Thèses sur le sujet « Relativistic Optics »

During the past decades, the development of laser technology has produced pulses with increasingly higher peak intensities. These can now be made such that their strength rivals, and even exceeds, the atomic potential at the typical distance of an electron from the nucleus. To understand the induced dynamics, one can not rely on perturbative methods and must instead try to get as close to the full machinery of quantum mechanics as practically possible. With increasing field strength, many exotic interactions such as magnetic, relativistic and higher order electric effects may start to play a significant role. To keep a problem tractable, only those effects that play a non-negligible role should be accounted for. In order to do this, a clear notion of their relative importance as a function of the pulse properties is needed.  In this thesis I study the interaction between atomic hydrogen and super-intense laser pulses, with the specific aim to contribute to the knowledge of the relative importance of different effects. I solve the time-dependent Schrödinger and Dirac equations, and compare the results to reveal relativistic effects. High order electromagnetic multipole effects are accounted for by including spatial variation in the laser pulse. The interaction is first described using minimal coupling. The spatial part of the pulse is accounted for by a series expansion of the vector potential and convergence with respect to the number of expansion terms is carefully checked. A significantly higher demand on the spatial description is found in the relativistic case, and its origin is explained. As a response to this demanding convergence behavior, an alternative interaction form for the relativistic case has been developed and presented. As a guide mark for relativistic effects, I use the classical concept of quiver velocity, vquiv, which is the peak velocity of a free electron in the polarization direction of a monochromatic electromagnetic plane wave that interacts with the electron. Relativistic effects are expected when vquiv reaches a substantial fraction of the speed of light c, and in this thesis I consider cases up to vquiv=0.19c. For the present cases, relativistic effects are found to emerge around vquiv=0.16c .

The quality of beam optics is of great importance for the performance of a high energy accelerator like the Relativistic Heavy Ion Collider (RHIC). The turn-by-turn (TBT) beam position monitor (BPM) data can be used to derive beam optics. However, the accuracy of the derived beam optics is often limited by the performance and imperfections of instruments as well as measurement methods and conditions. Therefore, a robust and model-independent data analysis method is highly desired to extract noise-free information from TBT BPM data. As a robust signal-processing technique, an independent component analysis (ICA) algorithm called second order blind identification (SOBI) has been proven to be particularly efficient in extracting physical beam signals from TBT BPM data even in the presence of instrument's noise and error. We applied the SOBI ICA algorithm to RHIC during the 2013 polarized proton operation to extract accurate linear optics from TBT BPM data of AC dipole driven coherent beam oscillation. From the same data, a first systematic estimation of RHIC BPM noise performance was also obtained by the SOBI ICA algorithm, and showed a good agreement with the RHIC BPM configurations. Based on the accurate linear optics measurement, a beta-beat response matrix correction method and a scheme of using horizontal closed orbit bumps at sextupoles for arc beta-beat correction were successfully applied to reach a record-low beam optics error at RHIC. This thesis presents principles of the SOBI ICA algorithm and theory as well as experimental results of optics measurement and correction at RHIC.

Ultrafast dynamical processes in magnetic systems have become the subject of intense research during the last two decades, initiated by the pioneering discovery of femtosecond laser-induced demagnetization in nickel. In this thesis, we develop theory for fast and ultrafast magnetization dynamics. In particular, we build relativistic theory to explain the magnetization dynamics observed at short timescales in pump-probe magneto-optical experiments and compute from first-principles the coherent laser-induced magnetization. In the developed relativistic theory, we start from the fundamental Dirac-Kohn-Sham equation that includes all relativistic effects related to spin and orbital magnetism as well as the magnetic exchange interaction and any external electromagnetic field. As it describes both particle and antiparticle, a separation between them is sought because we focus on low-energy excitations within the particle system. Doing so, we derive the extended Pauli Hamiltonian that captures all relativistic contributions in first order; the most significant one is the full spin-orbit interaction (gauge invariant and Hermitian). Noteworthy, we find that this relativistic framework explains a wide range of dynamical magnetic phenomena. To mention, (i) we show that the phenomenological Landau-Lifshitz-Gilbert equation of spin dynamics can be rigorously obtained from the Dirac-Kohn-Sham equation and we derive an exact expression for the tensorial Gilbert damping. (ii) We derive, from the gauge-invariant part of the spin-orbit interaction, the existence of a relativistic interaction that linearly couples the angular momentum of the electromagnetic field and the electron spin. We show this spin-photon interaction to provide the previously unknown origin of the angular magneto-electric coupling, to explain coherent ultrafast magnetism, and to lead to a new torque, the optical spin-orbit torque. (iii) We derive a definite description of magnetic inertia (spin nutation) in ultrafast magnetization dynamics and show that it is a higher-order spin-orbit effect. (iv) We develop a unified theory of magnetization dynamics that includes spin currents and show that the nonrelativistic spin currents naturally lead to the current-induced spin-transfer torques, whereas the relativistic spin currents lead to spin-orbit torques. (v) Using the relativistic framework together with ab initio magneto-optical calculations we show that relativistic laser-induced spin-flip transitions do not explain the measured large laser-induced demagnetization. Employing the ab initio relativistic framework, we calculate the amount of magnetization that can be imparted in a material by means of circularly polarized light – the so-called inverse Faraday effect. We show the existence of both spin and orbital induced magnetizations, which surprisingly reveal a different behavior. We establish that the laser-induced magnetization is antisymmetric in the light’s helicity for nonmagnets, antiferromagnets and paramagnets; however, it is only asymmetric for ferromagnets.

