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Conservative and dissipative fiber Bragg solitons (a review)

  • Nonlinear and Quantum Optics
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Abstract

We present a comparative review of two classes of optical solitons—conservative and dissipative solitons—propagating in single-mode optical fibers in which refractive-index gratings are induced such that their period is comparable with the radiation wavelength. Fibers that have the Kerr nonlinearity and negligibly small losses and that do not gain radiation (conservative system) are described by traditional equations of the approximation of slowly varying amplitudes, and effects caused by the nonlinearity of the medium, such as nonlinear switching, optical bistability, and formation of conservative Bragg solitons are considered. It is shown that the passage beyond the scope of the approximation of slowly varying amplitudes makes it possible to describe new important effects, including localization of soliton centers near maxima of the refractive-index grating. Bright and dark conservative solitons are demonstrated, which are formed when the Kerr nonlinearity is replaced by the nonlinearity of two-level atomic systems. The properties of conservative solitons in resonance semiconductor Bragg structures with quantum wells are considered. Results of experimental studies of nonlinear effects in fibers with Bragg gratings are presented. For an active single-mode fiber with a Bragg refractive-index grating and nonlinear gain and absorption, dissipative solitons are described using the approximation of slowly varying amplitudes and inertialess nonlinearity. It is shown that the dissipative factors qualitatively change the properties of solitons compared to the conservative case. Using the Maxwell-Bloch equations, it is demonstrated that the ratio between the gain and absorption relaxation times significantly affects the stability of localized structures. The interaction of dissipative optical Bragg solitons is described. It is shown that, beyond the scope of the approximation of slowly varying amplitudes, the average velocity of propagating dissipative Bragg solitons acquires only discrete values, and formation of pairs of solitons with two values of the phase difference becomes possible. For a birefringent fiber, dissipative vector optical Bragg solitons are demonstrated.

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References

  1. Yu. S. Kivshar and G. P. Agrawal, Optical Solitons: From Fibers to Photonic Crystals (Academic, Amsterdam, 2003; Fizmatlit, Moscow, 2005).

    Google Scholar 

  2. R. L. Freeman, Fiber-Optic Systems for Telecommunications (Wiley, New York, 2002; Tekhnosfera, Moscow, 2003).

    Google Scholar 

  3. R. Eashyap, Fiber Bragg Gratings (Academic, San Diego, 1999).

    Google Scholar 

  4. N. M. Litchinitser, B. J. Eggleton, D. B. Patterson, J. Lightwave Technol. 15, 1303 (1997).

    Article  ADS  Google Scholar 

  5. M. C. Amann et al., Appl. Phys. Lett. 54, 2532 (1989).

    Article  ADS  Google Scholar 

  6. A. D. Kersey, Optical. Fiber Technol. 2, 291 (1996).

    Article  ADS  Google Scholar 

  7. S. P. Abdullina, S. A. Babin, S. A. Vlasov, and S. I. Kablukov, Kvantovaya Élektron. (Moscow). 36(10), 966 (2006).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. C. M. De Sterke, Opt. Lett. 17, 914 (1992).

    ADS  Google Scholar 

  10. N. G. R. Broderick, D. Taverner, D. J. Richardson, et al., Opt. Expr. 3, 447 (1998).

    ADS  Google Scholar 

  11. Ultra Long-Haul Photonic Line System (June 2004); http://www.marconi.com.

  12. Yu. I. Voloshchenko, Yu. N. Ryzhov, and V. E. Sotin, Zh. Tekh. Fiz. 51, 902 (1981).

    Google Scholar 

  13. B. J. Eggleton, R. E. Slusher, C. M. de Sterke, et al., Phys. Rev. Lett. 76, 1627 (1996).

    Article  ADS  Google Scholar 

  14. Turukhin A. V. et al., Phys. Rev. Lett. 88, 023602 (2002).

  15. N. N. Rosanov, Spatial Hysteresis and Optical Patterns (Springer, Berlin, 2002).

    MATH  Google Scholar 

  16. N. N. Akhmediev and A. Ankiewicz, Solitons, Nonlinear Pulses and Beams (Chapman and Hall, London, 1997; Fizmatlit, Moscow, 2004).

