The problems of the scattering off the perfect conductor sphere and the dielectric sphere have the exact solutions. But there are no exact solutions for the scattering off a multi-layered dielectric sphere with a metallic cap like the Lunberg lens reflectors which is used as a strong omni-directional reflector found in many microwave applications. Haruo Sakurai applied the modal expansion technique and point-matching method (PMM) to study the scattering of the Lunberg lens reflectors. The problem is eventually formulated as 2MN by 2MN simultaneous matrix equation with M regions each having 2N unknowns due to two set of coupled polarization vectors. Strictly speaking, the formulae of the mode matching method for the problem of the scattering of the dielectric sphere are not exact. Furthermore, the size of the simultaneous matrix equation is also unnecessarily too larger. In this thesis, we employ an integral equation formulation in the Frequency-domain together with the modified impedance transformation technique for the spherically layers to study the scattering of the Lunberg lens reflectors. We show that the formulae of the integral equation are exact and using an equivalent matrix equation, that the entire problem can be reduced to a N by N matrix equation where N is the number of terms of the expansion of the unknown field in the opening. To verify our formulation we compute the total field of the plane wave incident upon the multi-layered micro lenses and compared the results with those from the geometric optics. We get good agreement for the regions that both theories apply. Small discrepancy is also observed and is consistent with the theoretical prediction.

Micro ring-cavity, like the Fabry-Perot cavity, is an optical device that resonates at certain frequencies. It is used as a phase compensator, and filter. Easily fabricated, the micro ring-cavity can be mass-produced, the ring-cavity is becoming evermore important as integrated opto-electronic technology advances. In this thesis, we begin with a novel one-dimensional theory that considers bi-directional traffic in the micro-ring cavity. By separating the device into easily manageable regions, and employing only fundamental modes in each of the sections, we obtain a closed-form formula for the transmission and reflection coefficient of this device. Under certain circumstances, when the directional coupler length is short but its coupling strength is strong, we observed a significant amount of reflection of optical energy at some frequencies. This phenomena is currently unknown to the opto-electronic industry. To further study this, we developed a more rigorous multi-mode propagation method for two-dimensional bi-directional ring cavities. The problem at hand is first being sliced into regions of multi-layered sections. Within each section, we can express the fields in terms of the underlying waveguide modes of the structure. At the interfaces of these sections, we construct coupled integral equations, which are derived from the continuity requirement of the tangential fields. We have complete formulations for both TE and TM cases, down to the coupled matrix equation for the unknown modal coefficients at each junction.

The design of high power lasers requires large mode areas to overcome various intensity driven nonlinear effects. Increasing the aperture size within the laser can overcome these effects, but typically result in multi-transverse mode output and reduced beam quality, limiting the brightness of the system. As one possible solution, the angular selectivity of a diffractive optical element is proposed as a spatial filter, allowing for the design of compact high brightness sources not possible with conventional methods of transverse mode selection. This thesis explores the angular selectivity of volume Bragg gratings (VBGs) and their use as spatial transverse mode filters in a laser resonator. Selection of the fundamental mode of a resonator is explored using transmission Bragg gratings (TBGs) as the spatial filter. Simulations and experimental measurements are made for a planar, 1 cm long resonator demonstrating near diffraction limited output (M2 < 1.4) for aperture sizes as large as 2.0 mm. Applications to novel fiber laser designs are explored. Single mode operation of a multi-mode Yb3+ doped ribbon fiber laser (core dimensions of 107.8 ?m x 8.3 ?m) is obtained using a single transmission VBG as the filter in an external cavity resonator. Finally, a novel method of selecting a pure higher order mode to oscillate within the gain medium while simultaneously converting this higher order mode to a fundamental mode at an output coupler is proposed and demonstrated. A multiplexed transmission VBG is used as the mode converting element, selecting the 12th higher order mode for amplifications in an Yb3+ doped ribbon fiber laser, while converting the higher order mode of a laser resonator to a single lobed output beam with diffraction limited divergence.

Experimental evidence is presented that supports the theory that beats between transverse modes are responsible for the fast modulation carried on occasions by laser relaxation oscillations. / Thesis / Master of Engineering (ME)

No description available.

