Abstract

The recent proposal of optical induction for producing nonlinear photonic lattices has revolutionized the study of nonlinear waves in waveguide arrays. In particular, it enabled the first observation of (2+1) dimensional lattice solitons, which were the first 2D solitons observed in any nonlinear periodic system in nature. Since then, progress has been rapid, with many fundamental discoveries made within the past two years. Here, we review our theoretical and experimental contributions to this effort.

© 2005 Optical Society of America

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  1. E. Yablonovich, �??Inhibited spontaneous emission in solid-state and electronics,�?? Phys. Rev. Lett. 58, 2059 (1987).
    [CrossRef]
  2. D.N. Christodoulides and R.I. Joseph, �??Discrete self-focusing in nonlinear arrays of coupled waveguides,�?? Opt. Lett. 13, 794 (1988).
    [CrossRef] [PubMed]
  3. A.L. Jones, �??Coupling of optical fibers and scattering in fibers,�?? J. Opt. Soc. Am. 55, 261 (1965).
    [CrossRef]
  4. J.M. Ziman, Principles of the theory of solids, 2nd ed. (Cambridge University Press, Cambridge, 1979
  5. S. Somekh, E. Garmire, A. Yariv, H.L. Garvin, and R.G. Hunsperger, �??Channel optical waveguide directional couplers,�?? Appl. Phys. Lett. 22, 46 (1973).
    [CrossRef]
  6. D.N. Christodoulides, F. Lederer, and Y. Silberberg, �??Discretizing light behavior in linear and nonlinear waveguide lattices,�?? Nature 424, 817 (2003).
    [CrossRef] [PubMed]
  7. P. St. J. Russell, �??Optics of Floquet-Bloch waves in dielectric gratings,�?? Appl. Phys. B 39, 231 (1986).
    [CrossRef]
  8. P. Russell, �??Photonic crystal fibers,�?? Science 299, 358 (2003).
    [CrossRef] [PubMed]
  9. H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, �??Diffraction Management,�?? Phys. Rev. Lett. 85, 1863 (2000).
    [CrossRef] [PubMed]
  10. 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]
  11. Y.S. Kivshar, �??Self-localization in arrays of defocusing waveguides,�?? Opt. Lett. 18, 1147 (1993).
    [CrossRef] [PubMed]
  12. J. Feng, �??Alternative scheme for studying gap solitons in infinite periodic Kerr media,�?? Opt. Lett. 18, 1302 (1993).
    [CrossRef] [PubMed]
  13. R. Morandotti, H.S. Eisenberg, Y. Silberberg, M. Sorel, and J.S. Aitchison, �??Self-focusing and defocusing in waveguide arrays,�?? Phys. Rev. Lett. 86, 3296 (2001).
    [CrossRef] [PubMed]
  14. 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, 023902 (2003).
    [CrossRef] [PubMed]
  15. M.J. Ablowitz and Z.H. Musslimani, �??Discrete diffraction managed spatial solitons,�?? Phys. Rev. Lett. 87, 254102 (2001).
    [CrossRef] [PubMed]
  16. W. Chen and D.L. Mills, �??Gap solitons and the nonlinear optical response of superlattices,�?? Phys. Rev. Lett. 58, 160 (1987);
    [CrossRef] [PubMed]
  17. D.N. Christodoulides and R.I. Joseph, �??Slow Bragg solitons in nonlinear periodic structures,�?? Phys. Rev. Lett. 62, 1746 (1989);
    [CrossRef] [PubMed]
  18. A.B. Aceves and S. Wabnitz, �??Self-induced transparency solitons in nonlinear refractive periodic media,�?? Phys. Lett. A 141, 37 (1989).
    [CrossRef]
  19. J.E. Sipe and H.G. Winful, �??Nonlinear Schrodinger solitons in a periodic structure,�?? Opt. Lett. 13, 132 (1988).
    [CrossRef] [PubMed]
  20. B.J. Eggleton, R.E. Slusher, C.M. deSterke, P.A. Krug, and J.E. Sipe, �??Bragg grating solitons,�?? Phys. Rev. Lett. 76, 1627 (1996).
    [CrossRef] [PubMed]
  21. O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D.N. Christodoulides, �??Multiband vector lattice solitons,�?? Phys. Rev. Lett. 91, 113901 (2003).
    [CrossRef] [PubMed]
  22. A.A. Sukhorukov and Y.S. Kivshar, �??Multigap discrete vector solitons,�?? Phys. Rev. Lett. 91, 113902 (2003).
    [CrossRef] [PubMed]
  23. N.K. Efremidis, J. Hudock, D.N. Christodoulides, J.W. Fleischer, O. Cohen, and M. Segev, �??Twodimensional optical lattice solitons,�?? Phys. Rev. Lett. 91, 213906 (2003).
    [CrossRef] [PubMed]
  24. P. Millar, J.S. Aitchison, J.U. Kang, G.I. Stegeman, A. Villeneuve, G.T. Kennedy, and W. Sibbett, �??Nonlinear waveguide arrays in AlGaAs,�?? J. Opt. Soc. Am. B 14, 3224 (1997).
    [CrossRef]
  25. N.K. Efremidis S. Sears, D.N. Christodoulides, J.W. Fleischer, and M. Segev, �??Discrete solitons in photorefractive optically induced photonic lattices,�?? Phys. Rev. E 66, 046602 (2002).
    [CrossRef]
  26. 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]
  27. A. Fratalocchi, G. Assanto, K.A. Brzdakiewicz, and M.A. Karpierz, �??Discrete propagation and spatial solitons in nematic liquid crystals,�?? Opt. Lett. 29, 1530 (2004).
    [CrossRef] [PubMed]
  28. T. Pertsch, U. Peshchl, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, �??Nonlinearity and disorder in fiber arrays,�?? Phys. Rev. Lett. 93, 053901 (2004).
    [CrossRef] [PubMed]
  29. E.J. Bochove, P.K. Cheo, and G.G. King, �??Self-organization in a multicore fiber laser array,�?? Opt. Lett. 28, 1200 (2003).
    [CrossRef] [PubMed]
