Les gyromètres laser He-Ne sont des senseurs inertiels dont la fiabilité et la précision sont reconnues depuis le milieu des années 1980. Leur grande sensibilité leur permet de mesurer des vitesses de rotation avec une précision qui atteint 10⁻³ °/ h dans le domaine aéronautique. Cependant, du fait d’un fonctionnement complexe basé sur une physique riche et variée, ses performances sont fortement dépendantes des conditions de fonctionnement et de toute modification du processus de fabrication. Dans ce cas, un travail de modélisation prend tout son sens, puisqu’il permet, outre une compréhension claire et précise des différents phénomènes physiques, un accès à des études paramétriques non envisageables expérimentalement. La modélisation globale du fonctionnement d’un gyrolaser He-Ne a ainsi été l’objectif principal de la collaboration entre la société Sagem (groupe Safran), un des leaders mondiaux dans le domaine des senseurs inertiels, et le Laboratoire de Physique des Gaz et des Plasmas (LPGP). Cette modélisation est « multiphysique » du fait de la diversité des domaines que couvre la physique du gyrolaser (Plasma, Physique Atomique, Lasers). C’est pourquoi nous avons développé trois modèles spécifiquement adaptés à chaque domaine. Le premier décrit la modélisation de la colonne positive du plasma de décharge dans une approche fluide. Ce modèle permet une description quantitative du plasma et l’accès aux grandeurs telles que la densité électronique et la fonction de distribution en énergie des électrons. Ces grandeurs sont les entrées nécessaires au second modèle qui traite la cinétique des états excités du plasma He-Ne. Un modèle collisionnel-radiatif à 1 dimension radiale (1D-CRM) a ainsi été développé. L’aspect 1D se justifie par l’importance des phénomènes de transport d’atomes et de rayonnement pouvant influer sur le profil radial de l’inversion de population du laser. Le transfert radiatif par auto-absorption des transitions radiatives résonantes a notamment été modélisé en résolvant l’équation de Holstein-Biberman à partir d’une méthode Monte-Carlo. Cet aspect constitue un élément majeur de ce travail de thèse. La diffusion des atomes excités du mélange He-Ne a également été prise en compte en résolvant l’équation de diffusion avec différentes conditions au bord à la surface du capillaire.A partir des populations et des taux cinétiques de peuplement et dépeuplement calculés par 1D-CRM, l’amplification laser dans la cavité a été modélisée dans le cadre d’une approche Maxwell-Bloch à 2 niveaux (NADIA) en incluant la saturation inhomogène du gain c’est-à-dire en tenant compte de la vitesse des atomes émetteurs dans la direction de propagation des faisceaux lasers. La cinétique de NADIA a été optimisée et les processus de transports dans l’espace des phases ont également été implémentés. Ce modèle a été utilisé pour étudier les performances du gyrolaser liées au milieu amplificateur et pour dériver les paramètres physiques nécessaires au développement d’un simulateur du gyrolaser.Dans ce simulateur, un modèle physique simplifié dérivé de NADIA, a été couplé à des modules « systèmes » dans le but de reproduire en sortie le signal opérationnel d’un gyrolaser. Ceci nous a permis de réaliser des études paramétriques sur les grandeurs caractérisant les performances d’un gyrolaser notamment le biais dynamique et le Random-Walk. Nous montrons en particulier que les performances de notre simulateur sont en bon accord avec celles observées en conditions opérationnelles. De plus, nos résultats montrent que ce simulateur est également un outil puissant pour l’analyse de données expérimentales. / Ring laser gyros (RLG) are inertial sensors whose reliability and accuracy have been recognised since the mid-1980s. Their high sensitivity enables them to measure angular velocity with an accuracy of 10⁻³ °/ h in aeronautics. However, because of a complex functioning based on a rich and varied physics, their performances are highly dependent on the working conditions and on any modification in the manufacturing process. In this case, a numerical modelling is pertinent since it allows both a clear understanding of the ring laser physics and parametric studies which are not experimentally feasible. The global modelling of a He-Ne RLG has been the main objective of the collaboration between Sagem (Safran group), which is one of the world leader in the inertial sensors field, and the Gas and Plasma Physics Laboratory (LPGP).This modelling is “multi-physics” since RLG physics involves several disciplines (plasma, atomic and laser physics). Therefore we have developed three models specifically adapted to each field. The first one describes the modelling of the positive column of the glow discharge following a fluid approach. This model allows a quantitative description of the plasma and gives access to fundamental quantities like the electron density or the electron