L'utilisation de l'équation de Dirac/Weyl conduit à une simplification conceptuelle dans une description de la structure de la bande dans les solides à faible échelle d'énergie. En particulier, les excitations d'électrons-trous peuvent être considérées comme analogues au cas relativiste tel que conductivité optique linéaire, le suppression de backscattering ou la manifestation des arcs de Fermi et la chiralité des particules. En outre, la phase semi-métallique est également un élément crucial pour la classification des matériaux. La taille de le gap est affectée qualitativement par le type de dispersion d'énergie par un croisement continu des bandes linéaires à paraboliques. Cela peut être compris comme une limite classique ou ultra-relativiste du mouvement d'une particule massive.La spectroscopie infrarouge de la transformation de Fourier est une technique unique pour étudier les excitations optiques dans une large gamme d'énergies et représente en combinaison avec le champ magnétique élevé un outil puissant pour sondage de la structure électronique et surmonte le principal obstacle des systèmes sans gap qui est un dopage fort en raison de désordre structurel.La première partie du travail est consacrée à l'arséniure de cadmium, où nous élaborons une approche de distinction qualitative entre les systèmes Dirac et Kane qui ont été utilisés pour prouver sur la base de la réponse magnéto-optique observée la réalisation du modèle Kane presque sans gap avec une similitude frappante avec HgCdTe, en contradiction avec l'existence de cônes purement Dirac. La magnéto-réflectivité dans un champ magnétique à champ élevé la résonance cyclotron caractéristiques par un radical-B dépendance avec un comportement particulier dans la limite quantique. En revanche, la magnéto-transmission montrait des transitions de niveau Landau qui doit être interprétées que comme un type plat-à-cône afin de préserver une cohérence totale du modèle. Les cônes de Dirac prédits par la théorie sont susceptibles de coexister dans le modèle de Kane sous la forme d'une sous-structure décrite par le modèle de Bodnar qui se rapproche de la structure cristalline complexe par une simple cellule antifluorite qui permet d'utiliser la théorie du k.p classique.Dans la deuxième partie, nous nous concentrons sur le bismuth comme isolant topologique 3D archétype. Nous étudions une condition particulière obéie pour le BHZ-hamiltonien qui apporte des propriétés intriguantes comme une relation inhabituelle de spin gap et la résonance du cyclotron, l'épinglage spécifique entre les fancharts des sous-groupes Landau ou les g-facteurs compensés dans les bandes de conduction et de valence. Les mesures de photoluminescence ont montré une émission directgap, ce qui donne un nouvel aperçu de la structure largement acceptée à partir des données ARPES, où la “chameau structure” de la bande de valence doit être expliquée dans le confinement de surface et le point de Dirac de l'état de surface doit être repositionné par rapport aux bandes en bulk. La réponse magnéto-optique peut être pleinement expliquée dans une image classique du paramagnétisme de Pauli comme un simple effet d'occupation. Un tel comportement se manifeste dans la transmission en tant que fractionnement progressif du bord d'absorption interbande avec une saturation successive due à la polarisation spin partielle ou totale des électrons. Le dichroïsme relatif entraîne également une forte rotation de Faraday linéaire décrite par un modèle simple de la constante Verdet qui ne dépend pas sur le niveau de Fermi
The use of the Dirac/Weyl equation leads to a conceptual simplification in a description of the band structure in solids at low energy scales. In particular, electron-hole excitations can be regarded as an analogue to the relativistic case with several expected phenomena to be observed in the condensed systems such as a suppressed back-scattering, linear optical conductivity or the manifestation of the Fermi arcs and particle's chirality. Moreover, the semimetallic phase also symbolizes a boundary between the trivial and topological insulators and thus play a crucial role for the material classification. The size of the gap qualitatively affects the type of the energy dispersion by a continuous crossover from the linear to parabolic bands. This fact can be easily understood as a classical or ultra-relativistic limit of the motion of a free massive particle.Infrared Fourier transform spectroscopy is a unique technique for studying optical excitations in a wide range of energies and it represents in combination with the high magnetic field a powerful tool for probing electronic structure and overcomes the main obstacle of the gapless systems that is a strong doping due to the structural disorder.The first part of the work is devoted to cadmium arsenide, where we elaborate an approach to qualitatively distinguish between the Dirac and Kane systems that was used to prove on the basis of the observed magneto-optical response the realization of the nearly gapless Kane model with a striking similarity to HgCdTe, contradicting the existence of purely Dirac cones. The magneto-reflectivity revealed a strong splitting of the plasma edge that turns into the cyclotron resonance characteristic by a squareroot-of-B dependence in the high magnetic field with a particular behaviour in the quantum limit independent on the initial Fermi level. In contrast, the magneto-transmission revealed interband Landau level transitions that could be only interpreted as a flat-to-cone type in order to preserve a full consistency of the model. The Dirac cones predicted by theory are feasible to coexist within the Kane model in the form of a substructure described by the Bodnar model that approximates the complex crystal structure by a simple antifluorite cell, which allows to use the conventional k.p-theory.In the second part, we focus on bismuth selenide entitled as an archetypal 3D topological insulator. We study a peculiar condition fulfilled for the BHZ-hamiltonian that brings intriguing properties such as an unusual relation of the spin gap and cyclotron resonance, the specific pinning between fancharts of Landau subsets or the compensated g-factors of the conduction and valence bands. The photoluminescence measurements showed a direct-gap emission, that gives a new insight to the widely accepted structure from ARPES data, where the declared camel-back structure of the valence band needs to be explained within the surface confinement and the Dirac point of the surface state should be repositioned with respect to the bulk bands. The magneto-optical response can be fully explained in a classical picture of the Pauli paramagnetism as a purely occupational effect. Such behaviour is evinced in the transmission as a gradual splitting of the interband absorption edge with a successive saturation due to the partial or total spin polarization of electrons. The related dichroism drives also a strong linear Faraday rotation described by a simple model of the Verdet constant that depends only on the Fermi level

