005).
    [Crossref] [PubMed]
  18. A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, “Signal processing by opto-optical interactions between self-localized and free propagating beams in liquid crystals,” Appl. Phys. Lett. 87, 261104 (2005).
    [Crossref]
  19. S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, “Spatial Soliton All-Optical Logic Gates,” Photon. Technol. Lett. 18, 1287–1289 (2006).
    [Crossref]
  20. M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nature Physics (London) 2, 737–742 (2006).
    [Crossref]
  21. D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988).
    [Crossref] [PubMed]
  22. A. B. Aceves, C.de Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
    [Crossref]
  23. 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]
  24. A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” J. Quantum Electron. 39, 31–50 (2003).
    [Crossref]
  25. D. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
    [Crossref] [PubMed]
  26. 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, 4756–4759 (1999).
    [Crossref]
  27. R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett.,  83, 2726 (1998).
    [Crossref]
  28. S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti,“Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96, 243901 (2006).
    [Crossref] [PubMed]
  29. T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
    [Crossref] [PubMed]
  30. T. Pertsch, U. Peschel, and F. Lederer, “All-optical switching in quadratically nonlinear waveguide arrays,” Opt. Lett. 28, 102–104 (2003).
    [Crossref] [PubMed]
  31. N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
    [Crossref] [PubMed]
  32. R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,“ Phys. Rev. Lett. 93, 113902 (2004).
    [Crossref] [PubMed]
  33. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete light propagation and self-trapping in liquid crystals,” Opt. Express 13, 1808–1813 (2005).
    [Crossref] [PubMed]
  34. A. Fratalocchi and G. Assanto, “Discrete light localization in one dimensional nonlinear lattices with arbitrary non locality,” Phys. Rev. E 72, 066608 (2005).
    [Crossref]
  35. A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “All-optical switching and beam steering in tunable waveguide arrays,” Appl. Phys. Lett. 86, 51112 (2005).
    [Crossref]

2006 (3)

S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, “Spatial Soliton All-Optical Logic Gates,” Photon. Technol. Lett. 18, 1287–1289 (2006).
[Crossref]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nature Physics (London) 2, 737–742 (2006).
[Crossref]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti,“Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

2005 (6)

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete light propagation and self-trapping in liquid crystals,” Opt. Express 13, 1808–1813 (2005).
[Crossref] [PubMed]

A. Fratalocchi and G. Assanto, “Discrete light localization in one dimensional nonlinear lattices with arbitrary non locality,” Phys. Rev. E 72, 066608 (2005).
[Crossref]

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “All-optical switching and beam steering in tunable waveguide arrays,” Appl. Phys. Lett. 86, 51112 (2005).
[Crossref]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and O. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

A. Alberucci, M. Peccianti, G. Assanto, G. Coschignano, A.De Luca, and C. Umeton, “Self-healing generation of spatial solitons in liquid crystals,” Opt. Lett. 30, 1381–1383 (2005).
[Crossref] [PubMed]

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, “Signal processing by opto-optical interactions between self-localized and free propagating beams in liquid crystals,” Appl. Phys. Lett. 87, 261104 (2005).
[Crossref]

2004 (4)

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of highly anisotropic spatial solitons and modulational instability in liquid crystals,” Nature (London) 432, 733M–737 (2004).
[Crossref]

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete propagation and spatial solitons in nematic liquid crystals,” Opt. Lett. 29, 1530–1532 (2004).
[Crossref] [PubMed]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,“ Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

2003 (6)

T. Pertsch, U. Peschel, and F. Lederer, “All-optical switching in quadratically nonlinear waveguide arrays,” Opt. Lett. 28, 102–104 (2003).
[Crossref] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[Crossref] [PubMed]

G. Assanto, M. Peccianti, and C. Conti, “Nematicons: optical spatial solitons in nematic liquid crystals,” Opt. Photon. News 14, 44–48 (2003).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” J. Quantum Electron. 39, 31–50 (2003).
[Crossref]

D. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref] [PubMed]

2002 (1)

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

2001 (1)

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]

2000 (2)

G. I. Stegeman, D. N. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” J. Sel. Top. Quantum Electron. 6, 1419–1426 (2000).
[Crossref]

M. Peccianti, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in Planar Nematic Liquid Crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

1999 (1)

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, 4756–4759 (1999).
[Crossref]

1998 (2)

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett.,  83, 2726 (1998).
[Crossref]

W. Królikowski, C. Denz, A. Stepkenz, M. Saffmanx, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclass. Opt. 10, 823–837 (1998).
[Crossref]

1996 (2)

K. Kos, H. Meng, G. Salamo, M.-F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
[Crossref]

A. B. Aceves, C.de Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

1988 (1)

Aceves, A. B.

