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Nonlinear Photonic Crystals pp 73–105Cite as

Self-transparency and Localization in Gratings with Quadratic Nonlinearity

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Part of the book series: Springer Series in Photonics ((PHOTONICS,volume 10))

Abstract

In noncentrosymmetric media, second-order or χ(2) nonlinearities dominate the nonlinear response of the material. It is therefore natural to wonder about the possibility to observe nonlinear behavior in periodic media made out of this class of materials, and in particular effects of self-transparency and switching mediated by localized envelopes such as those observed in cubic media (e.g., fibers [1] and A1GaAs [2]) and discussed elsewhere in this book. The first motivation to undertake these studies is that nowadays it is fairly well understood that χ(2) support spatial (non-diffractive) or temporal (non-dispersive) solitons in homogeneous media [3]. It is thus expected that trapping phenomena can be extended to periodic media. The second, more important reason is related to the availability of periodic structures in quadratic materials. A properly tailored periodicity of the effective χ(2) nonlinearity is commonly employed to achieve phase-matching of frequency conversion process, by means of so called quasi-phase-matching (QPM) techniques [4,5], recently extended in planar (2D) geometry [6,7]. On the other hand also periodic variations of linear properties over submicron scale has been introduced in quadratic materials to achieve Bragg gratings [8–13]

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References

  1. B.J. Eggleton, R.E. Slusher, C.M. de Sterke, P.A. Krug, J.E. Sipe: Phys. Rev. Lett. 76, 1627 (1996)

    Article  ADS  Google Scholar 

  2. P. Millar, R.M. De La Rue, T.F. Krauss, J.S. Aitchison, N.G.R. Broderick, D.J. Richardson: Opt. Lett. 24, 685 (1999)

    Article  ADS  Google Scholar 

  3. for a review see: G.I. Stegeman, D. J. Hagan, L. Torner: Opt. Quantum Electron. 28, 1691 (1996);

    Google Scholar 

  4. Y.S. Kivshar: Opt. Quantum Electron. 30, 571 (1998);

    Article  Google Scholar 

  5. A.V. Buryak, P. Di Trapani, D. Skryabin, S. Trillo: “Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications” Phys. Rep., in press

