Techn. University, Diss., 2006--Darmstadt.

No description available.

No description available.

Les travaux de recherche présentés ont pour objectif l'étude des non-linéarités photoréfractives en vue de la réalisation de composants optiques pour application dans le domaine de l'instrumentation pour des dispositifs de protection laser et dans le domaine des communications optiques pour des fonctions de routage, commutation et interconnexions optiques. Mise à part la limitation optique qui concerne plutôt l'optronique, ces applications s'inscrivent essentiellement dans des applications de traitement tout optique de l'information. Nous nous intéressons plus particulièrement à la propagation d'ondes solitaires spatiales dans des matériaux photoréfractifs et à la possibilité d'utiliser les phénomènes d'interactions de solitons pour application au routage et interconnexions optiques. Une possibilité est notamment la réalisation de fonctions simples ou plus complexes comme des liaisons point à point, des coupleurs (X ou Y). <br />Dans ces objectifs, des études, à la fois expérimentales et théoriques, des phénomènes d'autofocalisation photoréfractive et de solitons spatiaux ont été réalisées : elles concernent des travaux de recherches sur des matériaux isolants (Bi12TiO20, Sr1-xBaxNb2O6) pour la limitation optique et sur des matériaux semi-conducteurs (InP :Fe, SPS) pour les applications dans les communications optiques. Des études supplémentaires sur les interactions de solitons sont en cours pour la réalisation de démonstrateurs de routage et d'interconnexions optiques. Des travaux récents s'intéressent également à l'auto-organisation de lumière en cavité optique non-linéaire (formation de structures spatiales auto-organisées, structures localisées, solitons de cavité) pour des applications de télécommunications optiques.

In this thesis, we report the study of two-dimensional spatial solitons observing in planar nematic liquid crystal cells with applied AC voltage. Two 2-D spatial solitons can be produced in one channel. They will attract or repulse each other, if we make the media with non-uniform reflection index. We study their interacting phenomena and expect the two solitons can make a spiral structure.

Abstract There are three parts in this paper. The first, we study the mechanism of soliton in nematic liquid crystal (NLC), molecules of NLC will be rotated easily by optical field while we apply an external electric field. Then the effective refraction index is changed. The light beam in NLC will create spatial soliton by producing the effect of self-focusing to balance the diffraction. Second, we study the interaction between solitons. One soliton will create a potential well of refraction index. The other one will be attracted in the potential well. These two solitons propagate in the form of spiral, if the separated distance and the angle are suitable. And the third, we observe the phenomenon with probe beam in the path of soliton. The path of the soliton forms a channel like a wave guide. The probe beam insert into the path of the soliton with different angles. The probe beam collides with the soliton in the proper range of angles will follow its path.

This thesis examines the behaviour of two new models exhibiting topological solitons. This analysis is predominantly numerical, but a limited collective coordinate approach is attempted where appropriate. In chapter 1 we review the field of solitons. In particular the nature of topological solitons and their associated mathematical formalism are explained. A number of models admitting solitons are defined. In chapter 2 we look at the numerical methods necessary to solve the time evolution of topological solitons in the S(^2) sigma model and the baby Skyrme model. We also examine methods for finding static solutions of the equations of motion of such models. In chapter 3 we define the RP(^2) sigma and baby Skyrme models. We examine the behaviour of these models and find them to be identical to their (S^2) counterparts for most field configurations. The topological reason for this is explained. The existence of a topological object called a defect is noted and the behaviour of solitons in the presence of a defect is examined. A collective coordinate approach is used to examine the behaviour of solitons in the presence of a defect. In chapter 4 the easy plane baby Skyrme model is defined. An ansatz for the static skyrmions is proposed and its energy found to be accurate to 1.2% for the 1-skyrmion and about 0.5% for 2 to 4-skyrmions. These skyrmions are composed of two quasi- independent soliton like objects which we name "half lumps". These objects may not exist alone. The scattering properties of these objects are examined numerically. The behaviour of these scattering processes are explained in terms of the fields and potential energy of their intermediate states in the simulation. In chapter 5 we summarise our work and propose future work in this field.

Two areas of affine Toda field theory are explored in this thesis. First the introduction of a boundary into the real coupling affine Toda field theory. It has been shown by other authors that affine Toda field theory stays an integrable theory for certain boundaries. One such theory is the one corresponding to Its integrable boundary condition is described by two continuous parameters. Also, it is continuously connected to the natural Neumann condition, i.e. vanishing space derivative of the fields at the boundary. Classical reflection factors of incoming plane waves in the background of a static soliton solution are calculated for this theory. They fulfil a classical reflection bootstrap equation which is the classical limit of the reflection bootstrap equation for reflection matrices. The second part is concerned with the the αη(^1) affine Toda field theory with imaginary coupling. The behaviour of oscillatory solitonic solutions, breathers is investigated. Explicit construction for breather solution are given. They originate from two soliton solutions. It is found that there are two different types of breathers depending on their constituent solitons. The constituent solitons are either of the same species or are anti-species of each other. Also, the topological charges of breather solutions are calculated and they are either zero or equal to a certain one soliton solution. These topological charges lie in the tensor product representation of the fundamental representations associated with the topological charges of the constituent solitons. The breather masses are, as expected, less than the sum of the masses of the constituent solitons.

Zugl.: Münster (Westfalen), Univ., Diss., 2007

Universiẗat, Diss., 1990--Paderborn.