Les impulsions laser ultrabrèves nous permettent de suivre en temps réel les phénomènes ultrarapides au sein de la matière à l’échelle microscopique. C’est précisément pour l’invention de la chimie à l’échelle femtoseconde, ou femtochimie, qu’Ahmed Zewail se vit décerner le prix Nobel de chimie en 1999. Depuis les utilisateurs du laser cherchent à augmenter la résolution temporelle, c’est-à-dire réduire la durée des impulsions laser. Aujourd’hui, nous savons générer des flashs lumineux à l’échelle attoseconde dans le domaine spectral de l’extrême ultraviolet (XUV) mais l’efficacité de génération reste faible et le développement de sources laser attosecondes intenses constitue un sujet de recherche très actif sur le plan international.Notre groupe au LOA se concentre sur la génération d’impulsions attoseconde sur miroir plasma en régime relativiste. Pour cela, il cherche à développer une source d’impulsions femtosecondes à forte cadence et fort contraste et suffisamment énergétiques pour atteindre des intensités relativistes (>> 10^18W/cm2) lorsqu’elles sont fortement focalisées sur un plasma surdense. Un plasma surdense réfléchit la lumière incidente et par conséquent agit comme un miroir qui se déplaçant à vitesse relativiste et qui comprime l’impulsion incidente, produisant ainsi un flash attoseconde par cycle optique. En utilisant des impulsions proches d’un cycle optique, il est donc envisageable de générer une seule impulsion attoseconde intense pendant l’interaction.Dans la première partie de mon travail de thèse, j’ai réalisé un compresseur nonlinéaire pour réduire la durée des impulsions issues d’une chaîne à double dérive de fréquence (10mJ, 25fs, 1kHz) à phase enveloppe-porteuse (CEP) stabilisée. En propageant les impulsions du laser à haute intensité dans une fibre creuse remplie de gaz rare, j’ai réussi à générer des impulsions de 1.3 cycle optique avec une puissance crête autour de 1TW avec une CEP stabilisée. Dans un deuxième temps, j’ai mis en forme spatialement et temporellement les impulsions issues du compresseur à fibre pour générer à la fois des impulsions attosecondes intenses et des faisceaux d’électrons énergétiques sur un miroir plasma à gradient de densité contrôlé. Ces expériences nous permis, pour la première fois, de mettre en évidence la production d’impulsions attosecondes isolées dans l’XUV, l’émission corrélée de faisceaux d’électrons énergétiques en régime relativiste ainsi qu’un nouveau régime d’accélération d’électrons à très long gradient plasma
Very short light pulses allow us to resolve ultrafast processes in molecules, atoms and condensed matter. This started with the advent of Femtochemistry, for which Ahmed Zewail received the Novel Prize in Chemistry in 1999. Ever since, researcher have been trying to push the temporal resolution further and we have now reached attosecond pulse durations. Their generation, however, remains very challenging and various different generation mechanisms are the topic of heated research around the world.Our group focuses on attosecond pulse generation and ultrashort electron bunch acceleration on solid targets. In particular, this thesis deals with the upgrade of a high intensity, high contrast, kHz, femtosecond laser chain to reach the relativistic interaction regime on solid targets. Few cycle driving laser pulses should allow the generation of intense isolated attosecond pulses. A requirement to perform true attosecond pump-probe exeriments.To achive this, a HCF postcompression scheme has been conceived and implemented to shorten the duration of a traditional laser amplifier. With this a peak intensity of 1TW was achieved with near-single-cycle pulse duration. For controlled experiments, a vacuum beamline was developed and implemented to accurately control the laser and plasma conditions on target.During the second part of this thesis, this laser chain was put in action to drive relativistic harmonic generation on solid targets. It was the first time ever that this has been achieved at 1 kHz. By CEP gating the few-cycle-pulses, single attosecond pulses were generated. This conclusion has been supported by numerical simulations. Additionally a new regime to accelerate electron bunches on soft gradients has been detected

There are at least two common models for calculating the photoemission of accelerated electrons. The 'extended-charge-distribution' method uses the quantum probability current (multiplied by the electron charge) as a source current for Maxwell's equations. The 'point-like-emitter' method treats the electron like a point particle instead of like a diffuse body of charge. Our goal is to differentiate between these two viewpoints empirically. To do this, we consider a large electron wave packet in a high-intensity laser field, in which case the two viewpoints predict measurable photoemission rates that differ by orders of magnitude. Under the treatment of the 'extended-charge-distribution' model, the strength of the radiated field is significantly limited by interferences between different portions of the oscillating charge density. Alternatively, no suppression of photoemission occurs under the 'point-like-emitter' model because the electron is depicted as having no spatial extent. We designed an experiment to characterize the photoemission rates of electrons accelerated in a relativistic laser focus. Free electron wave packets are produced through ionization by an intense laser pulse at the center of a large vacuum chamber. These quantum wave packets can become comparable in size to the laser wavelength through natural spreading and interactions with the sharp ponderomotive gradients of the laser focus. Electron radiation emitted out the side of the focus is collected by one-to-one imaging into a 105-micron gold-jacketed fiber, which carries the light to a single photon detector located outside the chamber. The electron radiation is red-shifted due to mild relativistic acceleration, and we use this signature to spectrally filter the outgoing light to discriminate against background. In addition, the temporal resolution of the electronics allows distinction between light that travels directly from the focus into the collection system and laser light that may scatter from the chamber wall.

Le progrès continu de la technologie laser a récemment permis l’avancement spectaculaire d’accélérateurs de particules par onde de sillage. Cette technique permet la génération de champs électriques très forts, pouvant dépasser de trois ordres de grandeurs ceux présents dans les accélérateurs conventionnels. L’accélération résultante a lieu sur une distance très courte, par conséquent les effets de la charge d’espace et de la dispersion de vitesse sont considérablement réduits. Les paquets de particules ainsi générés peuvent alors atteindre des durées de l’ordre de la femtoseconde, qui en fait un outil prometteur pour la réalisation d’expériences de diffraction ultra-rapide avec une résolution inégalée de l’ordre de quelques femtosecondes. La génération de tels paquets d’électrons avec des lasers de 1 J et d’une durée de 30 fs est à présent bien établie. Ces paramètres permettent de produire des faisceaux d’électrons de quelques centaines de MeV, et sont donc inadaptés aux expériences de diffraction. De plus, le taux de répétition de ces lasers de haute puissance est limité à quelques Hz, ce qui est insuffisant pour des expériences exigeant une bonne statistique de mesure. Notre groupe a utilisé un laser de pointe développé au laboratoire par le groupe PCO générant des impulsions de quelques millijoules, d’une durée de 3.4 fs - à peine 1.3 cycle optique - à une cadence de 1 kHz, pour accélérer des électrons par onde de sillage. Ce travail de thèse présente d’une part la première démonstration d’un accélérateur des particules relativistes opéré dans le régime de la bulle à haute cadence. L’utilisation de buses microscopiques a permis l’obtention de charges de dizaines de pC par tir. De plus, cette thèse vise à l’élargissement de notre compréhension des lois d’échelle d’accélération laser-plasma. Nous espérons que notre travail visant à la fiabilisation et l’optimisation de cette source permettra à terme de proposer un instrument accessible et fiable à la communauté scientifique, que ce soit pour la diffraction d’électrons, l’irradiation ultra-brève d’échantillons ou la génération de rayons X
Continuing progress in laser technology has enabled dramatic advances in laser wakefield acceleration (LWFA), a technique that permits driving particles by electric fields three orders of magnitude higher than in conventional radio-frequency accelerators. Due to significantly reduced space charge and velocity dispersion effects, the resultant relativistic electron bunches have also been identified as a candidate tool to achieve unprecedented sub-10 fs temporal resolution in ultrafast electron diffraction (UED) experiments. High repetition rate operation is desirable to improve data collection statistics and thus washout shot-to-shot charge fluctuations inherent to plasma accelerators. It is well known that high-quality electron beams can be achieved in the blowout, or "bubble" regime, which is at present regularly accessed with ≈ 30 fs Joule-class lasers that can perform up to few shots per second. Our group on the contraryutilized a cutting edge laser system producing few-mJ pulses compressed nearly to a single optical cycle (3.4 fs) to demonstrate for the first time an MeV-grade particle accelerator with properties characteristic to the blowout regime operating at 1 kHz repetition rate. We further investigate the plasma density profile and exact laser pulse waveform effects on the source output, and show that using special gas microjets a charge of tens of pC/shot can be achieved. We expect this technique to lead to a generation of highly accessible and robust instruments for the scientific community to conduct UED experiments or to be used for other applications. This work also serves to expand our knowledge on the scalability of laser-plasma acceleration