    Google Scholar 

  6. S. Somekh, A. Yariv: Appl. Phys. Lett. 21, 140 (1972)

    Article  ADS  Google Scholar 

  7. M.M. Fejer, G.A. Magel, D.H. Jundt, R.L. Byer: IEEE J. Quantum Electron. QE-28, 2631 (1992)

    Google Scholar 

  8. V. Berger: Phys. Rev. Lett. 81, 4136 (1998)

    Article  ADS  Google Scholar 

  9. N.G.R. Broderick; G.W. Ross; H.L. Offerhaus, D.J. Richardson, D.C. Hanna,: Phys. Rev. Lett. 84, 4345 (2000)

    Article  ADS  Google Scholar 

  10. J. Söchtig: Electron. Lett. 24, 845 (1988)

    Article  Google Scholar 

  11. W.P. Risk, S.D. Lau: Opt. Lett. (1993)18; 272 (1999)

    Google Scholar 

  12. J. Söchtig, R. Grob, I. Baumann, W. Solder, H. Shütz; R. Widmer: Electron. Lett. 31, 551 (1995)

    Article  ADS  Google Scholar 

  13. Z. Weissman, A. Hardy, M. Katz, M. Oron, D. Eger: Opt. Lett. 20, 674 (1995)

    Article  ADS  Google Scholar 

  14. C. Becker, A. Greiner, Th. Oesselke, A. Pape, W. Sohler, H. Suche: Opt. Lett. 23, 1195 (1998)

    Article  ADS  Google Scholar 

  15. B. Wu, P.L. Chu, H. Hu, Z. Xiong: IEEE J. Quantum Electron. 35, 1369 (1999)

    Article  ADS  Google Scholar 

  16. H.G. Winful, J.H. Marburger, E. Garmire: Appl. Phys. Lett. 35, 379 (1979)

    Article  ADS  Google Scholar 

  17. A. Mecozzi, S. Trillo, S. Wabnitz: Opt. Lett. 12, 1008 (1987)

    Article  ADS  Google Scholar 

  18. W. Chen, D. L. Mills: Phys. Rev. Lett. 58, 160 (1987)

    Article  ADS  Google Scholar 

  19. C.M. de Sterke, J. E. Sipe: Phys. Rev. A 38, 5149 (1988);

    Article  ADS  Google Scholar 

  20. C.M. de Sterke, J. E. Sipe: Phys. Rev. A 39, 5163 (1989);

    Article  ADS  Google Scholar 

  21. C.M. de Sterke, J. E. Sipe: Phys. Rev. A 42, 550 (1990)

    Article  ADS  Google Scholar 

  22. A.B. Aceves, S. Wabnitz: Phys. Lett. A 141, 37 (1989)

    Article  ADS  Google Scholar 

  23. D.N. Christodoulides, R.I. Joseph: Phys. Rev. Lett. 62, 1746 (1989)

    Article  ADS  Google Scholar 

  24. J. Feng, F.K. Kneubül: J. Quantum Electron. QE-29, 590 (1993)

    Google Scholar 

  25. Y.S. Kivshar: Phys.;Rev. E 51, 1613 (1995)

    Google Scholar 

  26. S. Trillo: Opt. Lett. 21, 1732 (1996)

    Article  ADS  Google Scholar 

  27. C. Conti, S. Trillo, G. Assanto: Phys. Rev. Lett: 78, 2341 (1997);

    Article  ADS  Google Scholar 

  28. C. Conti, S. Trillo, G. Assanto: Opt. Lett. 22, 445 (1997)

    Article  ADS  Google Scholar 

  29. H. He, P.D. Drummond: Phys. Rev. Lett. 78, 4311 (1997);

    Article  ADS  Google Scholar 

  30. H. He, P.D. Drummond: Phys. Rev. E 58, 5025 (1998)

    Article  ADS  Google Scholar 

  31. T. Peschel, U. Peschel, F. Lederer, B.A. Malomed: Phys. Rev. E 55, 4730 (1997)

    Article  ADS  Google Scholar 

  32. C. Conti, G. Assanto, S. Trillo: Opt. Lett. 22, 1350 (1997)

    Article  ADS  Google Scholar 

  33. C. Conti, S. Trillo, G. Assanto: Phys. Rev. E 57, R1251 (1998)

    Article  ADS  Google Scholar 

  34. C. Conti, S. Trillo, G. Assanto: Opt. Lett. 23, 334 (1998);

    Article  ADS  Google Scholar 

  35. C. Conti, G. Assanto, S. Trillo: Electron. Lett. 34, 689 (1998)

    Article  Google Scholar 

  36. C. Conti, A. De Rossi, S. Trillo: Opt. Lett. 23, 1265 (1998)

    Article  ADS  Google Scholar 

  37. C. Conti, G. Assanto, S. Trillo: Opt. Exp. 3, 389 (1998)

    Article  ADS  Google Scholar 

  38. W.C.K. Mak, B. A. Malomed, P.L. Chu: Phys. Rev. E 58, 6708 (1998)

    Article  ADS  Google Scholar 

  39. A. Arraf, C.M. de Sterke: Phys. Rev. E 58, 7951 (1998)

    Article  ADS  Google Scholar 

  40. C. Conti, G. Assanto, S. Trillo: Phys. Rev. E 59, 2467 (1999)

    Article  ADS  Google Scholar 

  41. T. Iizuka, Y.S. Kivshar: Phys. Rev. E 59, 7148 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  42. A.V. Buryak, I. Towers, S. Trillo: Phys. Lett. A 267, 319 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  43. S. Trillo, C. Conti, G. Assanto, A.V. Buryak: Chaos 10, 590 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. T. Iizuka, C.M. de Sterke: Phys. Rev. E 62, 4246 (2000)

