Spatial Beam Dynamics Mediated by Hybrid Nonlinearity

  • Peng Zhang
  • Cibo Lou
  • Yi Hu
  • Sheng Liu
  • Jianlin Zhao
  • Jingjun Xu
  • Zhigang Chen
Part of the Springer Series in Optical Sciences book series (SSOS, volume 170)


We provide a brief overview of recent progresses on the study of a new type of nonlinearity, named hybrid nonlinearity: the coexistence of self-focusing and self-defocusing nonlinearities in the same material under identical conditions. Such hybrid nonlinearity is established in a nonconventionally biased photorefractive crystal, which offers enhanced anisotropy and nonlocality, leading to a variety of unusual nonlinear beam dynamics in both continuous and discrete regimes. In homogenous media, elliptical optical solitons, stabilization of nonlinear optical vortices, as well as orientation-induced transition between bright and dark solitons are demonstrated. In discrete media, hybrid nonlinearity enables the creation of an ionic-type photonic lattice with alternating positive and negative optical potentials, which in turn enables the reconfiguration of lattice structures and Brillouin zones for band-gap engineering and light manipulation. Moreover, a host of nonlinear discrete localized states mediated by such hybrid nonlinearity are uncovered, including elliptical discrete solitons and “saddle” solitons. The novel concept of hybrid nonlinearity opens a door for exploring spatial beam dynamics and related nonlinear phenomena in anisotropic nonlinear systems beyond optics.


Dark Soliton Vortex Beam Photorefractive Crystal Photonic Lattice Bloch Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported by US National Science Foundation, the Air Force Office of Scientific Research, and by the NPU Foundation for Fundamental Research, the Doctorate Foundation of NPU, the 973 Program, the 111 Project, NSFC, and PCSIRT in China. We are indebted to many of our collaborators over the years including F. Xiao, X. Gan, Q. Liu, Y. Gao, X. Tan, D. Yang, X. Wang, and J. Yang. We thank A. Miller for proofreading the chapter.


  1. 1.
    M.J. Ablowitz, P.A. Clarkson, Solitons, Nonlinear Evolution Equations, and Inverse Scattering (Cambridge University, Cambridge, 1991)MATHCrossRefGoogle Scholar
  2. 2.
    F. Abdullaev, V.V. Konotop, Nonlinear Waves: Classical and Quantum Aspects (Kluwer, New York, 2004)MATHGoogle Scholar
  3. 3.
    E. Infeld, G. Rowlands, Nonlinear Waves, Solitons, and Chaos (Cambridge University, Cambridge, 1990)MATHGoogle Scholar
  4. 4.
    J. Pedlosky, Waves in the Ocean and Atmosphere: Introduction to Wave Dynamics (Springer, Berlin, 2010)Google Scholar
  5. 5.
    A.S. Davydov, Solitons in Molecular Systems (Kluwer, Netherlands, 1991)CrossRefGoogle Scholar
  6. 6.
    Y.R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 2003)MATHGoogle Scholar
  7. 7.
    R.W. Boyd, Nonlinear Optics (Academic, New York, 2008)Google Scholar
  8. 8.
    R.A. Rupp, F.W. Drees, Appl. Phys. B 39, 223 (1986)ADSCrossRefGoogle Scholar
  9. 9.
    J.P. Huignard, A. Marrakchi, Opt. Commun. 38, 249 (1981)ADSCrossRefGoogle Scholar
  10. 10.
    J. Feinberg, Opt. Lett. 7, 486 (1982)ADSCrossRefGoogle Scholar
  11. 11.
    R.Y. Chiao, E. Garmire, C.H. Townes, Phys. Rev. Lett. 13, 479 (1964)ADSCrossRefGoogle Scholar
  12. 12.
    G.I. Stegeman, M. Segev, Science 286, 1518 (1999)CrossRefGoogle Scholar
  13. 13.
    H. Hasegawa, Y. Kodama, Solitons in Optical Communications (Oxford University, New York, 1995)MATHGoogle Scholar
  14. 14.
    Y.S. Kivshar, G.P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, San Diego, 2003)Google Scholar
  15. 15.