    Google Scholar 

  17. Dissipative Solitons, Ed. by N. Akhmediev and A. Ankiewicz (Springer, Berlin, 2005).

    MATH  Google Scholar 

  18. K. Staliunas, Phys. Rev. Lett. 91, 053901 (2003).

    Google Scholar 

  19. A. V. Yulin, D. V. Skryabin, and P. St. J. Russel, Opt. Expr. 13(9), 3529 (2005).

    Article  ADS  Google Scholar 

  20. N. N. Rozanov and S. Ch. Chan, Opt. Spektrosk. 101(2), 286 (2006) [Opt. Spectrosc. 101 (2), 271 (2006)].

    Article  Google Scholar 

  21. N. N. Rozanov and X. Tr. Tran, Izv. Akad. Nauk, Ser. Fiz. 70(9), 1251 (2006).

    Google Scholar 

  22. X. Tr. Tran, in Problems of Coherent and Nonlinear Optics, Ed. by S. A. Kozlov and I. P. Gurov (St. Petersburg, 2006) [in Russian].

  23. N. N. Rozanov and X. Tr. Tran, Opt. Spektrosk. 102(5), 805 (2007) [Opt. Spectrosc. 102 (5), 739 (2007)].

    Google Scholar 

  24. N. N. Rozanov and S. Ch. Chan, Kvantovaya Élektron. (Moscow). 37(8), 720 (2007).

    Article  Google Scholar 

  25. N. N. Rosanov and X. Tr. Tran, Chaos 17, 037114 (2007).

  26. X. Tr. Tran and N. N. Rosanov, Opt. Quant. Electron. (2008) (in press).

  27. X. Tr. Tran and N. N. Rozanov, Opt. Spektrosk. 104(4), 637 (2008) [Opt. Spectrosc. 104 (4), 558 (2008)].

    Article  Google Scholar 

  28. K. O. Hill, Y. Fujii, D. C. Johnson, and B. S. Kawasaki, Appl. Phys. Lett. 32, 647 (1978).

    Article  ADS  Google Scholar 

  29. G. Meltz, W. W. Morey, and W. H. Glenn, Opt. Lett. 14, 823 (1989).

    ADS  Google Scholar 

  30. A. Othonos and K. Kalli, Fiber Bragg Gratings: Fundamentals and Applications in Telecommunications and Sensing (Artech House, Norwood, 1999).

    Google Scholar 

  31. P. J. Lemaire, R. M. Atkins, et al., Electron. Lett. 29, 1191 (1993).

    Article  Google Scholar 

  32. M. B. Vinogradova, O. V. Rudenko, and A. P. Sukhorukov, The Theory of Waves, 2nd ed. (Nauka, Moscow, 1990) [in Russian].