    Article  ADS  Google Scholar 

  45. S.E. Harris: Appl. Phys. Lett. 9, 114 (1966)

    Article  ADS  Google Scholar 

  46. J.P. Van Der Ziel, L.M. Ilegems: Appl. Phys. Lett. 28, 437 (1976)

    Article  ADS  Google Scholar 

  47. J.U. Kang, Y.J. Ding, W.K. Burns, J.S. Mellinger: Opt. Lett. 22, 862 (1997)

    Article  ADS  Google Scholar 

  48. X. Gu, R.Y. Korotkov, Y.J. Ding, J.U. Kang, J.B. Khurgin: J. Opt. Soc. Am. B 15, 1561 (1998)

    Article  ADS  Google Scholar 

  49. X. Gu, M. Makarov, Y.J. Ding, J.B. Khurgin, W.P. Risk: Opt. Lett. 24, 127 (1999)

    Article  ADS  Google Scholar 

  50. X. Mu, I.B. Zotova, Y.J. Ding, W.P. Risk: Opt. Commun. 181, 153–159 (2000)

    Article  ADS  Google Scholar 

  51. P.S.J. Russell: IEEE J. Quantum Electron. 27, 830 (1991)

    Article  ADS  Google Scholar 

  52. Y.J. Ding, S.J. Lee, J.B. Khurgin: Phys. Rev. Lett. 75, 429 (1995)

    Article  ADS  Google Scholar 

  53. M. Matsumoto, K. Tanaka: J. Quantum. Electron. 31, 700 (1995)

    Article  ADS  Google Scholar 

  54. Y.J. Ding, J.B. Khurgin: Opt. Lett. 21, 1445 (1996);

    Article  ADS  Google Scholar 

  55. Y.J. Ding, J.B. Khurgin: IEEE J. Quantum Electron. 32, 1574 (1996)

    Article  ADS  Google Scholar 

  56. G. D’Alessandro, P.S.J. Russell, A.A. Wheeler: Phys. Rev. A 55, 3211 (1997)

    Article  ADS  Google Scholar 

  57. G.D. Landry, T. Maldonado: Opt. Lett. 22, 1400 (1997);

    Article  ADS  Google Scholar 

  58. G.D. Landry, T. Maldonado: Applied Optics 37, 7809 (1998);

    Article  ADS  Google Scholar 

  59. G.D. Landry, T. Maldonado: IEEE J. Lightwave Tech. 17, 316 (1999)

    Article  ADS  Google Scholar 

  60. P.M. Lushnikov, P. Lodahl, M. Saffman: Opt. Lett. 23, 1650 (1998)

    Article  ADS  Google Scholar 

  61. Y.J. Ding, J.U. Kang, J.B. Khurgin: IEEE J. Quantum Electron. 34, 966 (1998)

    Article  ADS  Google Scholar 

  62. A. Picozzi, M. Haelterman: Opt. Lett. 23, 1808 (1998);

    Article  ADS  Google Scholar 

  63. A. Picozzi, M. Haelterman: Phys. Rev. E 59, 3749 (1999)

    Article  ADS  Google Scholar 

  64. C. Conti, G. Assanto, S. Trillo: Opt. Lett. 25, 1134 (1999)

    Google Scholar 

  65. K. Gallo, P. Baldi, M. De Micheli, D.B. Ostrowsky, G. Assanto: Opt. Lett. 25, 966 (2000)

    Article  ADS  Google Scholar 

  66. C. Conti, S. Trillo, G. Assanto: Phys. Rev. Lett. 85, 2502 (2000)

    Article  ADS  Google Scholar 

  67. G. Cappellini, S. Trillo, S. Wabnitz, R. Chisari: Opt. Lett. 17, 637 (1992)

    Article  ADS  Google Scholar 

  68. P. Byrd, M. Friedman: Handbook of elliptic integrals for engineers and physicists ( Springer, Berlin Heidelberg 1971 )

    Book  Google Scholar 

  69. M. Picciau, G. Leo, G. Assanto: J. Opt. Soc. Am. B 13, 661 (1996)

    Article  ADS  Google Scholar 

  70. A.J. Lichtenberg and M.A. Lieberman: Regular and Stochastic Motion ( Springer, Berlin Heidelberg New York 1983 )

    Book  MATH  Google Scholar 

  71. M. Grillakis, J. Shatah, and W. Strauss: J. Funct. Anal. 74, 160 (1987);

    Article  MathSciNet  MATH  Google Scholar 

  72. M. Grillakis, J. Shatah, and W. Strauss: J. Funct. Anal. 94, 308 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  73. F.V. Marchevskii, V.L. Strizhevskii, V.P. Feshchenko: Sov. J. Quantum Electron. 14, 192 (1984)

    Article  ADS  Google Scholar 

  74. T.V. Makhviladze, M.E. Sarychev: Soy. Phys. JETP 44, 471 (1975)

    ADS  Google Scholar 

  75. A.P. Sukhorukov: Nonlinear Wave Interactions in Optics and Radiophysics ( Nauka, Moscow 1988 ) (in Russian)

    Google Scholar 

  76. J.M. Soto-Crespo, N.N. Akhmediev, V.V. Afanasjev: Opt. Commun. 118, 587 (1995)

    Article  ADS  Google Scholar 

  77. C.B. Clausen, O. Bang, Y.S. Kivshar: Phys. Rev. Lett. 78, 4749 (1997);

    Article  ADS  Google Scholar 

  78. O. Bang, C.B. Clausen, P.L. Christiansen, L. Torner: Opt. Lett. 24, 1413 (1999)

    Article  ADS  Google Scholar 

  79. B. Denardo, B. Galvin, A. Greenfield, A. Larraza, S. Putterman, W. Wright: Phys. Rev. Lett. 68, 1730 (1992)

    Article  ADS  Google Scholar 

  80. Y.S. Kivshar: Phys. Rev. Lett. 70, 3055 (1993)

    Article  ADS  Google Scholar 

  81. G. Huang, Z. Jia: Phys. Rev. B 51, 613 (1995)

    Article  ADS  Google Scholar 

  82. C.B. Clausen, Y.S. Kivshar, O. Bang, P.L. Christiansen: Phys. Rev. Lett. 83, 4740 (1999)

    Article  ADS  Google Scholar 

  83. B. Bourliaguet, V. Couderc, A. Barthelemy, G.W. Ross, P.G.R. Smith, D.C. Hanna, C. De Angelis: Opt. Lett. 24, 1410 (1999)