    M.D.I. Castillo, P.A. Marquez, J.J. Sanchez-Mondragon, S. Stepanov, V. Vysloukh, Appl. Phys. Lett. 64, 408 (1994)ADSCrossRefGoogle Scholar
  16. 16.
    A. Barthelemy, S. Maneuf, C. Frcehly, Opt. Commun. 55, 201 (1985)ADSCrossRefGoogle Scholar
  17. 17.
    J.E. Bjorkholm, A.A. Ashkin, Phys. Rev. Lett. 32, 129 (1974)ADSCrossRefGoogle Scholar
  18. 18.
    M. Peccianti, C. Conti, G. Assanto, A. De Luca, C. Umeton, Nature 432, 733 (2004)ADSCrossRefGoogle Scholar
  19. 19.
    C. Rotschild, O. Cohen, O. Manela, M. Segev, T. Carmon, Phys. Rev. Lett. 95, 213904 (2005)ADSCrossRefGoogle Scholar
  20. 20.
    P. Günter, J.P. Huignard, Photorefractive Materials and Their Applications I (Springer, Berlin, 1988)CrossRefGoogle Scholar
  21. 21.
    M. Segev, B. Crosignanim, A. Yariv, B. Fischer, Phys. Rev. Lett. 68, 923 (1992)ADSCrossRefGoogle Scholar
  22. 22.
    G.C. Duree Jr., J.L. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E.J. Sharp, R.R. Neurgaonkar, Phys. Rev. Lett. 71, 533 (1993)ADSCrossRefGoogle Scholar
  23. 23.
    W. Królikowski, B. Luther-Davies, C. Denz, IEEE J. Quantum Elect. 39, 3 (2003)ADSCrossRefGoogle Scholar
  24. 24.
    M. Segev, G.C. Valley, B. Crosignani, D. Di Porto, A. Yariv, Phys. Rev. Lett. 73, 3211 (1994)ADSCrossRefGoogle Scholar
  25. 25.
    D.N. Christodoulides, M.I. Carvalho, J. Opt. Soc. Am. B 12, 1628 (1995)ADSCrossRefGoogle Scholar
  26. 26.
    A. Guo, M. Henry, G.J. Salamo, M. Segev, G.L. Wood, Opt. Lett. 26, 1274 (2001)ADSCrossRefGoogle Scholar
  27. 27.
    M. Shih, P. Leach, M. Segev, M.M. Garrett, G. Salamo, G.C. Valley, Opt. Lett. 21, 324 (1996)ADSCrossRefGoogle Scholar
  28. 28.
    M. Taya, M.C. Bashaw, M.M. Fejer, M. Segev, G.C. Valley, Phys. Rev. Lett. 52, 3095 (1995)ADSGoogle Scholar
  29. 29.
    Z. Chen, M. Mitchell, M. Shih, M. Segev, M.H. Garrett, G.C. Valley, Opt. Lett. 21, 629 (1996)ADSCrossRefGoogle Scholar
  30. 30.
    Z. Chen, M. Segev, D.W. Wilson, R.E. Muller, P.D. Maker, Phys. Rev. Lett. 78, 2948 (1997)ADSCrossRefGoogle Scholar
  31. 31.
    Z. Chen, M. Shih, M. Segev, D.W. Wilson, R.E. Muller, P.D. Maker, Opt. Lett. 22, 1751 (1997)ADSCrossRefGoogle Scholar
  32. 32.
    Z. Chen, M. Segev, T.H. Coskun, D.N. Christodoulides, Opt. Lett. 21, 1436 (1996)ADSCrossRefGoogle Scholar
  33. 33.
    M. Mitchell, Z. Chen, M. Shih, M. Segev, Phys. Rev. Lett. 77, 490 (1996)Google Scholar
  34. 34.
    Z. Chen, M. Mitchell, M. Segev, T.H. Coskun, D.N. Christodolides, Science 280, 889 (1998)ADSCrossRefGoogle Scholar
  35. 35.
    G.S. Garacía-Quirino, M.D.I. Castillo, V.A. Vysloukh, J.J. Sánchez-Mondragón, S.I. Stepanov, G. Lugo-Martínez, G.E. Torres-Cisneros, Opt. Lett. 22, 154 (1997)ADSCrossRefGoogle Scholar
  36. 36.