    Google Scholar 

  33. H. A. Hause, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, 1984; Mir, Moscow, 1988).

    Google Scholar 

  34. A. Kozhekin and G. Kurizki, Phys. Rev. Lett. 74, 5020 (1995).

    Article  ADS  Google Scholar 

  35. A. Kozhekin, G. Kurizki, and B. Malomed, Phys. Rev. Lett. 81, 3647 (1998).

    Article  ADS  Google Scholar 

  36. T. Opartný, B. Malomed, and G. Kurizki, Phys. Rev. E 60, 6137 (1999).

    Article  ADS  Google Scholar 

  37. E. L. Ivchenko, V. P. Kochreshko, A. V. Platonov, et al., Fiz. Tverd. Tela (St. Petersburg) 39, 2072 (1997).

    Google Scholar 

  38. E. L. Ivchenko, in Optics of Nanostructures (Nedra, St. Petersburg, 2005), pp. 107–180 [in Russian].

    Google Scholar 

  39. E. L. Ivchenko and M. Willander, Phys. Stat. Sol. 215, 199 (1999).

    Article  Google Scholar 

  40. L. I. Deych and A. A. Lisyansky, Phys. Rev. B 62, 4242 (2000).

    Article  ADS  Google Scholar 

  41. I. B. Talania, Phys. Lett. A. 241, 179 (1998).

    Article  ADS  Google Scholar 

  42. G. Kurizki, A. Kozhekin, T. Opartný, and B. Malomed, cond-mat/0007007.

  43. Y. Merle d’Aubigné, A. Wasiela, H. Mariette, and T. Dietl, Phys. Rev. B. 54, 14003 (1996).

    Article  ADS  Google Scholar 

  44. M. Hübner, J. P. Prineas, C. Ell, et al., Phys. Rev. Lett. 83, 2841 (1999).

    Article  ADS  Google Scholar 

  45. R. H. Goodman, R. E. Slusher, and M. L. Weinstein, J. Opt. Soc. Am. B 19(7), 1635 (2002).

    Article  ADS  Google Scholar 

  46. B. Crosignani, A. Cutolo, and P. Di Porto, J. Opt. Soc. Am. 72, 515 (1982).

    Google Scholar 

  47. G. G. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, 1995; Mir, Moscow, 1996).

    Google Scholar 

  48. C. M. de Sterke and J. E. Sipe, Phys. Rev. A. 42, 2858 (1990).

    Article  ADS  Google Scholar 

  49. G. G. Agrawal, Application of Nonlinear Fiber Optics (Academic, San Diego, 2001).

    Google Scholar 

  50. H. G. Winful, R. Zamir, and S. Feldman, Appl. Phys. Lett. 58, 1001 (1991).

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  52. C. M. de Sterke, Phys. Rev. A. 45, 8252 (1992).

    Article  ADS  Google Scholar 

  53. B. J. Eggleton, C. M. de Sterke, R. E. Slusher, and J. E. Sipe, Electron. Lett. 32, 2341 (1996).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  55. W. Chen and D. L. Mills, Phys. Rev. Lett. 58, 160 (1987).

    Article  ADS  Google Scholar 

  56. W. Chen and D. L. Mills, Phys. Rev. B 36, 6269 (1987).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  58. A. B. Aceves and S. Wabnitz, Phys. Lett. A 141, 37 (1989).

    Article  ADS  Google Scholar 

  59. J. Feng and F. K. Kneubühl, IEEE J. Quant. Electron. 29, 590 (1993).

    Article  ADS  Google Scholar 

  60. C. Conti and S. Trillo, Phys. Rev. E 64, 036617 (2001).

  61. T. Iizuka and C. M. de Sterke Phys. Rev. E 61, 4491 (2000).

    Article  ADS  Google Scholar 

  62. A. A. Sukhorukov and Y. S. Kivshar, Phys. Rev. Lett. 97, 233901 (2006).

    Google Scholar 

  63. B. J. Eggleton, R. R. Slusher, C. M. de Sterke, et al., Phys. Rev. Lett. 76, 1627 (1996).

    Article  ADS  Google Scholar 

  64. C. M. de Sterke, N. G. R. Broderick, B. J. Eggleton, and M. J. Steel, Opt. Fiber Technol. 2, 253 (1996).

    Article  ADS  Google Scholar 

  65. M. Asobe, Opt. Fiber Technol. 3, 142 (1997).

    Article  ADS  Google Scholar 

  66. J. E. Sipe and H. G. Winful, Opt. Lett. 13, 132 (1988).

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  68. C. M. de Sterke, D. G. Salinas, and J. E. Sipe, Phys. Rev. E. 54, 1969 (1996).

    Article  ADS  Google Scholar 

  69. T. Iizuka and M. Wadati, J. Opt. Soc. Am. B. 14, 2308 (1997).

    Google Scholar 

  70. C. M. de Sterke and B. J. Eggleton, Phys. Rev. E. 59, 1267 (1999).

    Article  ADS  Google Scholar 

  71. V. E. Zakharov and A. B. Shabat, Zh. Éksp. Teor. Fiz. 61, 118 (1971).

    Google Scholar 

  72. V. E. Zakharov and A. B. Shabat, Zh. Éksp. Teor. Fiz. 64, 1627 (1973).

    Google Scholar 

  73. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: the Inverse Scattering Method (Plenum, New York, 1984).