A. B. Aceves, C.de Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

Agrawal, G. P.

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic Press, San Diego, 2003).

Aitchison, J. S.

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, 4756–4759 (1999).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett.,  83, 2726 (1998).
[Crossref]

Alberucci, A.

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, “Signal processing by opto-optical interactions between self-localized and free propagating beams in liquid crystals,” Appl. Phys. Lett. 87, 261104 (2005).
[Crossref]

A. Alberucci, M. Peccianti, G. Assanto, G. Coschignano, A.De Luca, and C. Umeton, “Self-healing generation of spatial solitons in liquid crystals,” Opt. Lett. 30, 1381–1383 (2005).
[Crossref] [PubMed]

Angelis, C.de

A. B. Aceves, C.de Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

Assanto, G.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nature Physics (London) 2, 737–742 (2006).
[Crossref]

S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, “Spatial Soliton All-Optical Logic Gates,” Photon. Technol. Lett. 18, 1287–1289 (2006).
[Crossref]

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, “Signal processing by opto-optical interactions between self-localized and free propagating beams in liquid crystals,” Appl. Phys. Lett. 87, 261104 (2005).
[Crossref]

A. Fratalocchi and G. Assanto, “Discrete light localization in one dimensional nonlinear lattices with arbitrary non locality,” Phys. Rev. E 72, 066608 (2005).
[Crossref]

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “All-optical switching and beam steering in tunable waveguide arrays,” Appl. Phys. Lett. 86, 51112 (2005).
[Crossref]

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete light propagation and self-trapping in liquid crystals,” Opt. Express 13, 1808–1813 (2005).
[Crossref] [PubMed]

A. Alberucci, M. Peccianti, G. Assanto, G. Coschignano, A.De Luca, and C. Umeton, “Self-healing generation of spatial solitons in liquid crystals,” Opt. Lett. 30, 1381–1383 (2005).
[Crossref] [PubMed]

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete propagation and spatial solitons in nematic liquid crystals,” Opt. Lett. 29, 1530–1532 (2004).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of highly anisotropic spatial solitons and modulational instability in liquid crystals,” Nature (London) 432, 733M–737 (2004).
[Crossref]

G. Assanto, M. Peccianti, and C. Conti, “Nematicons: optical spatial solitons in nematic liquid crystals,” Opt. Photon. News 14, 44–48 (2003).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

M. Peccianti, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in Planar Nematic Liquid Crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

C. Conti and G. Assanto, “Nonlinear Optics Applications: Bright Spatial Solitons,” Encyclopedia of Modern Optics, Vol.5, 43–55, R. D. Guenther, D. G. Steel, and L. Bayvel, eds., (Elsevier, Oxford, 2004).

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, Cambridge, 1999).
[PubMed]

Brauer, A.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

Brzdakiewicz, K. A.

Carmon, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and O. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Christodoulides, D.

D. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref] [PubMed]

Christodoulides, D. N.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[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]

G. I. Stegeman, D. N. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” J. Sel. Top. Quantum Electron. 6, 1419–1426 (2000).
[Crossref]

D. N. Christodoulides and R. I. Joseph, “Discrete self-focusing in nonlinear arrays of coupled waveguides,” Opt. Lett. 13, 794–796 (1988).
[Crossref] [PubMed]

Cianci, E.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti,“Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

Cohen, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and O. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[Crossref] [PubMed]

Conti, C.

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of highly anisotropic spatial solitons and modulational instability in liquid crystals,” Nature (London) 432, 733M–737 (2004).
[Crossref]

G. Assanto, M. Peccianti, and C. Conti, “Nematicons: optical spatial solitons in nematic liquid crystals,” Opt. Photon. News 14, 44–48 (2003).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

C. Conti and G. Assanto, “Nonlinear Optics Applications: Bright Spatial Solitons,” Encyclopedia of Modern Optics, Vol.5, 43–55, R. D. Guenther, D. G. Steel, and L. Bayvel, eds., (Elsevier, Oxford, 2004).

Coschignano, G.

Denz, C.