Le travail expérimental présenté dans ce manuscrit a été réalisé au Laboratoire d'Optique Appliquée (LOA, Palaiseau, France) sur un système laser compact multi-mJ kHz, capable de délivrer des impulsions quasi-mono-cycle à phase enveloppe-porteuse (CEP) stabilisée. Le premier volet expérimental a consisté à améliorer les performances de la source laser grâce à l’intégration d'un étage d’amplification multi-passage cryogéné dans la chaîne destiné à augmenter l'énergie d'impulsion disponible, à améliorer la stabilité de la CEP, ainsi qu’à fiabiliser les performances quotidiennes du laser. En parallèle, une nouvelle technique a été testée, basée sur la propagation nonlinéaire dans une cellule multi-passage (MPC), afin de post-comprimer temporellement et d’améliorer le contraste temporel des impulsions laser. Dans l’avenir, une fois mis à l’échelle et intégré dans la chaîne laser, ce dispositif innovant de mise en forme temporelle d’impulsions laser, augmenter encore plus l’éclairement atteignable pour les expériences.Le deuxième volet expérimental est axé sur l'utilisation de la chaîne laser afin de piloter des miroirs plasma relativistes et de générer du rayonnement attoseconde (1 as = 10-18 s) dans le domaine spectral de l’ultraviolet extrême, ainsi que des faisceaux d’électrons et d’ions fortement énergétiques. Nous avons pu produire des faisceaux d'électrons relativistes par injection localisée d’électrons du plasma dans le champ laser réfléchi de manière nonlinéaire par le miroir plasma. En outre, nous avons pu générer des faisceaux quasi-collimatés de protons avec des énergies proches du MeV dans le cadre d’une expérience pompe-sonde contrôlée. En stabilisant la forme d'onde des impulsions laser, nous avons pu restreindre temporellement le processus de génération d’harmoniques en-dessous du cycle laser et ainsi produire des impulsions attoseconde uniques. Nous avons réalisé une étude paramétrique complète afin d'optimiser les propriétés spatio-temporelles des impulsions attosecondes XUV ainsi émises, jetant ainsi les bases de leur refocalisation pour les applications
The experimental work presented in this manuscript was carried out at Laboratoire d’Optique Appliquée (LOA, Palaiseau, France) on a compact kHz multi-mJ energy laser system capable of delivering waveform-controlled near-single-cycle pulses. The first part of this work is focused on improving the performance of this laser source by integrating a cryogenically-cooled multi-pass amplifier in the laser chain in order to increase the output energy, enhance the laser waveform stability, making the laser source more stable and reliable, and with more overall reproducible day-to-day performance. Furthermore, we explore laser post-compression and temporal contrast enhancement in a multipass cell. In the future, this post-compression scheme when power-scaled and integrated into the laser chain will further enhance the focused pulse intensity for experiments.The second part of this work focuses on using the laser system to drive relativistic plasma mirrors on the surface of initially-solid targets to generate highly energetic particle beams (ions and electrons) and harmonic radiation in the extreme ultraviolet region, corresponding to attosecond pulses (1 as = 10-18 s) in the time domain. We could produce relativistic electron beams by localized injection of electrons into the nonlinearly reflected laser field by the plasma mirror. Additionally, we could generate nearly-collimated MeV-class proton beams in a controlled pump-probe experiment. By stabilizing the waveform of the driving laser pulses, we could temporally gate the interaction process on the target surface and produce isolated attosecond pulses. We performed a comprehensive parameter study to fully characterize and optimize the spatio-spectral properties of the emitted XUV attosecond pulses, laying the groundwork for their refocusing for applications

This thesis addresses the effects of chirality and nonlinearity in fiber optics. Most photonic applications are based on conventional optical fibers in the linear regime. Although nonlinear effects in fiber optics have been extensively studied, that is not the case with chirality. In fact, the study of chirality in fiber optics is in its very early stages. Maxwell’s equations are unified with Einstein’s special theory of relativity through a tensor formulation of classical electrodynamics. Through the study of a moving dielectric medium the general concept of bianisotropic media is introduced. A modified Lorentz model, based on the dipole response of a single helix, is developed. This model is used to obtain the dispersion behavior of the constitutive parameters of chiral isotropic media (also known as optically active media). The study of propagation in a symmetric planar chirowaveguide naturally evolves into the analysis of the propagation characteristics of chiral optical fibers. Dispersion diagrams for guided modes, surface and semileaky, are presented. Radiation loss in semileaky modes is also analyzed. Semileaky modes in chirowaveguides are physically explained through the study of the reflection problem at a planar interface between chiral media. Propagation of solitary waves is studied in the framework of multichannel nonlinear optical communication systems with dispersion management. A Lagrangian formulation is developed in order to obtain optimal dispersion maps for both filtered and unfiltered optical communication systems. A good agreement between the results obtained using this variational approach and the Split-Step Fourier Method was found.