    Google Scholar 

  74. I. V. Barashenkov, D. E. Pelinovsky, and E. V. Zemlyanaya, Phys. Rev. Lett. 80, 5117 (1998).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  76. J. Schöllmann, R. Scheibenzuber, A. S. Kovalev, et al., Phys. Rev. E. 59, 4618 (1999).

    Article  ADS  Google Scholar 

  77. I. V. Barashenkov and E. V. Zemlyanaya, Comp. Phys. Commun. 126, 22 (2000).

    Article  MATH  ADS  Google Scholar 

  78. J. Schöllmann and A. P. Mayer, Phys. Rev. E. 61, 5830 (2000).

    Article  ADS  Google Scholar 

  79. J. Schöllmann, Physica A 288, 218 (2000).

    Article  ADS  Google Scholar 

  80. B. J. Eggleton, C. M. de Sterke, and R. E. Slusher, J. Opt. Soc. Am. B. 16, 587 (1999).

    Article  ADS  Google Scholar 

  81. P. St. J. Russell, J. Mod. Opt. 38, 1599 (1991).

    Article  ADS  Google Scholar 

  82. H. G. Winful and V. Perlin Phys. Rev. Lett. 84, 3586 (2000).

    Article  ADS  Google Scholar 

  83. H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, San Diego, 1985; Mir, Moscow, 1988).

    Google Scholar 

  84. H. Kawaguchi, K. Inoue, T. Matsuoka, and K. Otsuka, IEEE J. Quant. Electron. 21, 1314 (1985).

    Article  ADS  Google Scholar 

  85. M. J. Adams and R. Wyatt, IEEE Proc. 134, 35 (1987).

    Google Scholar 

  86. M. J. Adams and R. Wyatt, Opt. Quant. Electron. 19, 37 (1987).

    Article  Google Scholar 

  87. G. P. Agrawal and S. Radic, IEEE Photon. Technol. Lett. 6, 995 (1994).

    Article  ADS  Google Scholar 

  88. S. Radic, N. George, and G. P. Agrawal, Opt. Lett. 19(21), 1789 (1994).

    ADS  Google Scholar 

  89. S. Radic, N. George, and G. P. Agrawal, J. Opt. Soc. Am. B 12(4), 671 (1995).

    ADS  Google Scholar 

  90. D. Taverner, N. G. R. Broderick, D. J. Richardson, et al., Opt. Lett. 23, 328 (1998).

    Article  ADS  Google Scholar 

  91. H. G. Winful and G. D. Cooperman, Appl. Phys. Lett. 40, 298 (1982).

    Article  ADS  Google Scholar 

  92. N. G. R. Broderick, D. J. Richardson, and M. Isben, Opt. Lett. 25, 536 (2000).

    Article  ADS  Google Scholar 

  93. S. Larochelle, V. Mizrahi, and G. Stegeman, Electron. Lett. 26, 1459 (1990).

    Article  Google Scholar 

  94. C. M. de Sterke, Opt. Lett. 17, 914 (1992).

    ADS  Google Scholar 

  95. N. G. R. Broderick, D. Taverner, D. J. Richardson, et al., Phys. Rev. Lett. 79, 4566 (1997); Opt. Lett. 22, 1837 (1997).

