This thesis presents an investigation into the behaviour of a laser beam of finite diameter in a plasma with respect to forces and optical properties, which lead to self-focusing of the beam. The transient setting of ponderomotive nonlinearity in a collisionless plasma has been studied, and consequently the self- focusing of the pulse, and the focusing of the plasma wave occurs. The description of a self-focusing mechanism of laser radiation in the plasma due to nonlinear forces acting on the plasma in the lateral direction, relative to the laser has been investigated in the non-relativistic regime. The behaviour of the laser beams in plasma, which is the domain of self-focusing at high or moderate intensity, is dominated by the nonlinear force. The investigation of self-focusing processes of laser beams in plasma result from the relativistic mass and energy dependency of the refractive index at high laser intensities. Here the relativistic effects are considered to evaluate the relativistic self-focusing lenghts for the neodymium glass radiation, at different plasma densities of various laser intensities. A sequence of code in C++ has been developed to explore in depth self-focusing over a wide range of parameters. The nonlinear plasma dielectric function to relativistic electron motion will be derived in the latter part of this thesis. From that, one can obtain the nonlinear refractive index of the plasma and estimate the importance of relativistic self-focusing as compared to ponderomotive non-relativistic self-focusing, at very high laser intensities. When the laser intensity is very high, pondermotive self-focusing will be dominant. But at some point, when the oscillating velocity of the plasma electron becomes very large, relativistic effects will also play a role in self-focusing. A numerical and theoretical study of the generation and propagation of oscillation in the semiclassical limit of the nonlinear paraxial equation is presented in this thesis. In a general setting of both dimension and nonlinearity, the essential differences between the 'defocusing' and 'focusing' cases hence is identified. Presented in this thesis are the nonlinearity and dispersion effects involved in the propagation of solitions which can be understood by using a numerical routines were implemented through the use of the mathematica program, and results give a very clear idea of this interesting phenomena / Doctor of Philosophy (PhD)

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2017-04-04T10:58:54Z No. of bitstreams: 2 Dissertação -Thais de Lima Silva - 2016.pdf: 2036779 bytes, checksum: d24a78c94accea059363389b0a888431 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-04-04T11:09:59Z (GMT) No. of bitstreams: 2 Dissertação -Thais de Lima Silva - 2016.pdf: 2036779 bytes, checksum: d24a78c94accea059363389b0a888431 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-04-04T11:09:59Z (GMT). No. of bitstreams: 2 Dissertação -Thais de Lima Silva - 2016.pdf: 2036779 bytes, checksum: d24a78c94accea059363389b0a888431 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-03-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Among the first attempts towards the unification of quantum and special relativity theories that which more highlighted was the Dirac’s electron theory. Amongst its achievements is the accurated calculation of the hydrogen spectrum and the antiparticles prediction. Even though it provides good results, some difficulties arise in this theory such as the existence of negative energy states for free particles. At the same time that it allows for the antiparticle discovery, it leads to questions like the trembling motion of a free electron (zitterbewegung). It is not a consensus whether this motion is real or just a theoretical failure in describing the reality. In this work we present a proposal to simulate the Dirac electron dynamics and, therefore, zitterbewegung, by means of a transformation of a paraxial light beam. The same transformation as is carried out on the vector state by the Dirac’s evolution operator is implemented in the transverse beam profile using wave plates and spatial light modulator. The proposal includes the cases of one and two spatial dimensions by simulating the spatial degrees of freedom into the transverse coordinates of the light beam, which offers a difficulty in simulating the three dimensional dynamics in general case. However, we show that it is possible for particular initial states. Our simulation presents some advantages over previously ones, namely: it does not require the construction of specificaly designed devices; the adjustable parameters are present on phases printed by the modulator and can be arbitrarily changed; it permits the measurement of the mean as well as the standard position operators; it permits the simulation in two and three spatial dimensions. / Dentre as primeiras tentativas de unificação da teoria quântica com a teoria de relatividade especial aquela que se destacou foi a teoria do elétron de Dirac. Entre seus sucessos está o cálculo com grande acurácia do espectro do átomo de hidrogênio e a predição da existência da antipartícula do elétron. Porém, apesar de seus bons resultados, alguns problemas surgem nessa teoria. A existência de estados com energia cinética negativa, ao mesmo tempo que permite a descoberta de antipartículas, leva a problemas como o movimento trêmulo zitterbewegung de um elétron livre. Não se sabe se esse movimento é real ou apenas uma inexatidão da teoria em descrever a realidade. Neste trabalho apresentamos uma proposta de emulação da dinâmica de um elétron de Dirac e, portanto, de zitterbewegung, por meio da transformação de um feixe luminoso paraxial. A mesma transformação efetuada pelo operador de evolução temporal de Dirac é implementada sobre o perfil transversal do feixe fazendo-o passar por placas de onda e imprimindo fases com um modulador espacial de luz. A proposta inclui os casos de uma e duas dimensões espaciais e, por emular a posição da partícula na posição sobre o plano transversal ao feixe, dispomos somente de dois graus de liberdade, dificultando a simulação no caso de o espaço ser tridimensional. Entretanto, mostramos que ainda assim é possível simular um caso particular nessa situação. Nossa simulação apresenta algumas vantagens sobre simulações implementadas anteriormente, são elas: não requer a construção de dispositivos para esse fim específico; os parâmetros ajustáveis estão presentes nas fases do modulador e podem ser variados arbitrariamente; permite a comparação entre o operador posição padrão e o operador posição média; permite a simulação nos casos de espaço bi e tridimensional.