A computer code was written to calculate elastic scattering cross sections using the Klein-Gordon equation. The reason for writing this code is because existing codes do not include relativistic kinematics and therefore are only valid for lower energies. This code was used to analyze alpha particle and pion scattering at relativistic energies upon different target nuclei and to find a relativistic potential for a system at a given energy. The target particles in the alpha study were 12C, 40,42,44,48Ca and other alphas. The pions were incident upon 12C and 40Ca. Optical potentials of different forms were used to compare with previous analyses and the experimental data. The potentials found in this study could be useful to understand the physics underlying other processes such as inelastic and particle transfer reactions. The computer code can be used to extend elastic scattering calculations to angles where data does not exist which can then be compared to future experiments. The code could also be used to create a database of potentials for several systems to study the effects of changing charge, mass or energy of the system.

Cette thèse expérimentale s’est essentiellement déroulée au Laboratoire d’Optique Appliquée à Palaiseau (France), sur un système laser capable de générer des impulsions proches du cycle optique en durée avec des énergies de plusieurs mJ à une cadence de 1 kHz : la Salle Noire 2. Ce système laser Titane:Sapphire est double CPA avec un filtre non-linéaire entre les deux étages (basé sur la génération d’onde de polarisation croisée ou ‘XPW’) pour améliorer le contraste temporel, suivi d’un étage de post-compression dans une fibre flexible étirée à cœur creux. Grâce à ce système, nous étudions l’interaction laser-matière en régime relativiste à haute cadence. Nous parvenons, d’une part, dans des jets de gaz, à accélérer des électrons dans le sillage du laser jusqu’ à une énergie de quelques MeV; et d’autre part, par interaction avec des miroirs plasma, à générer des harmoniques d’ordres élevés qui sont associées dans le domaine temporel à des impulsions attosecondes. Malgré la prouesse technique de ces expériences, les propriétés des faisceaux XUV et d’électrons ainsi générés restent encore peu compatibles avec des applications phares en aval. À la suite de travaux précédents en Salle Noire 2, l’objectif de cette thèse était d’obtenir des faisceaux aux propriétés stables, ce qui a été accompli en rendant le système laser plus stable et fiable, ainsi qu’en implémentant une boucle de contrôle rapide de la phase enveloppe-porteuse des impulsions laser. En variant la phase enveloppe-porteuse, nous avons ainsi pu générer des impulsions attosecondes uniques en formant une porte temporelle d’intensité relativiste à la surface du miroir plasma, et aussi produire des faisceaux d’électrons stables en énergie et en direction, en contrôlant l’injection d’ électrons dans l’accélérateur laser-plasma. De plus, différents régime d’interaction avec les miroirs plasma ont été étudiés expérimentalement, tels que l’accélération d’électrons dans les longs gr adients de densité plasma, et l’accélération de protons en face avant de la cible (la face sur laquelle le laser est incident) le long de la direction normale à la cible, afin de mesurer de nouvelles observables (spectre d’énergie des électrons, divergence des faisceaux de protons) et ainsi mieux comprendre la dynamique d’interaction laser-plasma
This experimental thesis was essentially conducted at Laboratoire d’Optique Appliquée in Palaiseau (France), on a laser system capable of delivering near-single-cycle duration pulses containing a few mJ of energy at 1kHz repetition rate: the Salle Noire 2. This laser is a Titanium:Sapphire double CPA system with a nonlinear filter in between (based on the crossed polarized wave generation effect) for temporal contrast enhancement, followed by a stretched-flexible hollow-core-fiber based post-compression stage. Using this system, we study laser-matter interaction in the relativistic regime at high repetition rate. We can, on one hand, in gas jets, accelerate electrons in the wakefield of the laser up to several MeVs; and on the other hand, by interacting with plasma mirrors, generate high order harmonics which are associated to bright attosecond pulses in the time domain. Despite the technological prowess in these experiments, the properties of the XUV and electron beams thus generated remain scarcely compatible with the main applications downstream. Following up on previous works in Salle Noire 2, the objective of this thesis was to obtain beams with stable properties, which was achieved by making the laser system more stable and reliable, as well as implementing a fast carrier-envelope phase control loop. By varying the carrier-envelope phase of the laser pulses, we could generate XUV continua/isolated attosecond pulses by forming a relativistic-intensity temporal gate at the surface of the plasma mirror, and also produce electron beams exhibiting stable energy and angle of emission, by controlling the electron injection within the plasma accelerator. Additionally, different regimes of interaction with plasma mirrors were experimentally investigated, such as wakefield acceleration of electrons in long plasma density gradients, and the acceleration of protons on the target’s front side (onto which the laser impinges) along the target no rmal direction, in order to measure new observables (electron energy spectra, proton beam divergence) and thus gain deeper insights into the laser-plasma dynamics

