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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Solitons propagation in a tandem arrangement of nonlinear materials

J. J. Sánchez-Mondragón, A. Alejo-Molina, Miguel Torres-Cisneros, O. Vázquez Buenos Aires, Daniel Alberto May-Arrioja, Alvaro Zamudio-Lara

Published Jun 10, 2009• 1 citation
Publisher

Abstract

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.

DOI
10.1117/12.839801

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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 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.
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.
Self-formation of one or several soliton-like pulses from a nonsoliton powerful laser pulse during its propagation through a two-component resonant amplifying—absorbing medium with an energy dissipation channel is studied numerically. Both components of the medium are simulated by two-level particles. Homogeneous mixtures of these components and media with consecutive amplifying and absorbing layers are considered. A qualitative analysis of the results is based on a simplified model of the process of soliton-like pulse propagation.
Investigating the behavior of an atom in response to the applied electric field when the latter frequency is in resonance with the natural frequency of the atom is an interesting subject. Near resonance, some of the most interesting optical phenomena such as dispersion, and absorption are more pronounced. Moreover, considering resonant and near resonant interaction of light with two-level atoms, uncovers fascinating physical phenomena such as area theorem and self-induced transparency describing stable pulse propagation regimes in which the pulses maintain their identity. Existence of these optical structures in on-resonance optical media has not been investigated in detail. In this thesis, the on-resonance interaction of optical field with atoms is considered and the formation of several novel self-similar and kink waves in linear and nonlinear resonant media is discovered and theoretically explored. First, self-similar pulse formation in homogeneous broadened linear amplifiers in a vicinity of an optical resonance is analyzed. It is demonstrated that the self-similar pulses serve as universal asymptotics of any near resonance short pulses propagating in coherent linear amplifiers. Second, ultrashort self-similar pulse propagation in coherent linear absorbers near optical resonance is investigated. Third, existence of self-similar optical waves with kink structure in resonant optical systems is discovered. Fourth, it is found that self-induced transparency quadratic solitons are realizable in the media with quadratic optical nonlinearities, doped with resonant impurities. Finally, stable spatial similaritons supported by homogeneous conservative optical media with quintic nonlinearities are explored. To experimentally realize the presented results, physical models are presented for all systems under consideration. The stability of the proposed near resonance optical systems is demonstrated through a series of numerical case studies.
We derive model equations for optical pulse propagation in a medium described by a two-level Hamiltonian, without the use of the slowly varying envelope approximation. Assuming that the resonance frequency of the two-level atoms is either well above or well below the inverse of the characteristic duration of the pulse, we reduce the propagation problem to a modified Korteweg--de Vries or a sine-Gordon equation. We exhibit analytical solutions of these equations which are rather close in shape and spectrum to pulses in the two-cycle regime produced experimentally, which shows that soliton-type propagation of the latter can be envisaged.