energy distribution function. These quantities are the required inputs for the second model which treats the kinetics of the excited states inside the He-Ne plasma. For this, a collisional-radiative model in a radial geometry (1D-CRM) has been developed. The radial geometry is justified by the importance of the transport processes of atoms and radiations which can influence the radial profile of the population inversion. Notably, the radiative transfer by self-absorption of the resonant radiative transitions has been modelled by solving the Holstein-Biberman equation by a Monte-Carlo method. This aspect is a major component of this PhD work. Diffusion of excited atoms inside the plasma has also been taken into account by solving the diffusion equation with different boundary conditions at the capillary surface. From the populations and the kinetic rates computed by 1D-CRM, the laser amplification inside the cavity has been modelled using a two-level Maxwell-Bloch approach (NADIA) taking into account the inhomogeneous gain saturation, which means to consider the thermal speed of the atoms in the direction of propagation of the laser beams. The kinetics of NADIA has been optimized and transport processes in the phase space have also been implemented. This model has been used to study the performances of the RLG linked to the amplifying medium and to derive the physical parameters needed for the development of a simulator.Concerning this simulator, a simplified physical model from NADIA has been coupled to system modules in order to reproduce the operating signal of a RLG. This allows to conduct parametric studies on the quantities defining the RLG performance in particular the dynamic bias and the so-called “Random Walk”. We showed notably that the results of our simulator are in good agreement with experimental measurements in operating conditions. Moreover, our results show that this simulator is a powerful tool for analysing experimental data.

Made available in DSpace on 2016-12-12T20:15:48Z (GMT). No. of bitstreams: 1 elementos pre-textuais.pdf: 162361 bytes, checksum: 82f1f3cdfd0bb7d2b36c65252dee4600 (MD5) Previous issue date: 2012-02-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The erbium-doped fiber dual-ring laser is a four-dimensional continuous-time dynamical system, modeled by a set of four autonomous, first-order ordinary differential equations, and has been investigated in the last years due to several applications, as an example, chaos control, chaos synchronization and telecommunications systems. In this work we study the nonlinear dynamics of an erbium-doped fiber dual-ring laser from two points of view, analytical and numerical. The analytical investigation consists in to analyse the stability of an equilibrium point, using the Routh-Hurwitz criterion and some eigenvalues of the Jacobian matrix. The numerical investigation was performed in a the two-dimensional parameter-space of a set autonomous, seven-parameter, four-dimensional first-order ordinary differential equation system, tuning two parameters that control the dynamics. By using the Lyapunov exponents spectrum as a measure of chaotic and periodic behaviors, we construct parameter-space diagrams to characterize the dynamics of the model. We study the self-organized periodic structures embedded in a chaotic region by means of bifurcation diagrams, showing that there are directions in two-dimensional parameter-spaces in which the periodic structures are arranged in period-adding bifurcation cascades. / O laser de fibra de dois anéis dopado a érbio é um sistema dinâmico quadridimensional a tempo contínuo, modelado por um conjunto de quatro equações diferenciais ordinárias de primeira ordem autônomas, e tem sido investigado nos últimos anos devido as diversas aplicações, como por exemplo, controle de caos, sincronização de caos e sistemas de telecomunicações. Neste trabalho estudamos a dinâmica não linear do laser de fibra de dois anéis dopado a érbio a partir de dois pontos de vista, analítico e numérico. A investigação analítica consiste em analisar a estabilidade de um ponto de equilíbrio do sistema, usando o critério de Routh-Hurwitz e alguns autovalores da matriz Jacobiana. A investigação numérica foi realizada em um espaço de parâmetros bidimensional de um conjunto de quatro equações diferencias ordinárias de primeira ordem autônomas com sete parâmetros, variando dois parâmetros que controlam a dinâmica. Usando o maior Expoente de Lyapunov como uma medida dos comportamentos caótico e periódico construímos diagramas do espaço de parâmetros para caracterizar a dinâmica do modelo. Estudamos as auto-organizações de estruturas periódicas imersas em uma região caótica usando diagramas de bifurcação, mostrando que existem direções específicas no espaço de parâmetros bidimensional em que tais estruturas periódicas são arranjadas em cascatas de bifurcação por adição de período.

