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Multiconference on Electronics and Photonics (MEP)

Solitons propagation in non-homogeneous periodic media by tandem arrangement of nonlinear materials

J. J. Sánchez-Mondragón, Miguel Torres-Cisneros, A. Alejo-Molina, José Amparo Andrade-Lucio, Rosenberg Javier Romero, M. A. Basurto‐Pensado

Published Jan 1, 2006• 0 citations
Publisher

Abstract

In this work we discuss the characteristics of the resonant pulse propagation through a sequence of two level atom media and in the presence of intensity dependent nonlinearities that occur in Kerr & photorefractive materials. The area theorem conveniently describe the evolution of the soliton eigenvalues through the stratified medium, an essential analytical tool lacking in the intensity dependent nonlinearities, thereof its understanding clarifies the general problem. We can conclude that rather than a mean soliton, we have a modulated solution.

DOI
10.1109/mep.2006.335680

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In this work we discuss the characteristics of the resonant pulse propagation through a sequence of two level atom media and in the presence of intensity dependent nonlinearities that occur in Kerr & photorefractive materials. The area theorem conveniently describe the evolution of the soliton eigenvalues through the stratified medium, an essential analytical tool lacking in the intensity dependent nonlinearities, thereof its understanding clarifies the general problem. We can conclude that rather than a mean soliton, we have a modulated solution.
Spatial and temporal solitons are at the core of many physical, geological, biological, transmission and information processing and other problems. However, in most cases we have focused on their steady behavior, and therefore on homogeneous media and their single soliton eigenvalues spectrum. This has been done even in the case of an all optical simultaneous loss and amplification, where we have assumed stability of those eigenvalues. However, the transient behavior has received little attention, often disregarded under a generic pulse reshaping or experimentally diafragmed as often occurs in large amplifiers. But such transient behavior can be frozen in a periodic nonhomogenous media, tandems, where such behavior corresponds to the soliton convergence in each tandem media, producing a regular but not steady behavior. We discuss the resonant pulse propagation in a two level atom media tandem, described by a real convergence and a Kerr intensity dependent nonlinearity, described by a complex convergence.
In this complement we discuss several examples of optical phenomena in media where the refractive index depends nonlinearly on the intensity , known as optical Kerr media. This nonlinear effect exists in all materials, even isotropic ones, like glass or fused silica, but it is particularly marked in certain physical systems to be exemplified in Section 7B.1. After investigating the propagation of light through such media in Section 7B.2, we shall discuss three applications of the optical Kerr effect (which can be studied in any order). We begin by describing a bistable optical system , when this nonlinear medium is inserted in a Fabry–Perot cavity (Section 7B.3). We then study phase conjugate mirrors and examine their potential applications in adaptive optics (Section 7B.4). Finally, we discuss certain effects occurring during the propagation of an isolated wave, bounded either transversely or temporally, in a Kerr medium, and describe self-focusing effects (Section 7B.5) and self-phase-modulation effects (Section 7B.6). In particular, we shall show that nonlinear effects and dispersion effects can compensate to produce stable structures known as solitons , which maintain their shape during propagation. Examples of third-order nonlinearities Nonlinear response of two-level atoms We begin by studying a simple case of a nonlinear interaction, namely a two-level quantum system under the effects of a plane wave.
Special features of generating a self-induced transparency in a medium with both resonant and non-resonant (Kerr-type) nonlinearities are considered. Soliton solutions of the Maxwell-Bloch equations are found, taking into account the diffraction divergence of the light beam. It is shown that solitons emerge in such a medium under conditions of two-dimensional optical beam scanning along the medium surface, and have non-coinciding propagating directions of the amplitude and phase fronts. As a necessary condition for the existence of solitons, there is a definite relationship between the scanning velocity and the parameters of the medium and radiation.
We have found a steady-state solution for a pulse propagating in imhogeneously broadened resonant two-level atoms embedded in a dispersive and nonlinear Kerr lossless host medium. The pulse is of an unchirped hyperbolic-secant form with a linear spatial phase delay. There are several salient features in this solution which are different from the results obtained previously. First, for the given parameters of the medium and carrier frequency, the group velocity, the amplitude, and the pulse width are uniquely determined. Second, the group velocity is independent of the density of the resonant atoms. Third, the solution exists in the positive dispersion region, which is different from solitons in fibers.
The area devoted to cross-Kerr nonlinearity and coherent driving fields is increasingly used to control optical solitons in atomic media. Recently, this area has been investigated by using the concepts of fractals theory. Since then, fractals theory has various applications in different disciplines of science and engineering. The said area has the capability to describe the complex geometry of dynamical problems. The propagation of light pulse and their solitonic behavior are investigated in a [Formula: see text] medium of four levels. Significant control over the absorption, dispersion, group refractive index and pulse propagation is reported with variation of coupled driving fields. The sublominal group velocity of [Formula: see text] and superlominal propagation of group velocity of [Formula: see text] is controlled. The bright and dark soliton pulse is modified with variation of driving fields in the superluminal and sublominal regions. Due subluminality of light dark soliton is reported and superluminality bright soliton is noted in the medium. The maximum of [Formula: see text] output pulse intensity is controlled. The intensity of the output pulse is an increasing and decreasing function of coupled driving fields’ Rabi frequencies. The modified solitons in this rubidium atomic medium are comparably more informative and significant to solitonic pulse intensity control in four-level cesium atomic medium under Doppler and inverse Doppler broadening effects. The modified results have useful application and soliton radar and communication technologies.