    W. Krolikowski, S.A. Holmstrom, Opt. Lett. 22, 369 (1997)ADSCrossRefGoogle Scholar
  37. 37.
    M. Shih, Z. Chen, M. Segev, T.H. Coskun, D.N. Christodoulides, Appl. Phys. Lett. 69, 4151 (1996)ADSCrossRefGoogle Scholar
  38. 38.
    M. Shih, M. Segev, G. Salamo, Phys. Rev. Lett. 78, 2551 (1997)ADSCrossRefGoogle Scholar
  39. 39.
    W. Krolikowski, M. Saffman, B. Luther-Davies, C. Denz, Phys. Rev. Lett. 80, 3240 (1998)ADSCrossRefGoogle Scholar
  40. 40.
    D.N. Christodoulides, F. Lederer, Y. Silberberg, Nature 424, 817 (2003)ADSCrossRefGoogle Scholar
  41. 41.
    F. Lederer, G.I. Stegeman, D.N. Christodoulides, G. Assanto, M. Segev, Y. Silberberg, Phys. Rep. 463, 1 (2008)ADSCrossRefGoogle Scholar
  42. 42.
    D. Mandelik, H.S. Eisenberg, Y. Silberberg, R. Morandotti, J.S. Aitchison, Phys. Rev. Lett. 90, 053902 (2003)ADSCrossRefGoogle Scholar
  43. 43.
    H.S. Eisenberg, Y.S. Silberberg, R. Morandotti, J.S. Aitchison, Phys. Rev. Lett. 85, 1863 (2000)ADSCrossRefGoogle Scholar
  44. 44.
    T. Pertsch, T. Zentgraf, U. Peschel, A. Bräuer, F. Lederer, Phys. Rev. Lett. 88, 093901 (2002)ADSCrossRefGoogle Scholar
  45. 45.
    H. Trompeter, W. Krolikowski, D.N. Neshev, A.S. Desyatnikov, A.A. Sukhorukov, Y.S. Kivshar, T. Pertsch, U. Peschel, F. Lederer, Phys. Rev. Lett. 96, 053903 (2006)ADSCrossRefGoogle Scholar
  46. 46.
    K. Shandarova, C.E. Rüter, D. Kip, K.G. Makris, D.N. Christodoulides, O. Peleg, M. Segev, Phys. Rev. Lett. 102, 123905 (2009)ADSCrossRefGoogle Scholar
  47. 47.
    H.S. Eisenberg, Y. Silberberg, R. Morandotti, A.R. Boyd, J.S. Aitchison, Phys. Rev. Lett. 81, 3383 (1998)ADSCrossRefGoogle Scholar
  48. 48.
    D. Mandelik, R. Morandotti, J.S. Aitchison, Y. Silberberg, Phys. Rev. Lett. 92, 093904 (2004)ADSCrossRefGoogle Scholar
  49. 49.
    N.K. Efremidis, S. Sears, D.N. Christodoulids, J.W. Fleischer, M. Segev, Phys. Rev. E. 66, 046602 (2002)ADSCrossRefGoogle Scholar
  50. 50.
    Z. Chen, K. MacCarthy, Opt. Lett. 27, 2019 (2002)ADSCrossRefGoogle Scholar
  51. 51.
    C.R. Rosberg, D.N. Neshev, A.A. Sukhorukov, Y.S. Kivshar, W. Krolikowski, Opt. Lett. 30, 2293 (2005)ADSCrossRefGoogle Scholar
  52. 52.
    I. Makasyuk, Z. Chen, J. Yang, Phys. Rev. Lett. 96, 223903 (2006)ADSCrossRefGoogle Scholar
  53. 53.
    T. Schwartz, G. Bartal, S. Fishman, M. Segev, Nature 446, 52 (2007)ADSCrossRefGoogle Scholar
  54. 54.
    X. Wang, Z. Chen, P.G. Kevrekidis, Phys. Rev. Lett. 96, 083904 (2006)ADSCrossRefGoogle Scholar
  55. 55.