Les gyroscopes laser à gaz constituent une solution technique de haute performances dans les problématiques de navigation inertielle. Néanmoins, pour de très faibles vitesses de rotation, les petites imperfections des miroirs de la cavité optique font que les deux faisceaux contra-propageant sont verrouillés en phase. En conséquence, les mesures en quadrature de leur différence de phase ne permettent plus de remonter directement aux vitesses de rotation à l'intérieur d'une zone autour de zéro, dite zone aveugle statique, ou, si l'on utilise une procédure d'activation mécanique, dite zone aveugle dynamique. Ce travail montre qu'il est néanmoins possible, en utilisant des méthodes issues du filtrage et de l'estimation, de remonter aux vitesses de rotation mêmes si ces dernières sont en zone aveugle. Pour cela, on part d'une modélisation physique de la dynamique que l'on simplifie par des techniques de perturbations singulières pour en déduire une généralisation des équations de Lamb. Il s'agit de quatre équations différentielles non-linéaires qui décrivent la dynamique des intensités et des phases des deux faisceaux contra-propageant. Une étude qualitative par perturbations régulières, stabilité exponentielle des points d'équilibre et applications de Poincaré permet de caractériser les zones aveugles statiques et dynamiques en fonction des imperfections dues aux miroirs. Il est alors possible d'estimer en ligne avec un observateur asymptotique fondé sur les moindre carrés récursifs ces imperfections en rajoutant aux deux mesures en quadrature celles des deux intensités. La connaissance précise de ces imperfections permet alors de les compenser dans la dynamique de la phase relative, et ainsi d'estimer les rotations en zone aveugle. Des simulations numériques détaillées illustrent l'intérêt de ces observateurs pour augmenter la précision des gyroscopes à gaz. / Gaz ring laser gyroscopes provide a high performance technical solution for inertial navigation. However, for very low rotational speeds, the mirrors imperfections of the optical cavity induce a locking phenomena between the phases of the two counter-propagating Laser beams. Hence, the measurements of the phase difference can no longer be used when the speed is within an area around zero, called lock-in zone, or,if a procedure of mechanical dithering is implemented, dithering lock-in zone. Nevertheless, this work shows that it is possible using filtering and estimation methods to measure the speed even within the lock-in zones. To achieve this result, we exploit a physical modeling of the dynamics that we simplify, using singular perturbation techniques, to obtain a generalization of Lamb's equations. There are four non-linear differential equations describing the dynamics of the intensities and phases of the two counter-propagating beams. A qualitative study by regular perturbation theory, exponential stability of the equilibrium points and Poincaré maps allows a characterisation of the lock-in zones according to the mirrors imperfections. It is then possible to estimate online, with an asymptotic observer based on recursive least squares, these imperfections by considering the additional measurements of the beam intensities. Accurate knowledge of these imperfections enables us to compensate them in the dynamic of the relative phase, and thus to estimate rotational speeds within the lock-in zones. Detailed numerical simulations illustrate the interest of those observers to increase the accuracy of gas ring laser gyroscopes.

