Radiation reduction of optical solitons resulting from higher order dispersion terms in the nonlinear Schrödinger equation

Abstract

This paper will present the nonlinearity and dispersion effects involved in propagation of optical solitons, which can be understood by using a numerical routine to solve the nonlinear Schrödinger equation~NLSE!. Here, Mathematica v5 Wolfram, 2003! is used to explore in depth several features of optical solitons formation and propagation. These numerical routines were implemented through the use of Mathematica v5 and the results give a very clear idea of this interesting and important practical phenomenon. It is hoped that this work will open up an important new approach to the cause, effect, and correction of interference from secondary radiation found in the uses of soliton waves in lasers and in optical fiber telecommunication. It is believed that these results will be of considerable use in any work or research in this field and in self-focusing properties of the soliton~Osman et al., 2004a, 2004bHora, 1991!. In a previous paper on this topic~Beech & Osman, 2004!, it was shown that solitons of NLSE radiate. This paper goes on from there to show that these radiations only occur in solitons derived from cubic, or odd-numbered higher orders of NLSE, and that there are no such radiations from solitons of quadratic, or even-numbered higher order of NLSE. It is anticipated that this will stimulate research into practical means to control or eliminate such radiations.

Self‐focusing of an electromagnetic pulse in the ionosphere

“…The essential differences between the focusing and defocusing cases were investigated for an arbitrary nonlinearity. This theory was extended to the solution of the nonlinear Schrödinger equation with particular reference to solitons [Beech and Osman, 2005]. An interesting investigation, in which self-focusing of laser pulse plays an important role has been recently made by Laska et al [2006].…”

Self-focusing and self-phase modulation of an elliptic Gaussian laser beam in collisionless magnetoplasma

“…The value was confirmed by different derivations Palmer, 1971;Shearer & Eddleman, 1973;Kaw et al, 1973! andin subsequent publications~Jones et al, 1982;Hauser et al, 1988Hauser et al, , 1992Bret et al, 2005;Beech & Osman, 2005;Anderson et al, 2005!. It has been extensively studied in context of laser beam propagation since the earlier sixties Askar 'yan, 1962;Akhmanov et al, 1968;Sodha et al, 1976;Anderson et al, 1979;Berge, 1997!. In the plasma based applications, it is required that intense laser light be propagated through thousands of wavelengths of underdense plasma.…”

Stationary self‐focusing of Gaussian electromagnetic beams in the ionosphere

“…Using the formalism of Akhmanov et al [1968] and its extension by Sodha et al [1974, 1976] as well as the radial distribution of the dielectric function (as indicated in the preceding paragraph), the self‐focusing of an electromagnetic Gaussian beam in the ionosphere has been investigated in the paraxial approximation. There has been important work on the solution of the time‐dependent paraxial [ Osman et al , 2000, 2004] or nonlinear Schrödinger's equation with particular reference to solitons [ Beech and Osman , 2005]; however, this has not been made use of in the present investigation on account of the fact that the present analysis is confined to the steady state.…”