W. Królikowski, C. Denz, A. Stepkenz, M. Saffmanx, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclass. Opt. 10, 823–837 (1998).
[Crossref]

Dyadyusha, A.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nature Physics (London) 2, 737–742 (2006).
[Crossref]

Efremidis, N. K.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[Crossref] [PubMed]

Eisenberg, H. S.

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” J. Quantum Electron. 39, 31–50 (2003).
[Crossref]

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, 4756–4759 (1999).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett.,  83, 2726 (1998).
[Crossref]

Eugenieva, E. D.

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]

Fleischer, J. W.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[Crossref] [PubMed]

Foglietti, V.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti,“Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

Fratalocchi, A.

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete light propagation and self-trapping in liquid crystals,” Opt. Express 13, 1808–1813 (2005).
[Crossref] [PubMed]

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “All-optical switching and beam steering in tunable waveguide arrays,” Appl. Phys. Lett. 86, 51112 (2005).
[Crossref]

A. Fratalocchi and G. Assanto, “Discrete light localization in one dimensional nonlinear lattices with arbitrary non locality,” Phys. Rev. E 72, 066608 (2005).
[Crossref]

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “Discrete propagation and spatial solitons in nematic liquid crystals,” Opt. Lett. 29, 1530–1532 (2004).
[Crossref] [PubMed]

Gennes, P. G. de

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford U. Press, London, 1993).
[PubMed]

Hudock, J.

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[Crossref] [PubMed]

Iwanow, R.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,“ Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

Joseph, R. I.

Kaczmarek, M.

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nature Physics (London) 2, 737–742 (2006).
[Crossref]

Karpierz, M. A.

Khoo, I. C.

M. Peccianti, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in Planar Nematic Liquid Crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).

Kivshar, Y. S.

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” J. Quantum Electron. 39, 31–50 (2003).
[Crossref]

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic Press, San Diego, 2003).

Kos, K.

K. Kos, H. Meng, G. Salamo, M.-F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
[Crossref]

Królikowski, W.

W. Królikowski, C. Denz, A. Stepkenz, M. Saffmanx, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclass. Opt. 10, 823–837 (1998).
[Crossref]

Laporta, P.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti,“Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

Lederer, F.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,“ Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

T. Pertsch, U. Peschel, and F. Lederer, “All-optical switching in quadratically nonlinear waveguide arrays,” Opt. Lett. 28, 102–104 (2003).
[Crossref] [PubMed]

D. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

A. B. Aceves, C.de Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

Lobino, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti,“Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

Longhi, S.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti,“Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

Luca, A. De

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of highly anisotropic spatial solitons and modulational instability in liquid crystals,” Nature (London) 432, 733M–737 (2004).
[Crossref]

M. Peccianti, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in Planar Nematic Liquid Crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

Luca, A.De

Luther-Davies, B.

W. Królikowski, C. Denz, A. Stepkenz, M. Saffmanx, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclass. Opt. 10, 823–837 (1998).
[Crossref]

Manela, O.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and O. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Marangoni, M.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti,“Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

Meng, H.

K. Kos, H. Meng, G. Salamo, M.-F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
[Crossref]

Min, Y.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,“ Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

Morandotti, R.

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, 4756–4759 (1999).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett.,  83, 2726 (1998).
[Crossref]

Muschall, R.

A. B. Aceves, C.de Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

Pasquazi, A.

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, “Signal processing by opto-optical interactions between self-localized and free propagating beams in liquid crystals,” Appl. Phys. Lett. 87, 261104 (2005).
[Crossref]

Peccianti, M.

S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, “Spatial Soliton All-Optical Logic Gates,” Photon. Technol. Lett. 18, 1287–1289 (2006).
[Crossref]

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nature Physics (London) 2, 737–742 (2006).
[Crossref]

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, “Signal processing by opto-optical interactions between self-localized and free propagating beams in liquid crystals,” Appl. Phys. Lett. 87, 261104 (2005).
[Crossref]

A. Alberucci, M. Peccianti, G. Assanto, G. Coschignano, A.De Luca, and C. Umeton, “Self-healing generation of spatial solitons in liquid crystals,” Opt. Lett. 30, 1381–1383 (2005).
[Crossref] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of highly anisotropic spatial solitons and modulational instability in liquid crystals,” Nature (London) 432, 733M–737 (2004).
[Crossref]

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

G. Assanto, M. Peccianti, and C. Conti, “Nematicons: optical spatial solitons in nematic liquid crystals,” Opt. Photon. News 14, 44–48 (2003).
[Crossref]

M. Peccianti, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in Planar Nematic Liquid Crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

Pertsch, T.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,“ Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

T. Pertsch, U. Peschel, and F. Lederer, “All-optical switching in quadratically nonlinear waveguide arrays,” Opt. Lett. 28, 102–104 (2003).
[Crossref] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

Peschel, T.