Para a espectroscopia de alta resolução e metrologia óptica em geral, é desejável um laser com linha espectral estável e de alta potência de saída para bombear diferentes tipos de ressonadores, como osciladores paramétricos óticos (OPO Optical Parametric Oscillator). Os lasers de frequência única disponíveis estão no alcance de potência de saída de 10 Watts, enquanto que, dependendo da aplicação e do tipo de OPO, é desejável uma maior potência (> 20 W). Neste trabalho foi desenvolvido um laser de frequência única e alta potência com base em módulos de bombeio por diodos e tendo como meio ativo o granada de alumínio de ítrio dopado com neodímio (Nd:YAG). Dois bastões de Nd:YAG bombeados transversalmente por diodo, foram utilizadas em uma configuração de ressonador em anel com saída polarizada de onda continua (CW continuous-wave), qualidade de feixe modo transversal eletromagnético (TEM00) e potência de saída de 105,2 W. A potência de saída alcançada é, a nosso entender, a mais alta para lasers em anel no modo fundamental transversal polarizado contínuo usando módulos Nd:YAG comuns com bombeamento lateral. O ressonador permitiu a sintonização de potência em uma grande faixa dinâmica e obteve excelente qualidade de feixe, usando uma placa de meia onda entre os dois bastões para compensação de birrefringência. A operação de frequência única foi alcançada usando cristal de granada de térbio-gálio (TGG-Terbium Gallium Garnet), dois imãs e um etalon, com uma potência de saída de 51,60 W e uma largura a meia altura da curva (FWHM) espectral de aproximadamente 17 MHz. / For high resolution spectroscopy, a high power, stable line output laser is desirable for pumping different types of optical parametric oscillator resonators (OPO). Single-frequency lasers are in the range of 10 watts of output power, while, depending on the application and the OPO type, higher power (> 20 W) is desirable. In this work a single frequency high power laser based on diode pumping modules with Nd:YAG as the active medium was developed. Two Nd:YAG bars transversally pumped by diodes were used in a configuration of a CW polarized ring resonator with beam quality TEM00 and output power of 105,2 W. The output power achieved is, to our knowledge, the highest for continuous polarized fundamental mode ring lasers using standard Nd:YAG modules with side pumping. The resonator allowed the tuning power in a large dynamic range and obtained excellent beam quality using a half-wave plate between the two rods for birefringence compensation. The single frequency operation was achieved using a TGG (Terbium Gallium Garnet) crystal, two magnets and an etalon, with an output power of 51.60 W and a 17 MHz full width at half maximum (FWHM) spectral width.

Made available in DSpace on 2016-03-15T19:38:49Z (GMT). No. of bitstreams: 1 2012_Lucia Akemi Miyazato Saito.pdf: 7872621 bytes, checksum: 4898bb89f5642047c4e878b18fc4f31a (MD5) Previous issue date: 2012-11-01 / Conselho Nacional de Desenvolvimento Científico e Tecnológico / We investigated the mechanisms responsible for pulse formation and evolution in Erbium-doped fiber lasers with cavity lengths varying from 16.4 m to 100.8 km that were actively mode-locked at repetition rate of 1 GHz. The variation of pulse widths and the peak powers in these lasers defined three regimes of propagation inside the cavities and we identified the mechanisms responsible for the pulse formation and evolution in each one of these regimes depending on the ratio between the cavity length (Lcav) and the dispersion length (LD) and nonlinear length (LNL). When Lcav is shorter than LD and LNL, there is neither dispersive nor nonlinear effect during pulse evolution (pulse has a duration of approximately 30 ps). In this regime, its final duration is determined by the standard theory of active modelocking. For Lcav shorter than LD but ~ LNL, the pulse evolution is in the nonlinearity-dominant regime where the self-phase modulation leads to spectral broadening. In addition, for cavities longer than 12.6 km, Lcav ~ LD and also longer then LNL. The pulse evolution is in the dispersion-dominant regime with its duration depending on the accumulated dispersion. In this regime the soliton effect takes place and the final pulse duration depends on the cavity length. Also, we present a comparison between an in-field