  30. T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, �??Discrete diffraction in two-dimensional arrays of coupled waveguides in silica,�?? Opt. Lett. 29, 468 (2004).
    [CrossRef] [PubMed]
  31. M. Segev, G.C. Valley, B. Crosignani, P.D. Porto, and A. Yariv, �??Steady-state spatial screening solitons in photorefractive materials with external applied field,�?? Phys. Rev. Lett. 73, 3211 (1994).
    [CrossRef] [PubMed]
  32. D.N. Christodoulides and M.I. Carvalho, �??Bright, dark, and gray spatial soliton states in photorefractive media,�?? J. Opt. Soc. Am B 12, 1628 (1995).
    [CrossRef]
  33. M. Klotz, H. Meng, G. Salamo, M. Segev, and S. R. Montgomery, �??Fixing the photorefractive soliton,�?? Opt. Lett. 24, 77 (1999).
    [CrossRef]
  34. G. I. Stegeman and M. Segev, �??Optical spatial solitons and their interactions: universality and diversity,�?? Science 286, 1518 (1999).
    [CrossRef] [PubMed]
  35. S. Lan, E. DelRe, Z. Chen, M. Shih and M. Segev, �??Directional coupler with soliton-induced waveguides,�?? Opt. Lett. 24, 475 (1999).
    [CrossRef]
  36. M. Klotz, M. Crosser, A. Guo, M. Henry, G.J. Salamo, M. Segev, and G.L. Wood, �??Fixing solitonic Y-junctions in photorefractive strontium barium niobate,�?? App. Phys. Lett. 79, 1423 (2001).
    [CrossRef]
  37. A. Guo, M. Henry, G.J. Salamo, M. Segev, and G.L. Wood, �??Fixing multiple waveguides induced by photorefractive solitons: directional couplers and beam splitters,�?? Opt. Lett. 26, 1274 (2001).
    [CrossRef]
  38. A. Bramati, W. Chinaglia, S. Minardi, and P. Di Trapani, �??Reconstruction of blurred images by controlled formation of spatial solitons,�?? Opt. Lett. 26, 1409 (2001).
    [CrossRef]
  39. J. Petter, J. Schröder, D. Träger, and C. Denz, �??Optical control of arrays of photorefractive screening solitons,�?? Opt. Lett. 28, 438 (2003).
    [CrossRef] [PubMed]
  40. H. Martin, E.D. Eugenieva, Z. Chen, and D.N. Christodoulides, �??Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,�?? Phys. Rev. Lett. 92, 123902 (2004).
    [CrossRef] [PubMed]
  41. Kartashov YV, Aleshkevich VA, Vysloukh VA, Egorov AA, Zelenina AS, �??Stability analysis of (1+1)-dimensional cnoidal waves in media with cubic nonlinearity�?? Phys. Rev. E 67, 036613 (2003).
    [CrossRef]
  42. A.S. Desyatnikov, E.A. Ostrovskaya, Y.S. Kivshar, and C. Denz, �??Composite Band-Gap Solitons in Nonlinear Optically Induced Lattices,�?? Phys. Rev. Lett. 91, 153902 (2003).
    [CrossRef] [PubMed]
  43. H.J. Shin, �??Solutions for solitons in nonlinear optically induced lattices,�?? Phys. Rev. E 69, 067602 (2004).
    [CrossRef]
  44. G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, and M. Segev, �??Brillouin zone spectroscopy of nonlinear photonic lattices,�?? submitted to Phys. Rev. Lett.
  45. F.S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, �??Josephson junction arrays with Bose-Einstein condensates,�?? Science 293, 843 (2001).
    [CrossRef] [PubMed]
  46. D. Mandelik, H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, �??Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,�?? Phys. Rev. Lett. 90, 053902 (2003).
    [CrossRef] [PubMed]
  47. T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, �??Optical Bloch oscillations in temperature tuned waveguide arrays,�?? Phys. Rev. Lett. 83, 4752 (1999).
    [CrossRef]
  48. R. Morandotti, U. Peschel, J.S. Aitchison, H.S. Eisenberg, and Y. Silberberg, �??Experimental observation of linear and nonlinear optics Bloch oscillations,�?? Phys. Rev. Lett. 83, 4756 (1999).
    [CrossRef]
  49. R. Morandotti, H.S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C.R. Stanley, and J.S. Aitchison, �??Interactions of discrete solitons with structural defects,�?? Opt. Lett. 28, 834 (2003).
    [CrossRef] [PubMed]
  50. J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J.S. Aitchison, �??Discrete vector solitons in Kerr nonlinear waveguide arrays,�?? Phys. Rev. Lett. 91, 143907 (2003).
    [CrossRef] [PubMed]
  51. 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]
  52. D. Mandelik, H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, �??Observation of mutually trapped multiband optical breathers in waveguide arrays,�?? Phys. Rev. Lett. 90, 253902 (2003).
    [CrossRef] [PubMed]
  53. J. Meier, G.I. Stegeman, D.N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J.S. Aitchison, �??Experimental observation of discrete modulational instability,�?? Phys. Rev. Lett. 92, 163902 (2004).
    [CrossRef] [PubMed]
  54. D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, �??Spatial solitons in optically induced gratings,�?? Opt. Lett. 28, 710 (2003).
    [CrossRef] [PubMed]
  55. J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, �??Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory and experiment,�?? Stud. App. Math. 113, 389 (2004).
    [CrossRef]
  56. J.W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D.N. Christodoulides, �??Observation of vortex-ring �??discrete�?? solitons in 2D photonic lattices,�?? Phys. Rev. Lett. 92, 123904 (2004).
    [CrossRef] [PubMed]