A. B. Aceves, C.de Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

Peschel, U.

T. Pertsch, U. Peschel, and F. Lederer, “All-optical switching in quadratically nonlinear waveguide arrays,” Opt. Lett. 28, 102–104 (2003).
[Crossref] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

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, 4756–4759 (1999).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett.,  83, 2726 (1998).
[Crossref]

Prost, J.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford U. Press, London, 1993).
[PubMed]

Ramponi, R.

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti,“Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

Rotschild, C.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and O. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Saffmanx, M.

W. Królikowski, C. Denz, A. Stepkenz, M. Saffmanx, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclass. Opt. 10, 823–837 (1998).
[Crossref]

Salamo, G.

K. Kos, H. Meng, G. Salamo, M.-F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
[Crossref]

Schiek, R.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,“ Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

Segev, M.

C. Rotschild, O. Cohen, O. Manela, M. Segev, and O. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[Crossref] [PubMed]

G. I. Stegeman, D. N. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” J. Sel. Top. Quantum Electron. 6, 1419–1426 (2000).
[Crossref]

K. Kos, H. Meng, G. Salamo, M.-F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
[Crossref]

Serak, S. V.

S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, “Spatial Soliton All-Optical Logic Gates,” Photon. Technol. Lett. 18, 1287–1289 (2006).
[Crossref]

Shih, M.-F.

K. Kos, H. Meng, G. Salamo, M.-F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
[Crossref]

Silberberg, Y.

D. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref] [PubMed]

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” J. Quantum Electron. 39, 31–50 (2003).
[Crossref]

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, 4756–4759 (1999).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett.,  83, 2726 (1998).
[Crossref]

Sohler, W.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,“ Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

Stegeman, G. I.

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,“ Phys. Rev. Lett. 93, 113902 (2004).
[Crossref] [PubMed]

G. I. Stegeman, D. N. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” J. Sel. Top. Quantum Electron. 6, 1419–1426 (2000).
[Crossref]

Stepkenz, A.

W. Królikowski, C. Denz, A. Stepkenz, M. Saffmanx, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclass. Opt. 10, 823–837 (1998).
[Crossref]

Sukhorukov, A. A.

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” J. Quantum Electron. 39, 31–50 (2003).
[Crossref]

Tabiryan, N. V.

S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, “Spatial Soliton All-Optical Logic Gates,” Photon. Technol. Lett. 18, 1287–1289 (2006).
[Crossref]

Torruellas, W. E.

S. Trillo and W. E. Torruellas,Spatial Solitons (Springer-Verlag, Berlin2001).

Trillo, S.

A. B. Aceves, C.de Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

S. Trillo and W. E. Torruellas,Spatial Solitons (Springer-Verlag, Berlin2001).

Umeton, C.

A. Alberucci, M. Peccianti, G. Assanto, G. Coschignano, A.De Luca, and C. Umeton, “Self-healing generation of spatial solitons in liquid crystals,” Opt. Lett. 30, 1381–1383 (2005).
[Crossref] [PubMed]

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of highly anisotropic spatial solitons and modulational instability in liquid crystals,” Nature (London) 432, 733M–737 (2004).
[Crossref]

M. Peccianti, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in Planar Nematic Liquid Crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

Valley, G. C.

K. Kos, H. Meng, G. Salamo, M.-F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
[Crossref]

Wabnitz, S.

A. B. Aceves, C.de Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, Cambridge, 1999).
[PubMed]

Zentgraf, T.

