Self-Similar Parabolic Optical Solitary Waves
- 86 Downloads
We study solutions of the nonlinear Schrödinger equation (NLSE) with gain, describing optical pulse propagation in an amplifying medium. We construct a semiclassical self-similar solution with a parabolic temporal variation that corresponds to the energy-containing core of the asymptotically propagating pulse in the amplifying medium. We match the self-similar core through Painlevé functions to the solution of the linearized equation that corresponds to the low-amplitude tails of the pulse. The analytic solution accurately reproduces the numerically calculated solution of the NLSE.
Unable to display preview. Download preview PDF.
- 1.G. I. Barenblatt, Scaling, Self-Similarity, and Intermediate Asymptotics, Cambridge Univ. Press, Cambridge (1996).Google Scholar
- 2.V. I. Kruglov, A. C. Peacock, J. M. Dudley, and J. D. Harvey, Opt. Lett., 25, 1753 (2000).Google Scholar
- 3.M. E. Fermann, V. I. Kruglov, B. C. Thomsen, J. M. Dudley, and J. D. Harvey, Phys. Rev. Lett., 84, 6010 (2000).Google Scholar
- 4.D. Anderson, M. Desaix, M. Karlsson, M. Lisak, and M. L. Quiroga-Teixeiro, J. Opt. Soc. Am. B, 10, 1185 (1993).Google Scholar
- 5.V. E. Zakharov and E. A. Kuznetsov, JETP, 64, 773 (1986).Google Scholar
- 6.N. Joshi and M. D. Kruskal, Phys. Lett. A, 130, 129 (1988); P. A. Clarkson and J. B. McLeod, Arch. Ration. Mech. Anal., 103, 97 (1988); N. Joshi, “Asymptotic studies of the Painlevé equations,” in: The Painlevé Property: One Century Later (R. Conte, ed.) (CRM Series Math. Phys.), Springer, New York (1999), p.181.Google Scholar
- 7.A. R. Its and V. Yu. Novokshenov, The Isomonodromic Deformation Method in the Theory of Painlevé Equations (Lect. Notes Math., Vol. 1191), Springer, Berlin (1986); S. P. Hastings and J. B. McLeod, Arch. Ration. Mech. Anal., 73, 31 (1980).Google Scholar
- 8.E. Desurvire, Erbium-Doped Fiber Amplifiers: Principles and Applications, Wiley, New York (1994).Google Scholar
- 9.O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural'tseva, Linear and Quasi-Linear Equations of Parabolic Type (Transl. Math. Monographs, Vol. 23), Amer. Math. Soc., Providence, R. I. (1968).Google Scholar