  57. D.N. Neshev, T.J. Alexander, E.A. Ostrovskaya, Y.S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, �??Observation of discrete vortex solitons in optically induced photonic lattices,�?? Phys. Rev. Lett. 92, 123903 (2004).
    [CrossRef] [PubMed]
  58. G. Bartal, O. Manela, O. Cohen, J.W. Fleischer, and M. Segev, �??Observation of 2nd-band vortex solitons in 2D photonic lattices,�?? submitted to Phys. Rev. Lett..
  59. O. Cohen, G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, and D.N. Christodoulides, �??Observation of random-phase lattice solitons,�?? Nature 433, 500 (2005).
    [CrossRef] [PubMed]
  60. O. Cohen, B. Freedman, J.W. Fleischer, M. Segev, and D.N. Christodoulides, �??Grating-mediated waveguiding,�?? Phys. Rev. Lett. 93, 103902 (2004).
    [CrossRef] [PubMed]
  61. B. Freedman, O. Cohen, O. Manela, J.W. Fleischer, M. Segev, and D.N. Christodoulides, �??Grating-mediated waveguiding and holographic solitons,�?? J. Opt. Soc. Am. B (to be published).
  62. O. Cohen, T. Carmon, M. Segev, and S. Odoulov, �??Holographic solitons,�?? Opt. Lett. 27, 2031 (2002).
    [CrossRef]
  63. A.A. Sukhorukov, D. Neshev, W. Krolikowski, and Y.S. Kivshar, �??Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices,�?? Phys. Rev. Lett. 92, 093901 (2004).
    [CrossRef] [PubMed]
  64. R. Morandotti, D. Mandelik, Y. Silberberg, J.S. Aitchison, M. Sorel, D. Christodoulides, A.A. Sukhorukov, and Y.S. Kivshar, �??Observation of discrete gap solitons in binary waveguide arrays,�?? Opt. Lett. 29, 2890 (2004).
    [CrossRef]
  65. D. Mandelik, R. Morandotti, J.S. Aitchison, and Y. Silberberg, �??Gap solitons in waveguide arrays,�?? Phys. Rev. Lett. 92, 093904 (2004).
    [CrossRef] [PubMed]
  66. D. Neshev, A.A. Sukhorukov, B. Hanna, W. Krolikowski, and Y.S. Kivshar, �??Controlled generation and steering of spatial gap solitons,�?? Phys. Rev. Lett. 93, 083905 (2004).
    [CrossRef] [PubMed]
  67. 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]
  68. 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]
  69. B.A. Malomed and P.G. Kevrekidis, �??Discrete vortex solitons,�?? Phys. Rev. E 64, 026601 (2001).
    [CrossRef]
  70. S. Darmanyan, A. Kobyakov, and F. Lederer, �??Stability of strongly localized excitations in discrete media with cubic nonlinearity,�?? JETP 86, 682 (1998).
    [CrossRef]
  71. J. Yang and Z.H. Musslimani, �??Fundamental and vortex solitons in a two-dimensional optical lattice,�?? Opt. Lett. 28, 2094 (2003).
    [CrossRef] [PubMed]
  72. C. Anastassiou, C. Pigier, M. Segev, D. Kip, E.D. Eugenieva, and D.N. Christodoulides, �??Self-trapping of bright rings,�?? Opt. Lett. 26, 911 (2001).
    [CrossRef]
  73. Y.S. Kivshar and B. Luther-Davies, �??Dark optical solitons: physics and applications,�?? Phys. Rep. 298, 81 (1998).
    [CrossRef]
  74. A.J. Sievers and S. Takeno, �??Intrinsic localized modes in anharmonic crystals,�?? Phys. Rev. Lett. 61, 970 (1988).
    [CrossRef] [PubMed]
  75. J.B. Page, �??Asymptotic solutions for localized vibrational modes in strongly anharmonic periodic systems,�?? Phys. Rev. B 41, 7835 (1990).
    [CrossRef]
  76. T.J. Alexander, A.A. Sukhorukov, and Y.S. Kivshar, �??Asymmetric vortex solitons in nonlinear periodic lattices,�?? Phys. Rev. Lett. 93, 063901 (2004).
    [CrossRef] [PubMed]
  77. P.G. Kevrekidis, B.A. Malomed, Z.G. Chen, and D.J. Frantzeskakis, �??Stable higher-order vortices and quasivortices in the discrete nonlinear Schrödinger equation,�?? Phys. Rev. E 70, 056612 (2004).
    [CrossRef]
  78. O. Manela, O. Cohen, G. Bartal, J.W. Fleischer, and M. Segev, �??Two-dimensional higher-band vortex lattice solitons,�?? Opt. Lett. 29, 2049 (2004).
    [CrossRef] [PubMed]
  79. S.V. Manakov, �??On the theory of two-dimensional stationary self-focusing of electromagnetic waves,�?? Sov. Phys. JETP 38, 248 (1974).
  80. M. Mitchell, Z. Chen, M. Shih, and M. Segev, �??Self-trapping of partially spatially incoherent light,�?? Phys. Rev. Lett. 77, 490 (1996).
    [CrossRef] [PubMed]
  81. S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, �??Strongly localized vectorial modes in nonlinear waveguide arrays,�?? Phys. Rev. E 57, 3520 (1998).
    [CrossRef]
  82. H. Buljan, O. Cohen, J.W. Fleischer, T. Schwartz, M. Segev, Z.H. Musslimani, N.K. Efremidis, and D.N. Christodoulides, �??Random-phase solitons in nonlinear periodic lattices,�?? Phys. Rev. Lett. 92, 223901 (2004).
    [CrossRef] [PubMed]
  83. Z. Chen, A. Bezryadina, I. Makasyuk, and J. Yang, �??Observation of two-dimensional lattice vector solitons,�?? Opt. Lett. 29, 1656 (2004).
    [CrossRef] [PubMed]
  84. E. Fermi, J. Pasta, and S. Ulam, �??Studies of nonlinear problems I,�?? S. Report LA-1940 (LANL, Los Alamos, 1955).
  85. H. Buljan, M. Segev, and A. Vardi, �??Incoherent matter wave solitons: mutual self-trapping of a Bose-Einstein condensate and its surrounding thermal cloud,�?? submitted to Phys. Rev. Lett.
  86. E.D. Eugenieva, N.K. Efremidis, and D.N. Christodoulides, �??Design of switching junctions in twodimensional discrete soliton networks,�?? Opt. Lett. 26, 1978 (2001).
    [CrossRef]