    C. Lou, X. Wang, J. Xu, Z. Chen, J. Yang, Phys. Rev. Lett. 98, 213903 (2007)ADSCrossRefGoogle Scholar
  56. 56.
    D.N. Neshev, T.J. Alexander, E.A. Ostrovskaya, Y.S. Kivshar, H. Martin, I. Makasyuk, Z. Chen, Phys. Rev. Lett. 92, 123903 (2004)ADSCrossRefGoogle Scholar
  57. 57.
    J.W. Fleischer, G. Bartal, O. Cohen, O. Manela, M. Segev, J. Hudock, D.N. Christodoulides, Phys. Rev. Lett. 92, 123904 (2004)ADSCrossRefGoogle Scholar
  58. 58.
    X. Wang, Z. Chen, J. Wang, J. Yang, Phys. Rev. Lett. 99, 243901 (2007)ADSCrossRefGoogle Scholar
  59. 59.
    O. Cohen, G. Bartal, H. Buljan, T. Carmon, J.W. Fleischer, M. Segev, D.N. Christodoulides, Nature 433, 500 (2005)ADSCrossRefGoogle Scholar
  60. 60.
    J.W. Fleischer, T. Carmon, M. Segev, N.K. Efremidis, D.N. Christodoulides, Phys. Rev. Lett. 90, 023902 (2003)ADSCrossRefGoogle Scholar
  61. 61.
    J.W. Fleischer, M. Segev, N.K. Efremidis, D.N. Christodoulides, Nature 422, 147 (2003)ADSCrossRefGoogle Scholar
  62. 62.
    H. Martin, E.D. Eugenieva, Z. Chen, D.N. Christodoulides, Phys. Rev. Lett. 92, 123902 (2004)ADSCrossRefGoogle Scholar
  63. 63.
    C. Crognale, L. Rosa, J. Lightwave Technol. 23, 2175 (2005)ADSCrossRefGoogle Scholar
  64. 64.
    P. Zhang, J. Zhao, C. Lou, X. Tan, Y. Gao, Q. Liu, D. Yang, J. Xu, Z. Chen, Opt. Express 15, 536 (2007)ADSCrossRefGoogle Scholar
  65. 65.
    P. Zhang, S. Liu, C. Lou, Y. Gao, J. Zhao, J. Xu, Z. Chen, Appl. Phys. B 95, 559 (2009)ADSCrossRefGoogle Scholar
  66. 66.
    N.V. Kukhtarev, V.B. Markov, S.G. Odulov, M.S. Soskin, V.L. Vinetskii, Ferroelectrics 22, 949 (1979)CrossRefGoogle Scholar
  67. 67.
    A.A. Zozulya, D.Z. Anderson, Phys. Rev. A 51, 1520 (1995)ADSCrossRefGoogle Scholar
  68. 68.
    A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984)Google Scholar
  69. 69.
    P. Zhang, Y. Ma, J. Zhao, D. Yang, H. Xu, Appl. Opt. 45, 2273 (2006)ADSCrossRefGoogle Scholar
  70. 70.
    J. Zhao, P. Zhang, J. Zhou, D.X. Yang, D.S. Yang, E. Li, Chin. Phys. Lett. 20, 1748 (2003)ADSCrossRefGoogle Scholar
  71. 71.
    P. Zhang, J. Zhao, S. Liu, Y. Gao, C. Lou, J. Xu, Z. Chen, CLEO/QELS, OSA Technical Digest, CTuE5 (2008)Google Scholar
  72. 72.
    V.I. Petviashvili, Sov. J. Plasma Phys. 2, 257 (1976)Google Scholar
  73. 73.
    A.A. Zozulya, D.Z. Anderson, A.V. Mamaev, M. Saffman, Phys. Rev. A 57, 522 (1998)ADSCrossRefGoogle Scholar
  74. 74.
    A.A. Zozulya, D.Z. Anderson, A.V. Mamaev, M. Saffman, Europhys. Lett. 36, 419 (1996)ADSCrossRefGoogle Scholar
  75. 75.