Pour générer des faisceaux d'électrons à hautes énergies, les accélérateurs conventionnels utilisent des ondes radiofréquences pour accélérer des particules chargées à des vitesses relativistes. Cependant, le champ électrique accélérateur produit est limité à quelques dizaines de mégavolts par mètre, dû notamment à un phénomène de claquage. Il faut donc des installations de très grande taille pour atteindre des énergies suffisamment élevées. Ainsi, l'accélérateur linéaire de Stanford (SLAC), qui est l'accélérateur linéaire le plus long au monde, accélère des électrons jusqu'à 50GeV sur 3.2km. Les accélérateurs laser-plasma peuvent produire des champs électriques dépassant 100 GV/m, soit environ trois ordres de grandeur plus grands que ceux obtenus par les accélérateurs à cavités radiofréquences. Ils pourraient ainsi permettre une diminution drastique de la taille des accélérateurs pour des applications scientifiques, médicales et industrielles. Cependant, plusieurs verrous devront être levés avant que ces applications puissent voir le jour. Il sera notamment nécessaire de démontrer la production efficace de faisceaux d'électrons de haute qualité, à des énergies de plusieurs GeV et à un taux de répétition élevé.Le projet doctoral s’attaque à cette problématique en explorant de nouvelles méthodes pour augmenter l'énergie des faisceaux d'électrons grâce à des techniques qui sont compatibles avec des puissances laser et des taux de répétition élevés et qui peuvent être alliées avec des méthodes d'injection contrôlée. En effet, des faisceaux d'électrons à haute énergie ou avec une injection contrôlée ont été obtenus séparément durant les quinze dernières années, mais jamais de manière combinée. Cette thèse présente les travaux réalisés sur les techniques de guidage ainsi que sur celles d'injection des électrons qui ont permis d'obtenir expérimentalement des faisceaux de bonne qualité à hautes énergies. Ce travail s'est fait notamment au travers de l'optimisation d'une optique nouvellement conçue au Laboratoire d'Optique Appliquée, l'axiparabole, ainsi que sur le développement de jets de gaz spécifiques à l'accélération laser-plasma
To generate high energy electron beams, conventional accelerators use radio frequency waves to accelerate charged particles to relativistic speeds. However, the accelerating electric field produced is limited to a few tens of megavolts per metre, mainly due to a breakdown phenomenon. Very large facilities are therefore needed to reach sufficiently high energies. For example, the Stanford Linear Accelerator (SLAC), which is the world's longest linear accelerator, accelerates electrons up to 50 GeV over a distance of 3.2 km. Laser-Plasma Accelerators can produce electric fields exceeding 100 GV/m, that are about three orders of magnitude larger than those obtained by radiofrequency-cavity accelerators. They could thus allow for a drastic decrease of the size of accelerators for scientific, medical and industrial applications. Yet, several bottlenecks have to be solved before these applications can be really implemented. It is notably necessary to demonstrate the efficient production of high-quality, multi-GeV electron beams at a high-repetition rate.The doctoral project tackles this problem by exploring new methods for increasing the energy of the electron beams thanks to techniques that are compatibles with arbitrarily high laser powers and repetition rates and that can be combined with controlled injection methods. Indeed, high energy or controlled injection electron beams have been obtained separately during the last fifteen years, but never combined. This thesis presents the work carried out on the guiding techniques as well as on the electron injection techniques which allowed to obtain experimentally good quality beams at high energies. This work was done in particular through the optimisation of a new optic designed at the Laboratoire d'Optique Appliquée, the axiparabola, as well as the development of gas jets specific to laser-plasma acceleration

L'interaction laser-plasma à très haute intensité (I " 1015 W/cm2) avec des impulsions ultra-courtes ( t " 100 fs) est un domaine en plein essor car il offre l'opportunité d'étudier des phénomènes physiques toujours plus brefs, regroupés sous l'appellation " science attoseconde ". L'interaction laser-plasma promet aussi l'avènement de nouvelles sources pour la génération de faisceaux de particules et de rayonnement X très énergétiques. Notre démarche se concentre sur la génération d'impulsions attosecondes sur miroir plasma à partir d'impulsions de quelques cycles optiques ( 5 fs à 800 nm), à haut taux de répétition (1 kHz) et avec un contrôle fin des paramètres laser. La génération et le contrôle temporel et spatial de l'émission d'harmoniques d'ordres élevés dans le régime non-relativiste ont récemment été démontrés par le groupe. L'objectif suivant est d'atteindre le régime relativiste, qui nécessite une intensité sur cible plus élevée. Ce travail de thèse s'inscrit donc dans la logique d'améliorer les performances de la chaine existante en termes d'énergie et de contraste temporel, tout en préservant les autres paramètres clés. Pour répondre à ces défis, l'objectif a été de mettre au point une architecture laser basée sur l'amplification à dérive de fréquence (CPA) délivrant des impulsions de 5 mJ, 5 fs à 1 kHz, avec un contraste temporel C = 1011 et une phase absolue (CEP) stabilisée à 200 mrad rms. La problématique de l'amélioration du contraste par la technique de génération de polarisation croisée (XPW) occupe une place centrale dans ce mémoire. Une étude extensive du mécanisme XPW a été menée. Elle a permis de confronter résultats expérimentaux et développements théoriques dans les régimes dits " extrêmes " tels que la génération à très haut rendement et le filtrage d'impulsions de quelques cycles optiques. En outre, un nouveau schéma de filtrage adaptable sur une large gamme d'énergie (de 100 μJ à 10 mJ) et efficace (20%) a été réalisé. La compression des impulsions d'un facteur supérieur à deux avec ce schéma a également été démontrée. La nouvelle chaine laser inclut un tel filtre dans une configuration en double CPA dont les performances finales visées sont les suivantes : 10 mJ, 20 fs, C = 1011 et CEP = 200 mrad rms. Le schéma d'étirement/compression a fait l'objet d'une étude détaillée pour permettre un étirement élevé (50 ps) tout en restant compact pour préserver la stabilité CEP. La configuration adoptée consiste en un étireur verre, un filtre acousto-optique dispersif programmable et un compresseur "grismes". Le mémoire présente enfin les perspectives de post-compression dans une fibre creuse remplie d'un gaz rare pour obtenir des impulsions de 5 mJ, 5 fs, C = 1011, CEP = 200 mrad rms à 1 kHz.

Ce travail de thèse s'intéresse aux corrections relativistes induites par une impulsion lumineuse ultra-brève et intense dans la matière condensée. Il s'inscrit dans la thématique nouvelle de la désaimantation ultra-rapide cohérente de systèmes ferromagnétiques induite par une impulsion laser femto-seconde [Nature 5, 515 (2009)] [1]. Un couplage de nature relativiste entre les spins et les photons a été proposé pour expliquer les résultats expérimentaux observés dans [1]. La première partie de ce travail étudie la limite non relativiste du formalisme de Dirac en présence d'un champ électromagnétique dépendant du temps. En utilisant la transformation de Foldy-Wouthuysen , le hamiltonien électronique de Dirac en présence d'un champ électromagnétique dépendant du temps est développé au cinquième ordre en 1/m. Les résultats obtenus ont permis de postuler une expression générale de l'interaction directe entre le spin et le champ électromagnétique sous la forme d'un développement en série entière. Un travail similaire est réalisé dans le cadre du problème relativiste à deux électrons en interaction coulombienne. La diagonalisation du hamiltonien de Breit au troisième ordre en 1/m fait apparaître une interaction singulière entre le spin, le champ coulombien et le champ électromagnétique externe dépendant du temps. Dans la deuxième partie, on propose un modèle classique pour modéliser une expérience de magnéto-optique non-linéaire réalisée sur des échantillons ferromagnétiques. Les prédictions théoriques des angles de rotation Faraday sont comparées aux résultats expérimentaux de la référence [1] et permettent d'ouvrir une discussion à propos des mécanismes physiques gouvernant les phénomènes magnéto-optiques observés. Le rôle joué par l'interaction spin-orbite entre les spins et le champ électrique du laser est discuté.