App. Phys. Lett. (1)

M. Klotz, M. Crosser, A. Guo, M. Henry, G.J. Salamo, M. Segev, and G.L. Wood, �??Fixing solitonic Y-junctions in photorefractive strontium barium niobate,�?? App. Phys. Lett. 79, 1423 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

S. Somekh, E. Garmire, A. Yariv, H.L. Garvin, and R.G. Hunsperger, �??Channel optical waveguide directional couplers,�?? Appl. Phys. Lett. 22, 46 (1973).
[CrossRef]

Apply. Phys. B (1)

P. St. J. Russell, �??Optics of Floquet-Bloch waves in dielectric gratings,�?? Appl. Phys. B 39, 231 (1986).
[CrossRef]

J. Opt. Soc. Am (1)

A.L. Jones, �??Coupling of optical fibers and scattering in fibers,�?? J. Opt. Soc. Am. 55, 261 (1965).
[CrossRef]

J. Opt. Soc. Am B (1)

D.N. Christodoulides and M.I. Carvalho, �??Bright, dark, and gray spatial soliton states in photorefractive media,�?? J. Opt. Soc. Am B 12, 1628 (1995).
[CrossRef]

J. Opt. Soc. Am. B (2)

P. Millar, J.S. Aitchison, J.U. Kang, G.I. Stegeman, A. Villeneuve, G.T. Kennedy, and W. Sibbett, �??Nonlinear waveguide arrays in AlGaAs,�?? J. Opt. Soc. Am. B 14, 3224 (1997).
[CrossRef]

B. Freedman, O. Cohen, O. Manela, J.W. Fleischer, M. Segev, and D.N. Christodoulides, �??Grating-mediated waveguiding and holographic solitons,�?? J. Opt. Soc. Am. B (to be published).