L'objet de cette thèse est l'étude de la sélection des structures transverses stationnaires dans les lasers. Nous nous attachons à décrire expérimentalement et à expliquer numériquement à l'aide d'une méthode de type Fox--Li les observations de modes transverses qui peuvent être réalisées dans un laser à état solide pompé longitudinalement. Ainsi, nous sommes amenés à explorer en profondeur le comportement des cavités non--dégénérées dans différentes situations de pompage, ainsi que les notions de dégénérescence exacte et de dégénérescence partielle. Nous sommes également amenés à étudier, bien que de manière assez qualitative, le rôle important des effets thermiques dans la formation des modes transverses dans les zones de dégénérescence de la cavité. Ces questions ont fait l'objet de multiples investigations depuis l'avènement du laser, mais nous mettons toutefois en évidence que de sérieux problèmes d'interprétations d'observations expérimentales persistent dans la littérature scientifique contemporaine. Une idée fausse assez répandue stipule par exemple qu'il est possible d'exciter un mode Laguerre--Gauss ou Ince--Gauss d'ordre élevé en utilisant un faisceau de pompe suffisamment petit afin qu'il recouvre parfaitement le lobe principal du mode visé. Nous montrons analytiquement, numériquement et vérifions expérimentalement que ceci est impossible dans une situation non--dégénérée, et expliquons comment certaines observations réalisées proches d'une dégénérescence peuvent contribuer à propager cette idée erronée. Bien que le modèle que nous utilisons n'élude pas les questions importantes concernant le rôle de la dynamique temporelle dans la formation des modes transverses dans un laser, sa pertinence réside dans sa simplicité et sa capacité à reproduire de manière très satisfaisante toutes les observations expérimentales. Ainsi, toutes les observations de modes transverses qu'il est possible de réaliser dans un laser peuvent être comprises à travers ce modèle, qui ne nécessite comme ingrédients principaux qu'une cavité, un gain saturé, des effets thermiques et éventuellement des effets de diaphragme. De plus, le modèle simple que nous présentons peut s'étendre sans difficulté à l'étude de cavités instables ou de cavités à miroirs asphériques qui offrent des possibilités nouvelles pour l'excitation de modes transverses originaux. / The main concern of this thesis is the selection of stationary transverse structures in lasers. Throughout the manuscript, we get involved into describing the observations that can be realized in a longitudinally pumped solid--state laser, from both experimental and numerical perspectives using Fox--Li simulations. We explore in detail, on the one hand, the particular behavior of non--degenerate cavities in various pumping situations, and on the other hand the exact and partial degeneracy situations. We also investigate the very influential role played by thermal effects concerning the formation of transverse structures in degeneracy regions, although this study is limited to a more qualitative description. These problems have been of great interest since the early development of laser, however we show in this manuscript that the contemporary scientific litterature still suffers from misinterpretations concerning experimental observations of transverse modes that can occur in lasers. For instance, there still remains the widespread belief that it is possible to excite a high-order Laguerre--Gaussian or Ince--Gaussian mode by strongly focusing the pump beam inside the active medium so that it matches the principal lobe of the targeted mode. We demonstrate analytically, numerically and experimentally that this idea is unfounded and show how some experiments that occur near a cavity degeneracy are misleading and can contribute to spread this misconception. Even if the model we use is unable to deal with some very significant issues concerning the mode formation in the time domain and the build--up of the laser oscillation, we believe that its strength lies into its simplicity and its ability to reproduce every experimental observation in a very accurate way. Hence, we managed to explain and interpret all the experimental observations we have realized given a very few assumptions including the presence of a cavity, a saturated gain, thermal effects and eventually diaphragm effects. Moreover, the simple model that we present can be extended without any difficulty to the case of unstable resonators, or to resonators built from graded--phase mirrors which offer new possibilities towards the excitation of original transverse modes.

The subject of this dissertation is to develop a rigorous transverse-mode integral equation formulation for analyzing TE/TM electromagnetic mode field solutions for dielectric waveguides. The main topics are composed of two related parts. The first part deals with scalar problems. In which we propose a transverse-mode integral-equation formulation for problems such as mode solutions of the ridged microwave waveguides. This same technique also applies to EM waves scattering off the facet of dielectric slab waveguides terminating in free space. For both problems we constructed a specifically chosen basis for the unknown tangential field functions, and we were able to reduce the kernel matrix size by more than one half without noticeable degradation of the field solutions. In the second part of the thesis, we apply a full-vector integral-equation formulation to analyze modal characteristics of the complex, two-dimensional, rectangular-like dielectric waveguide that is divisible into vertical slices of one-dimensional layered structures. The entire electromagnetic vector mode field solution is completely determined by the y-component electric and magnetic field functions on the interfaces between slices. These interfacial functions are governed by a system of vector-coupled transverse-mode integral equations (VCTMIE) whose kernels are made of orthonormal sets of both TE-to-y and TM-to-y modes from each slice. Finally, we show the numerical results to present the stable and quick convergence of this method as well as to improve the Gibb¡¦s phenomenon in the recreation of the transverse fields.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2016-08-18T13:04:44Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertacao-Version-Final.pdf: 16533060 bytes, checksum: 920aa7a96edb1e78d330ff1b83033a68 (MD5) / Made available in DSpace on 2016-08-18T13:04:44Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertacao-Version-Final.pdf: 16533060 bytes, checksum: 920aa7a96edb1e78d330ff1b83033a68 (MD5) Previous issue date: 2015-07-29 / CAPEs / CNPq / Neste trabalho é realizado um estudo sobre os efeitos das rugosidades nas propriedades magnéticas de nanofios de níquel para os modos de reversão curling e transversal. Para o estudo adotamos a simulação micromagnética como ferramenta fundamental e para ser implementada utilizamos OOMMF. Para mudar a rugosidade utilizamos uma cadeia de elipsóides e uma forma de variar este parâmetro foi fixando o comprimento dos fios em 1 μm e mudando o número de elipsóides na cadeia. Dessa forma a relação de aspecto dos elipsóides foi modificada para ser entendida como câmbios na rugosidade. Nas análises realizamos estudos dinâmicos e estáticos da reversão dos momentos. A simulação se baseia fundamentalmente na resolução da equação LLG. Nos estudos dinâmicos monitoramos a dependência temporal dos mapas de momentos a das componentes transversais da magnetização depois de ser invertido o campo aplicado. Foram simulados os ciclos de histerese através da minimização da energia livre de Gibbs. Nos estudos estáticos monitoramos a dependência ângular do campo coercitivo, campo de comutação e a magnetização remanente. Observamos em modo geral que há grandes efeitos das rugosidades sobre as propriedades magnéticase que nossos resultados reproduzem os reportados na literatura assim como as curvas experimentais. / This work is a study on the effects of roughness on the magnetic properties of nickel nanowires for their reversal modes (curling and transversal). For the study we adopted the micromagnetic simulation as a fundamental tool and we used OOMMF to implemented. To change the roughness use ellipsoids chain and a way to vary this parameter was securing the length of the wires in 1 μm and changing the number of ellipsoids in the sequence. Thus the ellipsoids of the aspect ratio has been modified to be understood as the exchange roughness. In the analyzes we perform static and dynamic studies of the reversal of moments. The simulation is based largely on the resolution of the LLG equation. In dynamic studies we monitor the time dependence of the maps of magnetic moments and the transverse components of the magnetization after being reversed the field applied. The hysteresis cycles were simulated by minimization of Gibbs free energy.In static studies we monitor the angular dependence of the coercive field, the switching field and remanent magnetization. We observe in general that there are major effects of roughness on the magnetic properties and that our results reproduce the reported in the literature as well as the experimental curves.

