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Mathematical Modelling in Fiber and Waveguide Grating Structures

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Part of the book series: Lecture Notes in Physics ((LNP,volume 613))

Abstract

In this chapter, I give an overview of mathematical modelling in fiber and waveguide grating structures. Studies on fiber and waveguide gratings and fiber arrays are presented. The possible formation of soliton-like and bullet-like pulses in such media are discussed.

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References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. B.J. Eggleton, R.E. Slusher, C.M. de Sterke, P.A. Krug, and J.E. Sipe:Phys. Rev. Lett. 76, 1627 (1996); B.J. Eggleton:J. Opt. Soc. Am. B 14, (1997).

    Article  ADS  Google Scholar 

  5. N. G. R. Broderick, D. J. Richardson and M. Ibsen:Opt. Lett. 25, 536 (2000).

    Article  ADS  Google Scholar 

  6. R. H. Goodman, R. E. Slusher and M. I. Weinstein, “Stopping Light on a Defect”:J. Opt. Soc. Am. B (to appear)

    Google Scholar 

  7. N. Aközbek and S. John: Phys. Rev. E 58, 3876(1998).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. V. Rupasov and M. Singh:Phys. Rev. A 54, 3614 (1996).

    Article  ADS  Google Scholar 

  10. O. Zobay, S. Potting, P. Meystre and E. M. Wright: Phys. Rev. A 59, 643 (1999).

    Article  ADS  Google Scholar 

  11. C.M. de Sterke and J.E. Sipe,: In:Progress in Optics, Vol XXXIII (North-Holland, Amsterdam), 203 (1994).

    Google Scholar 

  12. E. A. Kuznetsov, and A. V. Mikhailov: Teor. Mat. Fiz. 30, 193 (1977).

    Google Scholar 

  13. D. J. Kaup, and A. C. Newell: Lett. Nuovo Cimento 20, 325 (1977).

    Article  MathSciNet  Google Scholar 

  14. A.V. Mikhailov: Pis’ma Zh. Eksp. Teor. Fiz. 23, 356 (1976)

    ADS  Google Scholar 

  15. D. David, J. Harnad and S. Shnider: Lett. Math. Phys. 8, 27 (1984).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  16. R.F. Bikbaev:Teor. Mat. Fiz. 63, 377 (1985).

    Google Scholar 

  17. L. Brillouin, Wave propagation in periodic structures, (McGraw-Hill, New York, 1946).

    MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. D. L. Mills and S. E. Trullinger:Phys. Rev. B 36, 947 (1987).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  22. S. J. Chang, S. D. Ellis and B. W. Lee: Phys. Rev D 11, 3572 (1975).

    Article  ADS  Google Scholar 

  23. A. B. Aceves, G. Fibich and B. Ilan: Physica D (to appear).

    Google Scholar 

  24. N. Aközbek and S. John: Phys. Rev. E 57, 2287 (1998).

    Article  ADS  Google Scholar 

  25. S. F. Mingaleev and Y. S. Kivshar:Phys. Rev. Lett. 86, 5474 (2001).

    Article  ADS  Google Scholar 

  26. A. B. Aceves, B. Costantini and C. De Angelis: J. Opt. Soc. Am. B 12, 1475 (1995).

    Article  ADS  Google Scholar 

  27. N. M. Litchinitser, C. J. McKinstrie, C. M. de Sterke:J. Opt. Soc. Am. B 18, 45 (2001).

    Article  ADS  Google Scholar 

  28. C. Sulem and P.L. Sulem, The nonlinear Schrödinger equation, (Springer, New-York, 1999).

    MATH  Google Scholar 

  29. G. Fibich and G. C. Papanicolaou:SIAM J. of Appl. Math. 60, 183 (1999).

    Article  MATH  MathSciNet  Google Scholar 

  30. C.M. Bender and S. Orszag, Advanced Mathematical Methods for Scientists and Engineers. (McGraw-Hill New York, 1978).

    MATH  Google Scholar 

  31. G. Fibich and A. Gaeta: Opt. Lett. 25, 335 (2000)

    Article  ADS  Google Scholar 

  32. M.J. Landman, G.C. Papanicolaou, C. Sulem, P.L. Sulem and X.P. Wang: Physica D 47, 393 (1991)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  33. G. Fibich and B. Ilan:J. Opt. Soc. Am. B 17, 1749 (2000)

    Article  ADS  Google Scholar 

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Aceves, A.B. (2002). Mathematical Modelling in Fiber and Waveguide Grating Structures. In: Porsezian, K., Kuriakose, V.C. (eds) Optical Solitons. Lecture Notes in Physics, vol 613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36141-3_8

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  • DOI: https://doi.org/10.1007/3-540-36141-3_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00155-3

  • Online ISBN: 978-3-540-36141-1

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