There is a growing consensus among physicists that the classical notion of spacetime has to be drastically revised in order to nd a consistent formulation of quantum mechanics and gravity. One such nontrivial attempt comprises of replacing functions of continuous spacetime coordinates with functions over noncommutative algebra. Dynamics on such noncommutative spacetimes (noncommutative theories) are of great interest for a variety of reasons among the physicists. Additionally arguments combining quantum uncertain-ties with classical gravity provide an alternative motivation for their study, and it is hoped that these theories can provide a self-consistent deformation of ordinary quantum field theories at small distances, yielding non-locality, or create a framework for finite truncation of quantum field theories while preserving symmetries. In this thesis we study the gauge theories on noncommutative Moyal space. We nd new static solitons and instantons in terms of the so-called generalized Bose operators (GBO). GBOs are constructed to describe reducible representation of the oscillator algebra. They create/annihilate k-quanta, k being a positive integer. We start with giving an alternative description to the already found static magnetic flux tube solutions of the noncommutative gauge theories in terms of GBOs. The Nielsen-Olesen vortex solutions found in terms of these operators also reduce to the ones known in the literature. On the other hand, we nd a class of new instanton solutions which are unitarily inequivalent to the ones found from ADHM construction on noncommutative space. The charge of the instanton has a description in terms of the index representing the reducibility of the Fock space representation, i.e., k. After studying the static soliton solutions in noncommutative Minkowski space and the instanton solutions in noncommutative Euclidean space we go on to study the implications of the time-space noncommutativity in Minkowski space. To understand it properly we study the time-dependent transitions of a forced harmonic oscillator in noncommutative 1+1 dimensional spacetime. We also provide an interpretation of our results in the context of non-linear quantum optics. We then shift to the so-called DSR theories which are related to a different kind of noncommutative ( -Minkowski) space. DSR (Doubly/Deformed Special Relativity) aims to search for an alternate relativistic theory which keeps a length/energy scale (the Planck scale) and a velocity scale (the speed of light scale) invariant. We study thermodynamics of an ideal gas in such a scenario. In first chapter we introduce the subjects of the noncommutative quantum theories and the DSR. Chapter 2 starts with describing the GBOs. They correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the GBO. When used in conjunction with the noncommutative ADHM construction, we nd that these new instantons are in general not unitarily equivalent to the ones currently known in literature. Chapter 3 studies the time dependent transitions of quantum forced harmonic oscillator (QFHO) in noncommutative R1;1 perturbatively to linear order in the noncommutativity . We show that the Poisson distribution gets modified, and that the vacuum state evolves into a \squeezed" state rather than a coherent state. The time evolutions of un-certainties in position and momentum in vacuum are also studied and imply interesting consequences for modelling nonlinear phenomena in quantum optics. In chapter 4 we study thermodynamics of an ideal gas in Doubly Special Relativity. We obtain a series solution for the partition function and derive thermodynamic quantities. We observe that DSR thermodynamics is non-perturbative in the SR and massless limits. A stiffer equation of state is found. We conclude our results in the last chapter.

There is a growing consensus among physicists that the classical notion of spacetime has to be drastically revised in order to nd a consistent formulation of quantum mechanics and gravity. One such nontrivial attempt comprises of replacing functions of continuous spacetime coordinates with functions over noncommutative algebra. Dynamics on such noncommutative spacetimes (noncommutative theories) are of great interest for a variety of reasons among the physicists. Additionally arguments combining quantum uncertain-ties with classical gravity provide an alternative motivation for their study, and it is hoped that these theories can provide a self-consistent deformation of ordinary quantum field theories at small distances, yielding non-locality, or create a framework for finite truncation of quantum field theories while preserving symmetries. In this thesis we study the gauge theories on noncommutative Moyal space. We nd new static solitons and instantons in terms of the so-called generalized Bose operators (GBO). GBOs are constructed to describe reducible representation of the oscillator algebra. They create/annihilate k-quanta, k being a positive integer. We start with giving an alternative description to the already found static magnetic flux tube solutions of the noncommutative gauge theories in terms of GBOs. The Nielsen-Olesen vortex solutions found in terms of these operators also reduce to the ones known in the literature. On the other hand, we nd a class of new instanton solutions which are unitarily inequivalent to the ones found from ADHM construction on noncommutative space. The charge of the instanton has a description in terms of the index representing the reducibility of the Fock space representation, i.e., k. After studying the static soliton solutions in noncommutative Minkowski space and the instanton solutions in noncommutative Euclidean space we go on to study the implications of the time-space noncommutativity in Minkowski space. To understand it properly we study the time-dependent transitions of a forced harmonic oscillator in noncommutative 1+1 dimensional spacetime. We also provide an interpretation of our results in the context of non-linear quantum optics. We then shift to the so-called DSR theories which are related to a different kind of noncommutative ( -Minkowski) space. DSR (Doubly/Deformed Special Relativity) aims to search for an alternate relativistic theory which keeps a length/energy scale (the Planck scale) and a velocity scale (the speed of light scale) invariant. We study thermodynamics of an ideal gas in such a scenario. In first chapter we introduce the subjects of the noncommutative quantum theories and the DSR. Chapter 2 starts with describing the GBOs. They correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the GBO. When used in conjunction with the noncommutative ADHM construction, we nd that these new instantons are in general not unitarily equivalent to the ones currently known in literature. Chapter 3 studies the time dependent transitions of quantum forced harmonic oscillator (QFHO) in noncommutative R1;1 perturbatively to linear order in the noncommutativity . We show that the Poisson distribution gets modified, and that the vacuum state evolves into a \squeezed" state rather than a coherent state. The time evolutions of un-certainties in position and momentum in vacuum are also studied and imply interesting consequences for modelling nonlinear phenomena in quantum optics. In chapter 4 we study thermodynamics of an ideal gas in Doubly Special Relativity. We obtain a series solution for the partition function and derive thermodynamic quantities. We observe that DSR thermodynamics is non-perturbative in the SR and massless limits. A stiffer equation of state is found. We conclude our results in the last chapter.