JTEP (1)

S. Darmanyan, A. Kobyakov, and F. Lederer, �??Stability of strongly localized excitations in discrete media with cubic nonlinearity,�?? JETP 86, 682 (1998).
[CrossRef]

Nature (3)

O. Cohen, G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, and D.N. Christodoulides, �??Observation of random-phase lattice solitons,�?? Nature 433, 500 (2005).
[CrossRef] [PubMed]

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]

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

Opt. Lett. (21)

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

Y.S. Kivshar, �??Self-localization in arrays of defocusing waveguides,�?? Opt. Lett. 18, 1147 (1993).
[CrossRef] [PubMed]

J. Feng, �??Alternative scheme for studying gap solitons in infinite periodic Kerr media,�?? Opt. Lett. 18, 1302 (1993).
[CrossRef] [PubMed]

J.E. Sipe and H.G. Winful, �??Nonlinear Schrodinger solitons in a periodic structure,�?? Opt. Lett. 13, 132 (1988).
[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 (2004).
[CrossRef] [PubMed]

E.J. Bochove, P.K. Cheo, and G.G. King, �??Self-organization in a multicore fiber laser array,�?? Opt. Lett. 28, 1200 (2003).
[CrossRef] [PubMed]

T. Pertsch, U. Peschel, F. Lederer, J. Burghoff, M. Will, S. Nolte, and A. Tünnermann, �??Discrete diffraction in two-dimensional arrays of coupled waveguides in silica,�?? Opt. Lett. 29, 468 (2004).
[CrossRef] [PubMed]

M. Klotz, H. Meng, G. Salamo, M. Segev, and S. R. Montgomery, �??Fixing the photorefractive soliton,�?? Opt. Lett. 24, 77 (1999).
[CrossRef]

S. Lan, E. DelRe, Z. Chen, M. Shih and M. Segev, �??Directional coupler with soliton-induced waveguides,�?? Opt. Lett. 24, 475 (1999).
[CrossRef]

A. Guo, M. Henry, G.J. Salamo, M. Segev, and G.L. Wood, �??Fixing multiple waveguides induced by photorefractive solitons: directional couplers and beam splitters,�?? Opt. Lett. 26, 1274 (2001).
[CrossRef]

A. Bramati, W. Chinaglia, S. Minardi, and P. Di Trapani, �??Reconstruction of blurred images by controlled formation of spatial solitons,�?? Opt. Lett. 26, 1409 (2001).
[CrossRef]

J. Petter, J. Schröder, D. Träger, and C. Denz, �??Optical control of arrays of photorefractive screening solitons,�?? Opt. Lett. 28, 438 (2003).
[CrossRef] [PubMed]

D. Neshev, E. Ostrovskaya, Y. Kivshar, and W. Krolikowski, �??Spatial solitons in optically induced gratings,�?? Opt. Lett. 28, 710 (2003).
[CrossRef] [PubMed]

R. Morandotti, H.S. Eisenberg, D. Mandelik, Y. Silberberg, D. Modotto, M. Sorel, C.R. Stanley, and J.S. Aitchison, �??Interactions of discrete solitons with structural defects,�?? Opt. Lett. 28, 834 (2003).
[CrossRef] [PubMed]

J. Yang and Z.H. Musslimani, �??Fundamental and vortex solitons in a two-dimensional optical lattice,�?? Opt. Lett. 28, 2094 (2003).
[CrossRef] [PubMed]

C. Anastassiou, C. Pigier, M. Segev, D. Kip, E.D. Eugenieva, and D.N. Christodoulides, �??Self-trapping of bright rings,�?? Opt. Lett. 26, 911 (2001).
[CrossRef]

O. Manela, O. Cohen, G. Bartal, J.W. Fleischer, and M. Segev, �??Two-dimensional higher-band vortex lattice solitons,�?? Opt. Lett. 29, 2049 (2004).
[CrossRef] [PubMed]

O. Cohen, T. Carmon, M. Segev, and S. Odoulov, �??Holographic solitons,�?? Opt. Lett. 27, 2031 (2002).
[CrossRef]

R. Morandotti, D. Mandelik, Y. Silberberg, J.S. Aitchison, M. Sorel, D. Christodoulides, A.A. Sukhorukov, and Y.S. Kivshar, �??Observation of discrete gap solitons in binary waveguide arrays,�?? Opt. Lett. 29, 2890 (2004).
[CrossRef]

Z. Chen, A. Bezryadina, I. Makasyuk, and J. Yang, �??Observation of two-dimensional lattice vector solitons,�?? Opt. Lett. 29, 1656 (2004).
[CrossRef] [PubMed]

E.D. Eugenieva, N.K. Efremidis, and D.N. Christodoulides, �??Design of switching junctions in twodimensional discrete soliton networks,�?? Opt. Lett. 26, 1978 (2001).
[CrossRef]

Phys. Lett. A (1)

A.B. Aceves and S. Wabnitz, �??Self-induced transparency solitons in nonlinear refractive periodic media,�?? Phys. Lett. A 141, 37 (1989).
[CrossRef]

Phys. Rep. (1)

Y.S. Kivshar and B. Luther-Davies, �??Dark optical solitons: physics and applications,�?? Phys. Rep. 298, 81 (1998).
[CrossRef]

Phys. Rev. B (1)

J.B. Page, �??Asymptotic solutions for localized vibrational modes in strongly anharmonic periodic systems,�?? Phys. Rev. B 41, 7835 (1990).
[CrossRef]

Phys. Rev. E (5)

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

Kartashov YV, Aleshkevich VA, Vysloukh VA, Egorov AA, Zelenina AS, �??Stability analysis of (1+1)-dimensional cnoidal waves in media with cubic nonlinearity�?? Phys. Rev. E 67, 036613 (2003).
[CrossRef]