    Article  ADS  Google Scholar 

  84. K.Y. Kolossovski, A.V. Buryak, and R.A. Sammut: Opt. Lett. 24, 835 (1998)

    Article  ADS  Google Scholar 

  85. S.G. Murdoch, R. Leonhardt, J.D. Harvey, T.A.B. Kennedy: J. Opt. Soc. Am. B 14, 1816 (1997)

    Article  ADS  Google Scholar 

  86. Q. Li, C.T. Chen, K.M. Ho, C.M. Soukoulis: Phys. Rev. B 53, 15577 (1996)

    Article  ADS  Google Scholar 

  87. L. Brzozowski, E.H. Sargent: IEEE J. Quantum Electron. 36, 550 (2000)

    Article  ADS  Google Scholar 

  88. S. Wabnitz: Opt. Lett. 14, 1071 (1989)

    Article  ADS  Google Scholar 

  89. M.G. Vakhitov, A.A. Kolokolov: Radiophys. Quantum Electron. 16, 783 (1973)

    Article  ADS  Google Scholar 

  90. A.V. Buryak, Y.S. Kivshar, S. Trillo: Phys. Rev. Lett. 77, 5210 (1996)

    Article  ADS  Google Scholar 

  91. Bogolubsky: Phys. Lett. 73A, 87 (1979);

    Article  MathSciNet  Google Scholar 

  92. A. Alvarez, B. Carreras: Phys. Lett. 86A, 327 (1981);

    Article  MathSciNet  Google Scholar 

  93. W.A. Strauss, L. Vazques: Phys. Rev. D 34, 641 (1986);

    Article  MathSciNet  ADS  MATH  Google Scholar 

  94. A. Alvarez, M. Soler: Phys. Rev. D 34, 644 (1986)

    Article  ADS  Google Scholar 

  95. V.I. Barashenkov, D.E. Pelinovsky, E.V. Zemlyanaya: Phys. Rev. Lett. 80, 5117 (1998);

    Article  ADS  Google Scholar 

  96. V.I. Barashenkov, E.V. Zemlyanaya: Computer Phys. Commun. 126, 23 (2000)

    ADS  Google Scholar 

  97. A. De Rossi, C. Conti, S. Trillo: Phys. Rev. Lett. 81, 85 (1998)

    Article  ADS  Google Scholar 

  98. R. Gilmore: Catastrophe theory for scientists and engineers ( Dover, New York 1993 )

    Google Scholar 

  99. J. Schöllmann, R. Scheibenzuber, A.S. Kovalev, A.P. Mayer, A.A. Maradunin: Phys. Rev. E 59, 4618 (1999)

    Article  ADS  Google Scholar 

  100. D. Mihalache, D. Mazilu, L. Torner: Phys. Rev. Lett. 81, 4353 (1998)

    Article  ADS  Google Scholar 

  101. M. Johansson, Y.K. Kivshar: Phys. Rev. Lett. 82, 85 (1999)

    Article  ADS  Google Scholar 

  102. H.G. Winful, G.D. Cooperman: Appl. Phys. Lett. 40, 298 (1982)

    Article  ADS  Google Scholar 

  103. H.G. Winful, R. Zamir, S.F. Feldman: Appl. Phys. Lett. 58, 1001 (1991)

    Article  ADS  Google Scholar 

  104. A.B. Aceves, S. Wabnitz, C. De Angelis: Opt. Lett. 17, 1566 (1992)

    Article  ADS  Google Scholar 

  105. C.M. de Sterke: J. Opt. Soc. Am. B 15, 2660 (1998)

    Article  ADS  Google Scholar 

  106. H. He, A. Arraf, C.M. de Sterke, P.D. Drummond, B.A. Malomed: Phys. Rev. E 59, 6064 (1999)

    Article  ADS  Google Scholar 

  107. M. Yu, C.J. McKinstrie, G.P. Agrawal: J. Opt. Soc. Am. B 15, 607 (1998)

    Article  ADS  Google Scholar 

  108. A.R. Champneys, B.A. Malomed, M.J. Friedman: Phys. Rev. Lett. 80, 4169 (1998)

    Article  ADS  Google Scholar 

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  1. C. Conti
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  2. S. Trillo
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  1. Optical Physics Research Department, Lucent Technologies, 600 Mountain Avenue, 07974-0000, Murray Hill, NJ, USA

    Richard E. Slusher

  2. OFS, Laboratories & Specialty Photonics Division, 19 Schoolhouse Rd., 08873-0000, Somerset, NJ, USA

    Benjamin J. Eggleton

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Conti, C., Trillo, S. (2003). Self-transparency and Localization in Gratings with Quadratic Nonlinearity. In: Slusher, R.E., Eggleton, B.J. (eds) Nonlinear Photonic Crystals. Springer Series in Photonics, vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05144-3_5

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