This thesis is a collection of six papers. The first four constitute the heart of the thesis; they are concerned with quantum mechanical properties of certain harmonic-oscillator states. The first paper is a discourse on single-mode and two-mode Gaussian pure states (GPS), states produced when harmonic oscillators in their ground states are exposed to potentials that are linear or quadratic in oscillator position and moment um variables (creation and annihilation operators). The second and third papers develop a formalism for analyzing two-photon devices (e.g., parametric amplifiers and phase-conjugate mirrors), in which photons in the ouput modes arise from two-photon transitions, i.e., are created or destroyed two at a time. The states produced by such devices are single-mode and two-mode "squeezed states", special kinds of GPS whose low-noise properties make them attractive for applications in such fields as optical communications and gravitational wave detection. The fourth paper is an analysis of the noise in homodyne detection, a phase-sensitive detection scheme in which the special properties of (single-mode) squeezed states are revealed as an improved signal-to-noise ratio relative to that obtained with coherent states (the states produced, e.g., by a laser).

The fifth and sixth papers deal with problems of a different nature from that of the previous papers. The fifth paper considers the validity of the "standard quantum limit" (SQL) for measurements which monitor the posi­tion of a free mass. It shows specifically that when the pre-measurement wave functions of the free mass and the measuring apparatus(es) are Gaus­sian (in the general sense, which includes so-called "contractive states"), measurements described by linear couplings to the position or to both the position and momentum are limited by the SQL. The sixth paper develops the mathematical theory of torsional (toroidal) oscillations in fully general relativistic, nonrotating, spherical stellar models, and of the gravitational waves they emit.

Study of light rays (light world lines) plays a significant role in many of astro- physical applications. Light rays are mainly studied in terms of so-called grav- itational lensing. However, the majority of studies are mainly focused on light propagation in vacuum. If the refractive and dispersive medium characterised by refractive index n is considered, effects occurring due to the medium presence need to be taken into account, which significantly complicates the problem. In the present thesis, rays propagating through simple refractive and dispersive systems, such as plane differentially sheared medium, are studied. In order to simplify the problem, the Hamiltonian equations of motion are used. The ray trajectories in the vicinity of Kerr black hole as well as accessible regions for the rays are also studied. Radial variation of the medium velocity is considered. Due to the recent increase of publications focused on the gravitational lensing in plasma, a detailed review summarizing the results obtained recently is included. 1

The spin transport and dynamics of optically injected spin polarized carri- ers are studied with a high spatial and/or time resolution in semiconductor GaAs-based heterostructures in multiple transport regimes. An unexpectedly long-scale and high-speed spin diffusion transport is observed in a long-lived electron sub-system induced optically at an undoped single GaAs/AlGaAs heterointerface. A diffusion and drift-dominated spin transport is investi- gated using an electrical spin-detection via the inverse spin Hall effect in doped GaAs-based systems at room and low temperatures. It is shown that the inverse spin Hall signal and the spin transport parameters can be con- trolled by a direct application of an electric field or by expanding a depleted zone of a planar pn-junction.

abstract: What can classical chaos do to quantum systems is a fundamental issue highly relevant to a number of branches in physics. The field of quantum chaos has been active for three decades, where the focus was on non-relativistic quantumsystems described by the Schr¨odinger equation. By developing an efficient method to solve the Dirac equation in the setting where relativistic particles can tunnel between two symmetric cavities through a potential barrier, chaotic cavities are found to suppress the spread in the tunneling rate. Tunneling rate for any given energy assumes a wide range that increases with the energy for integrable classical dynamics. However, for chaotic underlying dynamics, the spread is greatly reduced. A remarkable feature, which is a consequence of Klein tunneling, arise only in relativistc quantum systems that substantial tunneling exists even for particle energy approaching zero. Similar results are found in graphene tunneling devices, implying high relevance of relativistic quantum chaos to the development of such devices. Wave propagation through random media occurs in many physical systems, where interesting phenomena such as branched, fracal-like wave patterns can arise. The generic origin of these wave structures is currently a matter of active debate. It is of fundamental interest to develop a minimal, paradigmaticmodel that can generate robust branched wave structures. In so doing, a general observation in all situations where branched structures emerge is non-Gaussian statistics of wave intensity with an algebraic tail in the probability density function. Thus, a universal algebraic wave-intensity distribution becomes the criterion for the validity of any minimal model of branched wave patterns. Coexistence of competing species in spatially extended ecosystems is key to biodiversity in nature. Understanding the dynamical mechanisms of coexistence is a fundamental problem of continuous interest not only in evolutionary biology but also in nonlinear science. A continuous model is proposed for cyclically competing species and the effect of the interplay between the interaction range and mobility on coexistence is investigated. A transition from coexistence to extinction is uncovered with a non-monotonic behavior in the coexistence probability and switches between spiral and plane-wave patterns arise. Strong mobility can either promote or hamper coexistence, while absent in lattice-based models, can be explained in terms of nonlinear partial differential equations.
Dissertation/Thesis
Ph.D. Electrical Engineering 2012

Tese de doutoramento em Física (Física Teórica) apresentada à Fac. de Ciências e Tecnologia da Universidade de Coimbra
The characterization of the electronic response of nanostructures to external electromagnetic fields is of great importance, both from the theoretical and technological points of view. In contrast to light elements, new physical processes and phenomena appear in heavy elements, where relativistic effects, like spin-orbit coupling cannot be ignored. In this work we develop the theoretical framework and the numerical tools needed to address those processes within time-dependent density functional theory (TDDFT). We first apply this methodology to the study of the photoabsorption cross-section of small cationic xenon clusters. Overall, we find our results to be in good agreement with experiment, except for the incorrect prediction of the relative intensities of the peaks. As a second application, we investigate the effect of spin-orbit coupling in the optical response of small gold clusters. We find that this effect is always noticeable, but its importance depends on the dimensionalities of the clusters (the effect is larger for wires than for 2D and 3D structures) and on the size of the clusters (the effect is “quenched” with increasing cluster size). Finally, we study the role of spin noncollinearity in the excited state properties of small chromium and iron clusters and its interplay with spin-orbit coupling. In particular, we compare the dipole and spin-dipole responses of clusters with collinear and noncollinear spin arrangements. We find that, in all cases, the different electronic structure of collinear and noncollinear configurations are reflected to some extent in the spectra. On the contrary, no direct evidence of spin-orbit coupling can be found in the spectra.