No description available.

The concept of generating horizontal-parallax-only (HPO) holograms by computer simulations is investigated. The simulations in this thesis are based on Optical Scanning Holography (OSH) aimed at acquiring HPO information electronically. The principles of OSH, a technique that allows the extraction of 3-D information by a 2-D optical scan of the object is first summarized. The HPO principles and simulation scenarios are then discussed. In order to illustrate the ideas, holograms were created and reconstructed using MATLAB simulations. The holograms are simulated by convolving the Fresnel zone plates (FZP) with the object. The simulations focus on generating HPO holograms using 1-D FZPs modeled as 1-D Gaussian chirp beams of varying waists. An optical reconstruction scheme by cylindrical lens was proposed and simulated. Three-dimensional imaging using HPO-holograms was also discussed. Several reconstruction scenarios were investigated by digitally convolving the complex HPO-hologram with the free space impulse response or the Gaussian chirp beam. Although many ideas of HPO-holography have been proposed and studied, to the best of our knowledge, this is the first proposed electronic technique to acquire HPO-holographic information. The simulations demonstrate that holographic information reduction techniques also help to alleviate the problems associated with the restricted field of view upon holographic reconstruction for 3-D display. The simulations show that horizontal-parallax-only holography is an excellent way to reduce holographic information. Suggested future work includes actual optical experimentation to verify the ideas presented in this thesis. / Master of Science

Dynamical maps for magnetic components are fundamental to studies of beam dynamics in accelerators. However, it is usually not possible to write down maps in closed form for anything other than simplified models of standard accelerator magnets. In the work presented here, the magnetic field is expressed in analytical form obtained from fitting Fourier series to a 3D numerical solution of Maxwell’s equations. Dynamical maps are computed for a particle moving through this field by applying a second order (with the paraxial approximation) explicit symplectic integrator. These techniques are used to study the beam dynamics in the first non-scaling FFAG ever built, EMMA, especially challenging regarding the validity of the paraxial approximation for the large excursion of particle trajectories. The EMMA lattice has four degrees of freedom (strength and transverse position of each of the two quadrupoles in each periodic cell). Dynamical maps, computed for a set of lattice configurations, may be efficiently used to predict the dynamics in any lattice configuration. We interpolate the coefficients of the generating function for the given configuration, ensuring the symplecticity of the solution. An optimisation routine uses this tool to look for a lattice defined by four constraints on the time of flight at different beam energies. This provides a way to determine the tuning of the lattice required to produce a desired variation of time of flight with energy, which is one of the key characteristics for beam acceleration in EMMA. These tools are then benchmarked against data from the recent EMMA commissioning.

Předkládaná práce se zabývá návrhem projektorové soustavy transmisního elektronového mikroskopu (TEM) pro metodu single particle analysis (SPA). Návrh projektorové soustavy byl vytvořen v programu Electron Optical Design (EOD) verze 4.020. Série buzení jednotlivých čoček pro zvětšení projektorové soustavy v rozsahu od 50 do 10000 byla vypočítaná pomocí přístupu využívajícího aproximaci tenké čočky, dále pomocí přístupu využívajícího aproximaci tlusté čočky, metodou linearního zaostření v programu EOD a metodou nelineárního zaostření v programu EOD ve verzi 5.003. Dosažené výsledky byly porovnány a ověřeny pomocí reálného trasování částic v programu EOD.