and in-laboratory 50 km ultralong Erbium fiber lasers actively mode-locked with repetition rate varying from 1 to 10 GHz generating pulses from 35.2 to 68.7 ps. The pulse widths generated at higher frequencies are in agreement with Kuizenga-Siegman theory. However, for lower frequencies the pulses have higher intracavity peak power which allows the soliton effect to take place. Depending on the pump power level, the repetition rate and the cavity length, both lasers can operate in active mode-locking or under the influence of the soliton regime that locks the pulse duration according to the dispersion and cavity length. Due to the soliton robustness, this condition eliminates most of the environmental influence in the in-field mode-locking regime and makes both lasers very similar. / O laser de fibra dopada com Érbio é apresentado nesta tese numa nova configuração: cavidade ultralonga, com dimensão da ordem de dezenas de quilômetros. Foram investigados os mecanismos responsáveis pela formação e evolução do pulso em cavidades com comprimentos de 16,4 m a 100,8 km operando em regime de acoplamento de modos ativo na taxa de repetição de 1 GHz. A variação da largura dos pulsos e da potência de pico nestes lasers definem três regimes de propagação no interior das cavidades sendo possível identificar os mecanismos responsáveis pela formação e evolução em cada um destes regimes, dependendo da relação entre o comprimento da cavidade (Lcav) e o comprimento de dispersão (LD) e também em relação ao comprimento não-linear (LNL). Quando Lcav é menor que LD e LNL, não há efeito dispersivo e não-linearidades apreciáveis na evolução do pulso, obtendo-se aproximadamente 30 ps. Neste regime, a duração final é determinada pela teoria de acoplamento de modos ativo. Para Lcav menor que LD mas ~LNL, a evolução do pulso é dominado pela não-linearidade onde a automodulação de fase resulta em alargamento espectral. Além disso, para cavidades mais longas que 12,6 km, Lcav ~ LD e Lcav mais longo que LNL, a duração do pulso na saída aumenta proporcionalmente com a dispersão acumulada e ocorre a propagação de pulsos sob efeito solitônico. Complementando o estudo, o laser na configuração em laboratório é comparado com o laser montado em campo, sendo utilizado em ambos 50 km de fibra padrão. O laser à fibra dopada com Érbio é modulado ativamente com taxa de repetição variando entre 1 e 10 GHz gerando pulsos de 35,2 a 68,7 ps. A duração dos pulsos gerados em frequências altas está de acordo com a teoria de Kuizenga-Siegman. No entanto, em baixas frequências os pulsos têm potência de pico intracavidade alta o que permite que haja a formação de pulsos solitônicos na propagação. Dependendo do nível da potência de bombeamento, da taxa de repetição e do comprimento da cavidade, os dois lasers podem operar em acoplamento de modos ativo ou sob a influência do regime solitônico que trava a duração do pulso de acordo com a dispersão e comprimento da cavidade. Devido à robustez do sóliton, esta condição elimina a maior parte da influência do ambiente no acoplamento de modos do laser na configuração em campo, tornando os dois lasers muito similares.

[pt] Objetivando suprimir as instabilidades dinâmicas de ganho em um amplificador à fibra dopada com Érbio (EDFA), uma nova configuração de laser em anel é apresentada e demonstrada. Neste trabalho, analizamos os efeitos da variação do nível de atenuação no laço de re-alimentação sobre a resposta transitória do EDFA. Particularmente, observamos as excursões de ganho experimentadas pelo canal sobrevivente quando sete dentre oito canais da rede são adicionados ou removidos, à exemplo do que ocorre em sistemas WDM reais. Sob esta análise, avaliamos o desempenho do sistema em suprimir as instabilidades dinâmicas de ganho do EDFA. / [en] A new ring laser configuration to eliminate the gain dynamic instabilities of an erbium doped fiber amplifier (EDFA) is proposed and demonstrated. We examine the effect of the attenuation level in the optical feedback path over thetransient response of the EDFA. In particular, we look at the transient gain excursions experienced by surviving channel when seven of eight channels are added or dropped, like in real WDM systems. Using this analysis as a guide, we highlight the robustness of the approach and evaluate its performance to EDFA gain stabilization.