H.J. Shin, �??Solutions for solitons in nonlinear optically induced lattices,�?? Phys. Rev. E 69, 067602 (2004).
[CrossRef]

P.G. Kevrekidis, B.A. Malomed, Z.G. Chen, and D.J. Frantzeskakis, �??Stable higher-order vortices and quasivortices in the discrete nonlinear Schrödinger equation,�?? Phys. Rev. E 70, 056612 (2004).
[CrossRef]

S. Darmanyan, A. Kobyakov, E. Schmidt, and F. Lederer, �??Strongly localized vectorial modes in nonlinear waveguide arrays,�?? Phys. Rev. E 57, 3520 (1998).
[CrossRef]

Phys. Rev. E. (1)

N.K. Efremidis S. Sears, D.N. Christodoulides, J.W. Fleischer, and M. Segev, �??Discrete solitons in photorefractive optically induced photonic lattices,�?? Phys. Rev. E 66, 046602 (2002).
[CrossRef]

Phys. Rev. Lett. (37)

H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, �??Diffraction Management,�?? Phys. Rev. Lett. 85, 1863 (2000).
[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]

M. Segev, G.C. Valley, B. Crosignani, P.D. Porto, and A. Yariv, �??Steady-state spatial screening solitons in photorefractive materials with external applied field,�?? Phys. Rev. Lett. 73, 3211 (1994).
[CrossRef] [PubMed]

T. Pertsch, U. Peshchl, J. Kobelke, K. Schuster, H. Bartelt, S. Nolte, A. Tünnermann, and F. Lederer, �??Nonlinearity and disorder in fiber arrays,�?? Phys. Rev. Lett. 93, 053901 (2004).
[CrossRef] [PubMed]

H. Martin, E.D. Eugenieva, Z. Chen, and D.N. Christodoulides, �??Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices,�?? Phys. Rev. Lett. 92, 123902 (2004).
[CrossRef] [PubMed]

B.J. Eggleton, R.E. Slusher, C.M. deSterke, P.A. Krug, and J.E. Sipe, �??Bragg grating solitons,�?? Phys. Rev. Lett. 76, 1627 (1996).
[CrossRef] [PubMed]

O. Cohen, T. Schwartz, J.W. Fleischer, M. Segev, and D.N. Christodoulides, �??Multiband vector lattice solitons,�?? Phys. Rev. Lett. 91, 113901 (2003).
[CrossRef] [PubMed]

A.A. Sukhorukov and Y.S. Kivshar, �??Multigap discrete vector solitons,�?? Phys. Rev. Lett. 91, 113902 (2003).
[CrossRef] [PubMed]

N.K. Efremidis, J. Hudock, D.N. Christodoulides, J.W. Fleischer, O. Cohen, and M. Segev, �??Twodimensional optical lattice solitons,�?? Phys. Rev. Lett. 91, 213906 (2003).
[CrossRef] [PubMed]

R. Morandotti, H.S. Eisenberg, Y. Silberberg, M. Sorel, and J.S. Aitchison, �??Self-focusing and defocusing in waveguide arrays,�?? Phys. Rev. Lett. 86, 3296 (2001).
[CrossRef] [PubMed]

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, 023902 (2003).
[CrossRef] [PubMed]

M.J. Ablowitz and Z.H. Musslimani, �??Discrete diffraction managed spatial solitons,�?? Phys. Rev. Lett. 87, 254102 (2001).
[CrossRef] [PubMed]

W. Chen and D.L. Mills, �??Gap solitons and the nonlinear optical response of superlattices,�?? Phys. Rev. Lett. 58, 160 (1987);
[CrossRef] [PubMed]

D.N. Christodoulides and R.I. Joseph, �??Slow Bragg solitons in nonlinear periodic structures,�?? Phys. Rev. Lett. 62, 1746 (1989);
[CrossRef] [PubMed]

E. Yablonovich, �??Inhibited spontaneous emission in solid-state and electronics,�?? Phys. Rev. Lett. 58, 2059 (1987).
[CrossRef]

A.S. Desyatnikov, E.A. Ostrovskaya, Y.S. Kivshar, and C. Denz, �??Composite Band-Gap Solitons in Nonlinear Optically Induced Lattices,�?? Phys. Rev. Lett. 91, 153902 (2003).
[CrossRef] [PubMed]

J. Meier, J. Hudock, D. Christodoulides, G. Stegeman, Y. Silberberg, R. Morandotti, and J.S. Aitchison, �??Discrete vector solitons in Kerr nonlinear waveguide arrays,�?? Phys. Rev. Lett. 91, 143907 (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. Mandelik, H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, �??Observation of mutually trapped multiband optical breathers in waveguide arrays,�?? Phys. Rev. Lett. 90, 253902 (2003).
[CrossRef] [PubMed]

J. Meier, G.I. Stegeman, D.N. Christodoulides, Y. Silberberg, R. Morandotti, H. Yang, G. Salamo, M. Sorel, and J.S. Aitchison, �??Experimental observation of discrete modulational instability,�?? Phys. Rev. Lett. 92, 163902 (2004).
[CrossRef] [PubMed]