Today there is a great need for communication between people and even between things, using systems onboard e.g. aircraft, cars, ships and satellites. As a consequence, these communications needs require antennas mounted on or integrated in the surfaces of different vehicles or platforms, i.e. conformal antennas. In order to ensure proper operation of the communication systems it is important to be able to determine the characteristics of these antennas. This thesis is about the analysis and design of conformal antennas using high frequency asymptotic methods. Commonly used eigenfunction solutions or numerical methods such as FDTD, FEM or MoM are difficult to use for arbitrarily shaped electrically large surfaces. However, the high frequency approximation approach together with an accurate ray tracing procedure offers a convenient solution for these surfaces. The geodesics (ray paths) on the surfaces are key parameters in the analysis and they are discussed in detail. In the first part of the thesis singly and doubly curved perfectly electrical conducting (PEC) surfaces are studied, with respect to the mutual coupling among aperture type elements. A synthesis problem is also considered where the effect of the mutual coupling is taken into account. As expected, the mutual coupling must be included in the synthesis procedure to be able to realize the prescribed pattern, especially in the shaped main lobe. Furthermore, the polarization of the antenna elements is very important when considering antennas on generally shaped surfaces. For such antennas the polarization must most likely be controlled in some way for a proper function. For verification of the results two experimental antennas were built at Ericsson Microwave Systems AB, Mölndal, Sweden. The first antenna is a circular cylinder with an array of rectangular waveguide fed apertures and the second antenna is a doubly curved surface (paraboloid) with circular waveguide fed apertures. It is found that it is possible to obtain very accurate results with the asymptotic method when it is combined with the Method of Moments, i.e. a hybrid method is used. The agreement compared to measurements is good at levels as low as –80 dB in many cases. The second part of the thesis is about the development of a high frequency approximation for surface field calculations on a dielectric covered PEC circular cylinder. When using conformal antennas in practice they have to be covered with a radome for protection and with the method developed here this cover can be included in the analysis. The method is a combination of two different solutions, one valid in the non-paraxial region of the cylinder and the other is valid in the paraxial region. The method is verified against measurements and reference results obtained from a spectral domain moment method code. / QC 20100616

Dans la première partie de cette thèse effectuée en collaboration avec le groupe expérimental de C. Chazaud (Clermont Université), nous avons étudié théoriquement un processus de différenciation cellulaire intervenant avant l’implantation de l’embryon dans l’utérus. Il s’agit de la spécification des cellules de la masse cellulaire interne (MCI) en épiblaste (EPI) et en endoderme primitif (EPr), processus dans lequel les facteurs de transcription Nanog et Gata6 jouent un rôle essentiel. En effet, en absence de Nanog, les cellules de la MCI acquièrent toutes une identité EPr, tandis qu’en absence de Gata6, elles se différencient toutes en EPI. De plus, la voie de signalisation Fgf/Erk active l’expression de Gata6 et inhibe celle de Nanog. Enfin, Nanog active la sécrétion dans le milieu extracellulaire de Fgf4, une molécule qui active la voie de signalisation Fgf/Erk en se liant au FgfR2. Nous avons développé un modèle mathématique pour ce réseau de régulations, fondé sur des équations différentielles ordinaires décrivant l’évolution temporelle des niveaux de protéines Nanog, Gata6, Fgf4 et Fgfr2 et de l’activité de la voie Fgf-Erk. Nous avons validé ce modèle en montrant qu’il récapitule les résultats expérimentaux obtenus in vivo, dans les embryons wild-type et dans les mutants Nanog-/- et Gata6-/-. De plus, l’analyse des résultats du modèle permet de proposer un nouveau mécanisme pour l’émergence d’une population mixte de cellules EPI et EPr au sein de la MCI. Ce mécanisme repose sur le fait que le système décrit par notre modèle peut présenter trois états stationnaires stables, dont les niveaux d’expression de Nanog et Gata6 correspondent à l’EPI, l’EPr et la MCI non-différenciée, respectivement. De plus, le modèle a été utilisé afin d’interpréter des résultats expérimentaux récents et contre-intuitifs, concernant les embryons hétérozygotes Gata6+/-. Enfin, nous avons établi des prédictions théoriques, dont certaines ont été ultérieurement vérifiées en laboratoire. <p>Dans la seconde partie de la thèse, effectuée dans le laboratoire d’O. Pourquié (Université de Strasbourg), nous avons étudié un processus de différenciation in vitro, par une approche expérimentale. Il s’agit de la différenciation des cellules souches embryonnaires (ES) en cellules de mésoderme paraxial, un tissu dont dérivent –au cours du développement embryonnaire– les cellules formant notamment les vertèbres, les côtes, la peau et les muscles squelettiques du dos.<p> / Doctorat en Sciences agronomiques et ingénierie biologique / info:eu-repo/semantics/nonPublished