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

Appl. Phys. Lett. (3)

M. Peccianti, G. Assanto, A. De Luca, C. Umeton, and I. C. Khoo, “Electrically assisted self-confinement and waveguiding in Planar Nematic Liquid Crystal cells,” Appl. Phys. Lett. 77, 7–9 (2000).
[Crossref]

A. Pasquazi, A. Alberucci, M. Peccianti, and G. Assanto, “Signal processing by opto-optical interactions between self-localized and free propagating beams in liquid crystals,” Appl. Phys. Lett. 87, 261104 (2005).
[Crossref]

A. Fratalocchi, G. Assanto, K. A. Brzdakiewicz, and M. A. Karpierz, “All-optical switching and beam steering in tunable waveguide arrays,” Appl. Phys. Lett. 86, 51112 (2005).
[Crossref]

J. Quantum Electron. (1)

A. A. Sukhorukov, Y. S. Kivshar, H. S. Eisenberg, and Y. Silberberg, “Spatial optical solitons in waveguide arrays,” J. Quantum Electron. 39, 31–50 (2003).
[Crossref]

J. Sel. Top. Quantum Electron. (1)

G. I. Stegeman, D. N. Christodoulides, and M. Segev, “Optical spatial solitons: historical perspectives,” J. Sel. Top. Quantum Electron. 6, 1419–1426 (2000).
[Crossref]

Nature (1)

D. Christodoulides, F. Lederer, and Y. Silberberg, “Discretizing light behaviour in linear and nonlinear waveguide lattices,” Nature 424, 817–823 (2003).
[Crossref] [PubMed]

Nature (London) (1)

M. Peccianti, C. Conti, G. Assanto, A. De Luca, and C. Umeton, “Routing of highly anisotropic spatial solitons and modulational instability in liquid crystals,” Nature (London) 432, 733M–737 (2004).
[Crossref]

Nature Physics (London) (1)

M. Peccianti, A. Dyadyusha, M. Kaczmarek, and G. Assanto, “Tunable refraction and reflection of self-confined light beams,” Nature Physics (London) 2, 737–742 (2006).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Opt. Photon. News (1)

G. Assanto, M. Peccianti, and C. Conti, “Nematicons: optical spatial solitons in nematic liquid crystals,” Opt. Photon. News 14, 44–48 (2003).
[Crossref]

Photon. Technol. Lett. (1)

S. V. Serak, N. V. Tabiryan, M. Peccianti, and G. Assanto, “Spatial Soliton All-Optical Logic Gates,” Photon. Technol. Lett. 18, 1287–1289 (2006).
[Crossref]

Phys. Rev. E (3)

K. Kos, H. Meng, G. Salamo, M.-F. Shih, M. Segev, and G. C. Valley, “One-dimensional steady-state photorefractive screening solitons,” Phys. Rev. E 53, R4330–R4333 (1996).
[Crossref]

A. B. Aceves, C.de Angelis, T. Peschel, R. Muschall, F. Lederer, S. Trillo, and S. Wabnitz, “Discrete self-trapping, soliton interactions, and beam steering in nonlinear waveguide arrays,” Phys. Rev. E 53, 1172–1189 (1996).
[Crossref]

A. Fratalocchi and G. Assanto, “Discrete light localization in one dimensional nonlinear lattices with arbitrary non locality,” Phys. Rev. E 72, 066608 (2005).
[Crossref]

Phys. Rev. Lett. (10)

N. K. Efremidis, J. Hudock, D. N. Christodoulides, J. W. Fleischer, O. Cohen, and M. Segev, “Two-dimensional optical lattice solitons,” Phys. Rev. Lett. 91, 213906 (2003).
[Crossref] [PubMed]

R. Iwanow, R. Schiek, G. I. Stegeman, T. Pertsch, F. Lederer, Y. Min, and W. Sohler, “Observation of discrete quadratic solitons,“ Phys. Rev. Lett. 93, 113902 (2004).
[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]

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, 4756–4759 (1999).
[Crossref]

R. Morandotti, U. Peschel, J. S. Aitchison, H. S. Eisenberg, and Y. Silberberg, “Dynamics of discrete solitons in optical waveguide arrays,” Phys. Rev. Lett.,  83, 2726 (1998).
[Crossref]

S. Longhi, M. Marangoni, M. Lobino, R. Ramponi, P. Laporta, E. Cianci, and V. Foglietti,“Observation of Dynamic Localization in Periodically Curved Waveguide Arrays,” Phys. Rev. Lett. 96, 243901 (2006).
[Crossref] [PubMed]

T. Pertsch, T. Zentgraf, U. Peschel, A. Brauer, and F. Lederer, “Anomalous refraction and diffraction in discrete optical systems,” Phys. Rev. Lett. 88, 093901 (2002).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Route to nonlocality and observation of accessible solitons,” Phys. Rev. Lett. 91, 073901 (2003).
[Crossref] [PubMed]

