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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 532610, 6 pages
http://dx.doi.org/10.1155/2012/532610
Research Article

Stable One-Dimensional Periodic Wave in Kerr-Type and Quadratic Nonlinear Media

Department of Constructive and Technological Engineering—Lasers and Fibre Optic Communications, National Institute of R&D for Optoelectronics INOE 2000, 409 Atomistilor Street, P.O. Box MG-5, 077125 Magurele, Ilfov, Romania

Received 6 December 2011; Revised 9 February 2012; Accepted 13 February 2012

Academic Editor: Cristian Toma

Copyright © 2012 Roxana Savastru et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present the propagation of optical beams and the properties of one-dimensional (1D) spatial solitons (“bright” and “dark”) in saturated Kerr-type and quadratic nonlinear media. Special attention is paid to the recent advances of the theory of soliton stability. We show that the stabilization of bright periodic waves occurs above a certain threshold power level and the dark periodic waves can be destabilized by the saturation of the nonlinear response, while the dark quadratic waves turn out to be metastable in the broad range of material parameters. The propagation of (1+1) a dimension-optical field on saturated Kerr media using nonlinear Schrödinger equations is described. A model for the envelope one-dimensional evolution equation is built up using the Laplace transform.