D. Mandelik, H.S. Eisenberg, Y. Silberberg, R. Morandotti, and J.S. Aitchison, �??Band-gap structure of waveguide arrays and excitation of Floquet-Bloch solitons,�?? Phys. Rev. Lett. 90, 053902 (2003).
[CrossRef] [PubMed]

T. Pertsch, P. Dannberg, W. Elflein, A. Brauer, and F. Lederer, �??Optical Bloch oscillations in temperature tuned waveguide arrays,�?? Phys. Rev. Lett. 83, 4752 (1999).
[CrossRef]

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

O. Cohen, B. Freedman, J.W. Fleischer, M. Segev, and D.N. Christodoulides, �??Grating-mediated waveguiding,�?? Phys. Rev. Lett. 93, 103902 (2004).
[CrossRef] [PubMed]

J.W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, and D.N. Christodoulides, �??Observation of vortex-ring �??discrete�?? solitons in 2D photonic lattices,�?? Phys. Rev. Lett. 92, 123904 (2004).
[CrossRef] [PubMed]

D.N. Neshev, T.J. Alexander, E.A. Ostrovskaya, Y.S. Kivshar, H. Martin, I. Makasyuk, and Z. Chen, �??Observation of discrete vortex solitons in optically induced photonic lattices,�?? Phys. Rev. Lett. 92, 123903 (2004).
[CrossRef] [PubMed]

G. Bartal, O. Manela, O. Cohen, J.W. Fleischer, and M. Segev, �??Observation of 2nd-band vortex solitons in 2D photonic lattices,�?? submitted to Phys. Rev. Lett..

A.A. Sukhorukov, D. Neshev, W. Krolikowski, and Y.S. Kivshar, �??Nonlinear Bloch-wave interaction and Bragg scattering in optically induced lattices,�?? Phys. Rev. Lett. 92, 093901 (2004).
[CrossRef] [PubMed]

D. Mandelik, R. Morandotti, J.S. Aitchison, and Y. Silberberg, �??Gap solitons in waveguide arrays,�?? Phys. Rev. Lett. 92, 093904 (2004).
[CrossRef] [PubMed]

D. Neshev, A.A. Sukhorukov, B. Hanna, W. Krolikowski, and Y.S. Kivshar, �??Controlled generation and steering of spatial gap solitons,�?? Phys. Rev. Lett. 93, 083905 (2004).
[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]

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]

T.J. Alexander, A.A. Sukhorukov, and Y.S. Kivshar, �??Asymmetric vortex solitons in nonlinear periodic lattices,�?? Phys. Rev. Lett. 93, 063901 (2004).
[CrossRef] [PubMed]

A.J. Sievers and S. Takeno, �??Intrinsic localized modes in anharmonic crystals,�?? Phys. Rev. Lett. 61, 970 (1988).
[CrossRef] [PubMed]

H. Buljan, O. Cohen, J.W. Fleischer, T. Schwartz, M. Segev, Z.H. Musslimani, N.K. Efremidis, and D.N. Christodoulides, �??Random-phase solitons in nonlinear periodic lattices,�?? Phys. Rev. Lett. 92, 223901 (2004).
[CrossRef] [PubMed]

M. Mitchell, Z. Chen, M. Shih, and M. Segev, �??Self-trapping of partially spatially incoherent light,�?? Phys. Rev. Lett. 77, 490 (1996).
[CrossRef] [PubMed]

H. Buljan, M. Segev, and A. Vardi, �??Incoherent matter wave solitons: mutual self-trapping of a Bose-Einstein condensate and its surrounding thermal cloud,�?? submitted to Phys. Rev. Lett.

Science (3)

F.S. Cataliotti, S. Burger, C. Fort, P. Maddaloni, F. Minardi, A. Trombettoni, A. Smerzi, and M. Inguscio, �??Josephson junction arrays with Bose-Einstein condensates,�?? Science 293, 843 (2001).
[CrossRef] [PubMed]

P. Russell, �??Photonic crystal fibers,�?? Science 299, 358 (2003).
[CrossRef] [PubMed]

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

Sov. Phys. JETP (1)

S.V. Manakov, �??On the theory of two-dimensional stationary self-focusing of electromagnetic waves,�?? Sov. Phys. JETP 38, 248 (1974).

Stud. App. Math. (1)

J. Yang, I. Makasyuk, A. Bezryadina, and Z. Chen, �??Dipole and quadrupole solitons in optically induced two-dimensional photonic lattices: theory and experiment,�?? Stud. App. Math. 113, 389 (2004).
[CrossRef]

Other (3)

G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, and M. Segev, �??Brillouin zone spectroscopy of nonlinear photonic lattices,�?? submitted to Phys. Rev. Lett.

J.M. Ziman, Principles of the theory of solids, 2nd ed. (Cambridge University Press, Cambridge, 1979

E. Fermi, J. Pasta, and S. Ulam, �??Studies of nonlinear problems I,�?? S. Report LA-1940 (LANL, Los Alamos, 1955).

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Figures (9)

Fig. 1.
Fig. 1.

Linear band structure and diffraction properties of a 1D waveguide array. (a) Transmission spectrum consisting of bands of allowed propagation constants separated by forbidden gaps. (b) Modes in convex regions experience normal diffraction. (c) Modes in concave regions experience anomalous diffraction.