    L.M. Pismen, Vortices in Nonlinear Fields: From Liquid Crystals to Superfluids, From Non-equilibrium Patterns to Cosmic Strings (Oxford University, New York, 1999)MATHGoogle Scholar
  76. 76.
    D.G. Grier, Nature 424, 810 (2003)ADSCrossRefGoogle Scholar
  77. 77.
    A.S. Desyatnikov, Y.S. Kivshar, L. Torner, Prog. Opt. 47, 291 (2005)CrossRefGoogle Scholar
  78. 78.
    G.A. Swartzlander Jr., C.T. Law, Phys. Rev. Lett. 69, 2503 (1992)ADSCrossRefGoogle Scholar
  79. 79.
    V. Tikhonenko, J. Christou, B. Luther-Daves, J. Opt. Soc. Am. B 12, 2046 (1995)ADSCrossRefGoogle Scholar
  80. 80.
    D. Briedis, D.E. Petersen, D. Edmundson, W. Krolikowski, O. Bang, Opt. Express 13, 435 (2005)ADSCrossRefGoogle Scholar
  81. 81.
    A.V. Mamaev, M. Saffman, A.A. Zozulya, Phys. Rev. Lett. 77, 4544 (1996)ADSCrossRefGoogle Scholar
  82. 82.
    A.V. Mamaev, M. Saffman, A.A. Zozulya, Phys. Rev. Lett. 78, 2108 (1997)ADSCrossRefGoogle Scholar
  83. 83.
    G. Duree, M. Morin, G. Salamo, M. Segev, B. Crosignani, P. Di Porto, E. Sharp, A. Yariv, Phys. Rev. Lett. 74, 1978 (1995)ADSCrossRefGoogle Scholar
  84. 84.
    X. Gan, P. Zhang, S. Liu, Y. Zheng, J. Zhao, Z. Chen, Opt. Express 17, 23130 (2009)ADSCrossRefGoogle Scholar
  85. 85.
    N.R. Heckenberg, R. McDuff, C.P. Smith, A.G. White, Opt. Lett. 17, 221 (1992)ADSCrossRefGoogle Scholar
  86. 86.
    J.S. Blakemore, Solid State Physics (Cambridge University, Cambridge, 1985)Google Scholar
  87. 87.
    J.D. Joannopoulos, R.D. Meade, J.N. Winn, Photonic Crystals: Molding the Flow of Light (Princeton University, New Jersey, 1995)MATHGoogle Scholar
  88. 88.
    M. Lu, C. Zhang, L. Feng, J. Zhao, Y. Chen, Y. Mao, J. Zi, Y. Zhu, S. Zhu, N. Ming, Nat. Mater. 6, 744 (2007)ADSCrossRefGoogle Scholar
  89. 89.
    X. Hu, C.T. Chan, Phys. Rev. Lett. 95, 154501 (2005)ADSCrossRefGoogle Scholar
  90. 90.
    E.A. Ostrovskaya, Y.S. Kivshar, Phys. Rev. Lett. 90, 160407 (2003)ADSCrossRefGoogle Scholar
  91. 91.
    Y. Liu, G. Bartal, D.A. Genov, X. Zhang, Phys. Rev. Lett. 99, 153901 (2007)ADSCrossRefGoogle Scholar
  92. 92.
    P. Zhang, C. Lou, S. Liu, F. Xiao, J. Zhao, J. Xu, Z. Chen, Opt. Photonics News 19, 25 (2008)ADSCrossRefGoogle Scholar
  93. 93.
    P. Zhang, J. Zhao, F. Xiao, C. Lou, J. Xu, Z. Chen, Opt. Express 16, 3865 (2008)ADSCrossRefGoogle Scholar
  94. 94.
    P. Zhang, S. Liu, C. Lou, F. Xiao, X. Wang, J. Zhao, J. Xu, Z. Chen, Phys. Rev. A 81, 041801(R) (2010)Google Scholar
  95. 95.
    P. Zhang, C. Lou, S. Liu, J. Zhao, J. Xu, Z. Chen, Opt. Lett. 35, 892 (2010)CrossRefGoogle Scholar
  96. 96.