    Article  ADS  Google Scholar 

  96. S. Ha, A. A. Sukhorukov, and Y. S. Kivshar, Opt. Lett. 32, 1429 (2007).

    Article  ADS  Google Scholar 

  97. S. Lee, and S. T. Ho, Opt. Lett. 18, 962 (1993).

    Article  ADS  Google Scholar 

  98. W. Samir, S. J. Garth, and C. Pask J. Opt. Soc. Am. B 11, 64 (1994).

    ADS  Google Scholar 

  99. W. Samir, C. Pask, and S. J. Garth, Opt. Lett. 19, 338 (1994).

    Article  ADS  Google Scholar 

  100. S. Pereira and J. E. Sipe, Opt. Exp. 3, 418 (1998).

    Article  ADS  Google Scholar 

  101. R. E. Slusher, S. Spalter, B. J. Eggleton, et al., Opt. Lett. 25, 749 (2000).

    Article  ADS  Google Scholar 

  102. S. Pereira, J. E. Sipe, R. E. Slusher, and S. Spalter J. Opt. Soc. Am. B 19, 1509 (2002).

    Article  ADS  Google Scholar 

  103. D. Taverner, N. G. R. Broderick, D. J. Richardson, et al., Opt. Lett. 23, 259 (1998).

    Article  ADS  Google Scholar 

  104. S. Broderick, Opt. Commun. 148, 90 (1999).

    Article  ADS  Google Scholar 

  105. Y. P. Shapira and M. Horowitz, Opt. Lett. 32, 1211 (2007).

    Article  ADS  Google Scholar 

  106. E. Kamke, Differentialgleichungen. Lösungsmethoden und Lösungen, Bd. I: Gewöhnliche Differentialgleichungen (Geest und Portig, Leipzig, 1959; Fizmatgiz, Moscow, 1961).

    Google Scholar 

  107. A. G. Vladimirov, D. V. Skryabin, G. Kozyreff, et al., Opt. Exp. 14, 1 (2006).

    Article  ADS  Google Scholar 

  108. I. V. Babushkin, N. A. Loĭko, and N. N. Rozanov, Opt. Spektrosk. 102(2), 285 (2007) [Opt. Spectrosc. 102 (2), 248 (2007)].

    Article  Google Scholar 

  109. B. Luo and S. Chi, Opt. Lett. 22, 2216 (2003).

    Article  ADS  Google Scholar 

  110. V. I. Bespalov and V. I. Talanov, JETP Lett. 3, 471 (1966)].

    Google Scholar 

  111. Ya. I. Khanin, Principles of Laser Dynamics (Elsevier, Amsterdam, 1995).

    Google Scholar 

  112. S. V. Fedorov, A. G. Vladimirov, G. A. Khodova, and N. N. Rosanov, Phys. Rev. E 61, 5814 (2000).

    Article  ADS  Google Scholar 

  113. N. N. Rozanov, S. V. Fedorov, and A. N. Shatsev, in Problems of Coherent and Nonlinear Optics, Ed. by I. P. Gurov and S. A. Kozlov (ITMO (TU), St. Petersburg, 2006), pp. 133–176 [in Russian].

    Google Scholar 

  114. A. B. Aceves and S. Wabnitz, Phys. Lett. A. 141, 37 (1989).

    Article  ADS  Google Scholar 

  115. N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Phys. Rev. Lett. 95, 053903 (2005).

    Google Scholar 

  116. N. N. Rosanov, S. V. Fedorov, and A. N. Shatsev, Appl. Phys. B 81(7), 937 (2005).

    Article  ADS  Google Scholar 

  117. N. N. Rozanov, S. V. Fedorov, and A. N. Shatsev, Zh. Éksp. Teor. Fiz. 129(4), 625 (2006) [JETP 102 (4), 547 (2006).

    Google Scholar 

  118. K. A. Gorshkov and L. A. Osrtovsky, Phys. D (Amsterdam) 3, 428 (1981).

    ADS  Google Scholar 

  119. N. N. Rozanov, V. E. Semenov, and N. V. Vysotina, Kvantovaya Élektron. (Moscow), 38, 137 (2008).

    Article  Google Scholar 

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  1. St. Petersburg State University of Information Technologies, Mechanics, and Optics, St. Petersburg, 197101, Russia

    X. Tr. Tran & N. N. Rosanov

  2. Vavilov State Optical Institute, Institute of Laser Physics, St. Petersburg, 199034, Russia

    N. N. Rosanov

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Original Russian Text © X.Tr. Tran, N.N. Rosanov, 2008, published in Optika i Spektroskopiya, 2008, Vol. 105, No. 3, pp. 432–477.

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Tran, X.T., Rosanov, N.N. Conservative and dissipative fiber Bragg solitons (a review). Opt. Spectrosc. 105, 393–435 (2008). https://doi.org/10.1134/S0030400X08090130

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