C. Conti, M. Peccianti, and G. Assanto, “Observation of optical spatial solitons in a highly nonlocal medium,” Phys. Rev. Lett. 92, 113902 (2004).
[Crossref] [PubMed]

C. Rotschild, O. Cohen, O. Manela, M. Segev, and O. Carmon, “Solitons in Nonlinear Media with an Infinite Range of Nonlocality,” Phys. Rev. Lett. 95, 213904 (2005).
[Crossref] [PubMed]

Quantum Semiclass. Opt. (1)

W. Królikowski, C. Denz, A. Stepkenz, M. Saffmanx, and B. Luther-Davies, “Interaction of spatial photorefractive solitons,” Quantum Semiclass. Opt. 10, 823–837 (1998).
[Crossref]

Other (6)

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, 2nd ed. (Oxford U. Press, London, 1993).
[PubMed]

I. C. Khoo, Liquid Crystals: Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Cambridge University Press, Cambridge, 1999).
[PubMed]

S. Trillo and W. E. Torruellas,Spatial Solitons (Springer-Verlag, Berlin2001).

Y. S. Kivshar and G. P. Agrawal, Optical Solitons (Academic Press, San Diego, 2003).

C. Conti and G. Assanto, “Nonlinear Optics Applications: Bright Spatial Solitons,” Encyclopedia of Modern Optics, Vol.5, 43–55, R. D. Guenther, D. G. Steel, and L. Bayvel, eds., (Elsevier, Oxford, 2004).

Supplementary Material (3)

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Figures (12)

Fig. 1.
Fig. 1. (a). Inverse surface of wave normals with yz the extraordinary principal plane (ρ=ρ 0, ξ=0). (b). k0 , ke describe in the principal plane yz a circle and an ellipse, respectively, for the latter being Se the Poynting vector at an angle δ with ke ∥ k.

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Fig. 2.
Fig. 2. (a). Sketch of the planar NLC cell. (b). The application of a low-frequency electric field ELF1 (1 kHz) enables to tune the director orientation in the mid-plane at h/2. (c). The e-field A = A∙t̂ and Poynting vector S e =Se ∙ŝ lie in the extraordinary plane n̂k̂, with A⊥Se (i.e., t̂ ⊥ŝ). In (c) we introduce for convenience the rotated frame rts with r̂ = t̂+ŝ .

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Fig. 3.
Fig. 3. Spatial soliton trajectories versus applied external bias: a 5 mW Gaussian beam with wavevector along ẑ is injected into the NLC. The nematicon propagates at an angle owing to walk-off: the observable Poynting vector is steered with bias from 7 to ≈0°.

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Fig. 4.
Fig. 4. Effect of a defocusing perturbation induced by a control beam on the nematicon. (a) A perturbation (white circle) on-axis induces beam splitting; (b) A perturbation slightly off-axis deviates the nematicon, (c) with an effective steering linear on control power Pc .[18]

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Fig. 5.
Fig. 5. (a). Sketch of the NLC cell with an interface. On the top, two electrodes are separated by a straight gap. Voltages V1 and V2 are applied to regions 1 and 2, respectively, and define the orientation ξ and ρ of the director. (b) In the coordinate system xtp, p is along the gap and t̂ = p̂+x̂ (c) The distribution of ξ and ρ in the x̂t̂ plane are calculated by integration of system (3) for V 1=1.5 V and V 2=0.7 V in a 100 μm thick cell with the liquid crystal E7.

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Fig. 6.
Fig. 6. Evolution of a 4.5 mW nematicon impinging the interface at an angle of 79° with respect to t in a sample with ρ0 =0.5π and ξ0 =3°. (a). For ∆V= V 1-V 2 ≤ 0 V the beam refracts as it goes through the interface. (b). When ∆V≥0.5 V and above the critical angle of incidence the nematicon undergoes TIR.

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Fig. 7.
Fig. 7. (a). Sketch and (b) photograph of a one-dimensional NLC photonic lattice.

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Fig. 8.
Fig. 8. Optical microphotographs of the array through cross polarizers for various biases V.