    P. Zhang, S. Liu, J. Zhao, C. Lou, J. Xu, Z. Chen, Opt. Lett. 33, 878 (2008)ADSCrossRefGoogle Scholar
  97. 97.
    Y. Hu, C. Lou, S. Liu, P. Zhang, J. Zhao, J. Xu, Z. Chen, Opt. Lett. 34, 1114 (2009)ADSCrossRefGoogle Scholar
  98. 98.
    Y. Hu, C. Lou, P. Zhang, J. Xu, J. Yang, Z. Chen, Opt. Lett. 34, 3259 (2009)ADSCrossRefGoogle Scholar
  99. 99.
    S. Liu, P. Zhang, X. Gan, F. Xiao, J. Zhao, Appl. Phys. B 99, 727 (2010)ADSCrossRefGoogle Scholar
  100. 100.
    G. Bartal, O. Cohen, H. Buljan, J.W. Fleischer, O. Manela, M. Segev, Phys. Rev. Lett. 94, 163902 (2005)ADSCrossRefGoogle Scholar
  101. 101.
    D. Träger, R. Fischer, D.N. Neshev, A.A. Sukhorukov, C. Denz, W. Królikowski, Y.S. Kivshar, Opt. Express 14, 1913 (2006)ADSCrossRefGoogle Scholar
  102. 102.
    C. Luo, S.G. Johnson, J.D. Joannopoulos, J.B. Pendry, Phys. Rev. B 65, 201104 (2002)ADSCrossRefGoogle Scholar
  103. 103.
    M. Born, E. Wolf, Principles of Optics (Cambridge University, Cambridge, 1999)Google Scholar
  104. 104.
    M. Straub, M. Ventura, M. Gu, Phys. Rev. Lett. 91, 043901 (2003)ADSCrossRefGoogle Scholar
  105. 105.
    A.R. Kolovsky, H.J. Korsch, Phys. Rev. A 67, 063601 (2003)ADSCrossRefGoogle Scholar
  106. 106.
    D. Witthaut, F. Keck, H.J. Korsch, S. Mossmann, New J. Phys. 6, 41 (2004)ADSCrossRefGoogle Scholar
  107. 107.
    J. Hudock, N.K. Efremidis, D.N. Christodoulides, Opt. Lett. 29, 268 (2004)ADSCrossRefGoogle Scholar
  108. 108.
    Z. Chen, H. Martin, E.D. Eugenieva, J. Xu, A. Bezryadina, Phys. Rev. Lett. 92, 143902 (2004)ADSCrossRefGoogle Scholar
  109. 109.
    C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, J. Trull, Phys. Rev. Lett. 90, 170406 (2003)ADSCrossRefGoogle Scholar
  110. 110.
    Y. Silberberg, Opt. Lett. 15, 1282 (1990)ADSCrossRefGoogle Scholar
  111. 111.
    R. Fischer, D. Träger, D.N. Neshev, A.A. Sukhorukov, W. Krolikowski, C. Denz, Y.S. Kivshar, Phys. Rev. Lett. 96, 023905 (2006)ADSCrossRefGoogle Scholar
  112. 112.
    N.K. Efremidis, J. Hudock, D.N. Christodoulides, J.W. Fleischer, O. Cohen, M. Segev, Phys. Rev. Lett. 91, 213906 (2003)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Peng Zhang
    • 1
    • 2
  • Cibo Lou
    • 3
  • Yi Hu
    • 2
    • 3
    • 4
  • Sheng Liu
    • 1
  • Jianlin Zhao
    • 1
  • Jingjun Xu
    • 3
  • Zhigang Chen
    • 2
    • 3
  1. 1.The Key Laboratory of Space Applied Physics and Chemistry, Ministry of Education and Shaanxi Key Laboratory of Optical Information Technology, School of ScienceNorthwestern Polytechnical UniversityXi’anChina
  2. 2.Department of Physics and AstronomySan Francisco State UniversitySan FranciscoUSA
  3. 3.The Key Laboratory of Weak-Light Nonlinear Photonics, Ministry of Education and TEDA Applied Physics SchoolNankai UniversityTianjinChina
  4. 4.INRS-EMTUniversity of QuebecVarennesCanada

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