Explicit Variational Solution of the Cubic-Quintic Nonlinear Schrödinger Equation for Pulse Propagation in Optical Fibers

Abstract

With a variational method, we study the cubic-quintic nonlinear Schrödinger equation for pulse propagation in optical fibers. Anomalous dispersion that gives rise to fundamental bright solitary waves is considered. It is shown that within the specified limits, the present variational model demonstrates (for 1 picosecond pulse) good agreements with its analytical equivalent. It is proved that for negative coefficient of the fifth-order nonlinearity existence of the two-state solitary wave solution is a peculiarity of the variational formulation.

Nonlinear Propagation of a Mixture of TEM00and TEM01Modes of a Laser Beam in a Cubic Quintic Medium

“…Thus, in order to investigate laser beam propagation in such materials it is necessary to consider higher order nonlinearities in place of usual Kerr nonlinearity. The simplest form of higher order nonlinearities is encountered in a cubic quintic nonlinear medium also known as parabolic medium, in which the refractive index of the medium is modeled as [26,[28][29][30]…”

Stable and Quasistable Spatio-Temporal Solitons in Cubic Quintic Nonlinear Media

“…22,23 Experimental results of nonlinear absorption 24 in semiconductor-doped glass and other composite materials show that nonlinearity saturates at moderate intensities. The simplest form of saturating nonlinearity is encountered in a cubic quintic nonlinear (CQNL) medium in which the refractive index of the medium is modelled as [25][26][27][28] …”

“…Spatial and temporal soliton propagation in a quintic nonlinear medium have been investigated by many authors. [25][26][27][28][29]31,32 Three-dimensional spatio-temporal bright vortex soliton in a bulk dispersive cubic quintic optical medium has been predicted recently. 33 In addition, 2D and 3D spatio-temporal spinning solitons with focusing cubic and defocusing quintic nonlinearity have also been investigated by several workers.…”