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Fig. 9.
Fig. 9. (a). (2.067Kb). Movie on the generation of a discrete soliton in a waveguide array for increasing input power P, as predicted by CMT. [Media 1] (b). (268Kb). Movie showing BPM-calculated light propagation in the plane ŷẑ of the sample, evolving from discrete diffraction to discrete soliton as the power launched into a single channel ramps from 0.1.to 1.0 mW. Here V=0.74 V. [Media 2]

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Fig. 10.
Fig. 10. (177Kb). Movie showing the experimental generation of a discrete nematicon for increasing input power P. The cell parameters are ∧=h=6 μm and V=0.74 V. [Media 3]

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Fig. 11.
Fig. 11. Simulations of discrete beam steering: a) linear (P=0.1 mW) and b) nonlinear (P=2.0 mW) propagation in ŷẑ; c) corresponding intensity distributions in z=2 mm.

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Fig. 12.
Fig. 12. Observation of nonlinear beam steering. a) Discrete diffraction of a tilted beam for P=1mW; b) discrete soliton for P=7 mW; c) output intensity profiles in z=2 mm.

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Equations (13)

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F d = 1 2 Κ 11 ( ∇ ∙ n ̂ ) 2 + 1 2 Κ 22 ( n ̂ ∙ ∇ × n ̂ ) 2 + 1 2 Κ 33 ( n ̂ × ∇ × n ̂ ) 2 + F field
F field = − 1 2 〈 D ∙ E 〉 time = − ε 0 1 2 [ Δ ε LF ( n ̂ ∙ E LF ) 2 + 1 2 Δ ε opt ∣ n ̂ ∙ A ∣ 2 ] + g
{ ∂ F d ∂ ξ − ∑ j∊ ( x , y , z ) ∂ ∂ j ∂ F d ∂ ξ ∂ j = 0 ∂ F d ∂ ρ − ∑ j∊ ( x , y , z ) ∂ ∂ j ∂ F d ∂ ρ ∂ j = 0
2 ik 0 n e cos ( δ ) ∂ A ∂ s + D t ∂ 2 A ∂ t 2 + D r ∂ 2 A ∂ r 2 + k 0 2 Δ ε opt TψA = 0
D t = n ⊥ 2 ( Δ ε opt + n ⊥ 2 ) [ Δ ε + 2 n ⊥ 2 + Δ ε opt cos ⁡ ( 2 θ 0 ) ] 2 [ Δ ε opt 2 + 2 Δ ε opt n ⊥ 2 + 2 n ⊥ 4 + Δ ε opt ( Δ ε opt + 2 n ⊥ 2 ) cos ⁡ ( 2 θ 0 ) ] 2
D r = n ⊥ 2 [ Δ ε + 2 n ⊥ 2 + Δ ε opt cos ⁡ ( 2 θ 0 ) ] [ Δ ε opt 2 + 2 Δ ε opt n ⊥ 2 + 4 n ⊥ 4 + Δ ε opt ( Δ ε opt + 2 n ⊥ 2 ) cos ⁡ ( 2 θ 0 ) ] 2
T = n ⊥ 2 ( Δ ε opt + n ⊥ 2 ) sin ⁡ ( 2 θ 0 ) ( Δ ε opt + n ⊥ 2 ) 2 + n ⊥ 2 + [ ( Δ ε opt + n ⊥ 2 ) 2 − n ⊥ 2 ] cos ⁡ ( 2 θ 0 )
Κ ∇ ⊥ 2 ψ − Γ ( θ 0 ) ψ + ε 0 Δ ε opt 4 sin [ 2 θ 0 − 2 δ ] ∣ A ∣ 2 = 0
I = P 2 πη ( D t D r ) 1 4 exp [ − P η ( t 2 D t + r 2 D r ) ]
Κ ∇ xy 2 θ + ε 0 ( Δε LF ∣ E LFx ∣ 2 2 + Δε opt ∣ A x ∣ 2 4 ) sin 2 θ = 0
∂ ∂ x [ ( ε ⊥ + Δε LF sin 2 θ ) ∂ V ∂ x ] + n 0 2 ∂ V ∂ y = 0
i ∂ ϕ m ∂ ξ + ( ϕ m + 1 + ϕ m − 1 − 2 ϕ m ) + 2 ϕ m ∑ j = − ∞ ∞ exp ( − κ ∣ j + m ∣ ) coth ( κ 2 ) ∣ ϕ m ∣ 2 = 0
ϕ m = 8 cosh ( κ 2 ) sinh 3 μ sinh 3 ( μ + κ 2 ) 3 sinh 2 ( κ 2 ) [ sinh μ + sinh ( 3 μ + κ ) ( − 1 + 2 cosh 2 μ ) ] exp ( μ ∣ m ∣ )

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