Le contexte de ce travail repose sur l'étude des instabilités de combustion au sein des moteurs-fusées à propergols liquides. Cette étude se concentre sur les effets des champs acoustiques transverses de haute amplitude sur l'injection coaxiale en conditions non-réactives. La réponse acoustique du système d'injection est dépendante des propriétés locales du champ acoustique dans la cavité d'injection. La modification du processus d'atomisation, induit par le champ acoustique, a été analysée dans des configurations simples et multiinjection. Des expériences ont été menées pour des régimes d'atomisation de faibles et hauts nombres de Weber. Trois phénomènes ont été observés: un aplatissement du jet, une amélioration du processus d'atomisation et la déviation du système liquide. La combinaison de ces trois phénomènes en configuration multi-injection résulte en un phénomène de regroupement de gouttes. En présence de combustion, un tel regroupement pourraitmener à un dégagement de chaleur non-uniforme susceptible de déclencher ou d'entretenir des instabilités de combustion. Un modèle théorique basé sur les équations d'acoustique non-linéaire a été développé pour donner les expressions générales de pression de radiation et de forces de radiations résultantes appliqué aux objets sphériques et cylindriques en champ stationnaire ou progressif. Le modèle a été utilisé pour interpréter et quantifier les observations expérimentales en configurations liquide/gaz, trans-critique/super-critique et gaz/gaz, et a permis de montrer que le nombre de Helmholtz qui caractérise le champ acoustique, et le rapport de densité qui caractérise les deux milieux, sont deux paramètres cruciaux. Les principales conclusions montrent que le phénomène observé peut être interprété comme résultant de l'acoustique non-linéaire, dont le paramètre clé étant le ratio de densité. Cela exige que la couche séparant les deux milieux, vue comme une interface, ne doive pas être réduite uniquement à une interface liquide/gaz. / The context of this work relies to high frequency combustion instabilities in Liquid Rocket Engines (LRE). The present research focuses on the effects of high amplitude transverse acoustic fields on non-reactive coaxial injection. The acoustic response of injection domes is found to be dependent on the local properties of the acoustic field in the injection cavity. The modification of the atomization process, induced by the acoustic field, has been analyzed in single and multi-injection configurations. Experiments were performed from low to high Weber number atomization regimes. Three phenomena are observed: jet flattening, improvement of the atomization process and deviation. The combination of these phenomena in multi-injection configurations leads to a droplet clustering phenomenon. In the presence of combustion, such a clustering could lead to non-uniform heat release rate which can trigger or sustain combustion instabilities. A theoretical model based on non-linear acoustics has been developed, providing general expressions of radiation pressure and resulting radiation force, for spherical and cylindrical objects in standing and progressive wave field. The model has been successfully used to interpret and quantify experimental observations in liquid/gas, trans-critical/super-critical and gas/gas configurations and showed that the Helmholtz number α characterizing the acoustic field and the density ratio η characterizing the two media are two parameters of importance. The major conclusions are that the observed phenomena can be interpreted as resulting from non-linear acoustics, the key feature being the density ratio. It is claimed that the layer separating the two media, seen as an interface, does not need to be restricted only to a liquid/gas interface.