In this thesis, we investigate the propagation of some coherent and partially coherent laser beams, including a dark hollow beam (DHB), an elliptical Gaussian beam (EGB), a flat-topped beam and a twisted anisotropic Gaussian Schell-model (TAGSM) beam, through a paraxial optical system or a turbulent atmosphere. Several theoretical models are proposed to describe a DHB of circular or non-circular symmetry. Approximate analytical formulas for a DHB and a partially coherent TAGSM beam propagating through an apertured paraxial optical system are derived based on the generalized Collins formula. Analytical formulas for a DHB, an EGB, a flat-topped beam and a partially coherent TAGSM beam propagating in a turbulent atmosphere are derived in a tensor form based on the extended Huygens-Fresnel integral formula. It is found that after a long propagation distance these beams become circular Gaussian beams in a turbulent atmosphere, and this is quite different from their propagation properties in free space. The conversion of any of these beams to a circular Gaussian beam becomes quicker and the beam spot in the far field spreads more rapidly for a larger structure constant of the turbulent atmosphere, a shorter wavelength and a smaller waist size of the initial beam. Lower coherence and larger twist have a stronger effect of anti-circularization of the beam spot. Our analytical formulas provide a convenient way for studying the propagation of various laser beams through a paraxial optical system or a turbulent atmosphere. The concept of coincidence fractional Fourier transform (FRT) with an incoherent or partially coherent beam is introduced, and the optical system for its implementation is designed. The coincidence FRT is demonstrated experimentally with a partially coherent beam, and the experimental results are consistent with the theoretical results. / QC 20100831

The spatial evolution of a pair of resonant Bragg modes through a medium characterized by a complex one-dimensional PT -symmetric periodic relative electric permittivity is thoroughly investigated. By using the two wave model, analytic solutions of Maxwell’s equations are derived in the nonparaxial regime in order to investigate the periodic energy exchange between the Bragg modes for the Hermitian optical lattices as well as for complex lattices and also to investigate the spatial evolution of the real part of the electric field that propagates through this medium. Three regimes defined by the symmetry breaking point are discussed: below it, above it and at it. These regimes are determined by the existence of four complex eigenvalues below the symmetry breaking point, which collide and coalesce into a pair of complex doubly degenerate eigenvalues at the breaking point. Above the critical value each member of the pair bifurcates into a pair of complex values and now they have a nonzero real part. In the Hermitian case, it is demonstrated that a complete reciprocal energy transfer between the pair of Bragg modes, in a manner similiar to the Pendellösung effect known from X-ray diffraction by a crystal, takes place. When the optical lattice is complex, the dynamics of the energy transfer is completely different from the Hermitian case: below the symmetry breaking point there exist a very nonreciprocal beating-like oscillatory behavior of the energy transfer between the Bragg modes; above the symmetry breaking point the spatial evolution of the energy transfer grows unlimited but an oscillatory evolution still takes place; and at the symmetry breaking point the phenomenon of mode trapping does not occur in this nonparaxial regime (previously seen in PT -symmetric optical lattices in the paraxial regime). For the complex lattice, all these regimes share the common features: existence of a preferable mode for which the energy is transferred and a spatial evolution of this transfer in a nonreciprocal fashion, some of the characteristics very well known of PT -symmetric optical systems. / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / A evolução espacial de um par de modos de Bragg ressonantes através de um meio descrito por uma permissividade elétrica relativa PT -simétrica é completamente investigada. Usando o modelo de duas ondas, soluções analíticas para as equações de Maxwell são derivadas no regime não-paraxial a fim de investigar a transferência de energia entre esses modos de Bragg para uma rede ótica Hermitiana bem como para uma rede ótica complexa e também estudar a evolução espacial da parte real do campo elétrico que se propaga através desse meio. Três regimes definidos pela quebra de simetria são discutidos: abaixo, acima e no ponto de quebra de simetria. Estes regimes são determinados pela existência de quatro autovalores complexos distintos abaixo da quebra de simetria, que colidem e coalescem num par de autovalores valores complexos duplamente degenerados no ponto de quebra de simetria. Acima do ponto de quebra, quatro autovalores complexos distintos voltam a existir e agora cada um possui uma parte real não-nula. No caso Hermitiano, é demonstrado que uma transferência de energia completamente recíproca entre o par de modos de Bragg, numa maneira similiar ao efeito Pendellösung conhecido da difração de raios X por cristais, ocorre. Quando a rede ótica é complexa, a dinâmica da transferência de energia é completamente diferente do caso Hermitiano: abaixo do ponto de quebra de simetria existe um comportamento oscilatório do tipo batimento muito não-recíproco para a transferência de energia entre os modos de Bragg; acima do ponto de quebra de simetria a evolução espacial da transferência de energia cresce ilimitadamente mas um evolução oscilatória ainda ocorre; no ponto de quebra o fenômeno do aprisionamento de modo não ocorre nesse regime não-paraxial (anteriormente visto em redes óticas PT -simétricas no regime paraxial). Para a rede ótica complexa, todos estes regimes compartilham características em comum: existência de um modo preferencial para o qual a energia é transferida e uma evolução espacial dessa transferência de maneira não-recíproca, algumas das características muito bem conhecidas de sistemas óticos PT simétricos.