Fig. 2.
Fig. 2.

1D discrete or lattice solitons from the first band (a) 1D transmission spectrum showing the nonlinear propagation constants for the fundamental LS (base of the BZ zone) and spatial gap soliton (edge of BZ zone). (b) The fundamental LS has an in-phase structure that requires a self-focusing nonlinearity (positive defect). (c) The first-band gap soliton has a staggered phase structure that requires a defocusing nonlinearity (negative defect).

Fig. 3.
Fig. 3.

Band structure and optical induction of a square waveguide array. (a,b) Band structure of a 2D square lattice, with high-symmetry points labeled in (b). (c) Interference of four plane waves to optically induce a 2D square array of 2D waveguides. (d) Photograph of a typical output face, showing a lattice with an 11µm period.

Fig. 4.
Fig. 4.

Principles of grating-mediated waveguiding. (a) Type-I guide, with a bell-shaped y-profile. (b) Type-II guide, with a trough-shaped y-profile. (c) Index grating with three different amplitudes, corresponding to three different y-planes. (d) The dispersion/diffraction curves near the edge of the first Brillouin zone for gratings with index profile n(x,y)=n 0[1+εA(y)cos(πx/D)]. (e,f) Typical index amplitudes A(y) of (e) Type-I gratings and (f) Type-II gratings. (g) The effective waveguide structure in y: Type-I beams need a cos(πx/D) dependence and Type-II beams need a sin(πx/D) dependence to experience grating-mediated waveguiding. Taken from [60].

Fig. 5.
Fig. 5.

Experimental scheme and resutls of a Type-II (trough-shaped) grating-mediated waveguide. (a) Schematic of optical induction of waveguide. (b) Photograph of input beam. (c) Waveguiding when position and phase of (b) match with grating structure. (d–f) Diffraction in unguided conditions: (d) Free-space diffraction of (b) in absence of waveguide. (e) Diffraction when the input is not Bragg-matched with the grating. (f) Diffraction when the input (b) is Bragg-matched but has the “wrong” phase relative to the grating. In (b–f), the intensity in each figure is normalized to its own peak intensity. Taken from [60].

Fig. 6.
Fig. 6.

Experimental observation of discrete diffraction and solitons in 1D optically-induced waveguide arrays. (a–c) Propagation for an on-axis input probe. Discrete diffraction (a) in the linear regime. Soliton intensity (b) and relative phase (c) in the nonlinear regime (+1.6kV/cm). The phase information (c) is obtained by interfering the output signal (b) with a plane wave. (d–f) Propagation at the Bragg angle, corresponding to the edge of the first Brillouin zone. Discrete diffraction (d) in the linear regime. Soliton intensity (e) and relative phase (f) in the nonlinear regime (-2.0kV/cm). Note that the central peak experiences destructive interference, while the surrounding lobes experience constructive interference. Note also the need for defocusing nonlinearity (negative voltage) to create the 1D gap soliton (e). Taken from [14].

Fig. 7.
Fig. 7.

Experimental observation of discrete diffraction and solitons in 2D optically-induced waveguide arrays. (a–c) Propagation for an on-axis input probe. Discrete diffraction (a) in the linear regime. Soliton intensity (b) and relative phase (c) in the nonlinear regime (+1.6kV/cm). The phase information (c) is obtained by interfering the output signal (b) with a plane wave. (d–f) Propagation at the Bragg angle, corresponding to the corner of the first Brillouin zone (M-point in Fig. 4c). Discrete diffraction (d) in the linear regime. Soliton intensity (e) and relative phase (f) in the nonlinear regime (-1.6kV/cm). Note that the central peak experiences destructive interference, while the surrounding lobes experience constructive interference. Note also the need for defocusing nonlinearity (negative voltage) to create the 2D gap soliton (e). Taken from [26].

Fig. 8.
Fig. 8.

Experimental observation of discrete vortex solitons in 2D optically-induced waveguide arrays. (a) Discrete diffraction and (b) spiral phase structure (formed by interfering the output (a) with a plane wave) in the linear regime. (b) Soliton intensity and (c) relative phase in the nonlinear regime (+1.6kV/cm) for a vortex with its singularity centered on-site. (d) Soliton intensity and (e) relative phase in the nonlinear regime (+1.6kV/cm) for a vortex with its singularity centered in-between sites. The vortex solitons keep their relative phase, despite the fact that the conservation of angular momentum (topological charge) is not guaranteed in a lattice. Taken from [56].

Fig. 9.
Fig. 9.

Theoretical characterization of random-phase lattice soliton (RPLS). (a) Modes are taken statistically from regions of the transmission spectrum with the same band curvature. (b,c) Power spectrum in the (b) Fouier basis and (c) Floquet-Bloch basis. Note the sharp cut-offs in (c), implying that the F-B representation is more appropriate for lattice modes. (d,e) Statistical properties of RPLS. The blue lines indicate the centers of each waveguide in the 1D array. (d) Mutual coherence/correlation function centered on the central waveguide. (e) Soliton profile in black and correlation length in red. (f) Modal structure as given by waveguide theory. See text for its relation to the correlation behavior in (e). Taken from [82].

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