Pulse Propagation in a Non-Linear Medium

Gaston Edah 1 , Villévo Adanhounmè 2 , Antonin Kanfon 1 , François Guédjé 2 , and Mahouton Norbert Hounkonnou 2
  • 1 Département de Physique, Faculté des Sciences et Techniques, Université d’Abomey-Calavi, Bénin
  • 2 International Chair of Mathematical Physics and Applications (ICMPA-Unesco Chair), Université d’Abomey-Calavi, Bénin

Abstract

This paper considers a novel approach to solving the general propagation equation of optical pulses in an arbitrary non-linear medium. Using a suitable change of variable and applying the Adomian decomposition method to the non-linear Schrödinger equation, an analytical solution can be obtained which takes into accountparameters such as attenuation factor, the second order dispersive parameter, the third order dispersive parameter and the non-linear Kerr effect coefficient. By analysing the solution, this paper establishes that this method is suitable for the study of light pulse propagation in a non-linear optical medium.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] G. Zhang and X. Zhang, Opt. Commun., 270, 379-383 (2007).

  • [2] J. R. Bogning, Chaos Solitons and Fractals, 27,148-153 (2006).

  • [3] V. I. Kruglov, A.C. Peacock and J.D. Harvey, Phys. Rev. E-Stat. Nonlinear Soft Matter Phys.,71, 056619-056630, (2005).

  • [4] G. Adomian, Kluwer Aca-demic, Dordrecht, (1994).

  • [5] G. Adomian, Math. Comput. Simulat. 30, 325-329, (1988).

  • [6] G. Adomian and R. Rach, J. Math. Anal. Appl. 174, 118-137, (1993).

  • [7] G. Adomian and R. Rach,23, 615-619, (1994).

  • [8] K. Scott and Y. P. Sun. In: C. G. Vayenas, R. E. White and M. E. Gamboa-Adelco (Eds.), Modern Aspects of Electrochemistry 41, Springer, New York, 222-304, (2007).

  • [9] K. Abbaoui and Y. Cherruault, Comput.Math. Appl., 28, 103-109, (1994).

  • [10] A. Abdelrazec and D. Pelinosky, Numer. Methods Partial Differential Equations,27, 749-766, (2011).

  • [11] Y. Cherruault, Convergence of Adomian’s method, (Kybernetes, 18(2), 31-38, (1989).

  • [12] S. Ghosh, D. Roy, A., and D. Roy, Comput. Meth. Appl.Mech.Engrg., 196, 1133-1153, (2007).

  • [13] H. Jafari, and V. Daftardar-Gejji, Appl. Math. Comput., 175, 17, 598-608, (2006).

  • [14] S. Pamuk, Phys.Lett. A, 344, 184-188, (2005).

  • [15] X. Zhang, J. Comput. Appl. Math.,180, 377-389, (2005).

  • [16] D. Kaya, and A. Yokus, Math. Comput. Simul., 60, 507-512, (2002).

OPEN ACCESS

Journal + Issues

Search