Dissertations / Theses on the topic 'Laguerre- Gaussian'

Thesis (M.S. in Physics)--Naval Postgraduate School, June 2007.
Thesis Advisor(s): William B. Colson, Robert L. Armstead. "June 2007." Includes bibliographical references (p. 71-72). Also available in print.

This thesis covers two areas of laser physics: optical cooling of rare-earth-doped solids by anti-Stokes fluorescence and the generation of pure Laguerre-Gaussian laser modes using a ring-shaped pump beam. A novel laser-based approach to determining local variations in the temperature of transparent samples is developed. This technique is based on monitoring the frequency-shift of the axial modes of a simple, diode-pumped solid-state laser resonator in which the sample is placed. A theoretical resolution of <4.5mK is calculated for a perfectly isolated probe resonator. The technique is validated by comparison to thermocouple measurements of a control sample. The advantages of this diagnostic technique have been demonstrated for the discrimination of local optical cooling from parasitic heating effects. Local cooling of 1.4±0.1K has for the first time been observed in Yb3+:CaF2 using this measurement technique. During the course of the optical cooling experiments regular pulse packets have been observed for sustained self-pulsing in a fibre laser operating significantly above the lasing threshold. This regular pulsing behaviour is observed to break down to irregular pulsing behaviour close to threshold. Extending the resonator length has been demonstrated as a technique for the suppression of self-pulsing. A hollow-core-fibre beam-shaping technique has been developed to selectively generate pure Laguerre-Gaussian laser modes. An astigmatic mode-converter analysis of these modes has proven that an axial mode cannot simultaneously possess both senses of azimuthal phase. The sense of the azimuthal phase has been observed to flip around the peak of the gain spectrum.

Esta tesis aborda las interacciones no colineales de los modos Laguerre-Gaussianos. Estas interacciones se utilizan para lograr la transferencia del momento angular orbital (OAM) en la mezcla de ondas no lineales. Esto se hace mediante conmutación controlada por polarización. Ajustando la geometría de los haces de entrada, es posible producir una salida OAM de tres canales con cargas topológicas arbitrarias que se generan simultáneamente y se resuelven espacialmente en la longitud de onda del segundo armónico. El uso de grados de libertad de trayectoria y polarización permite una conmutación óptica casi perfecta entre las diferentes operaciones OAM. Se propone un modelo teórico que muestra un muy buena concordancia con los experimentos.
Tesis

Les modes de Laguerre-Gauss sont une des solutions de l’équation de propagation de la lumière dans l’approximation paraxiale en coordonnées cylindriques. Ces modes sont caractérisés par deux indices (azimutal et radial) et présentent des propriétés particulières : une structure en forme d’anneau et une phase en hélice. Ces propriétés ont été mises au profit pour plusieurs applications allant de la microscopie à l’astronomie. Cette thèse a été dédiée à l’étude de ces modes et à leur application dans le domaine des atomes froids. Dans un premier temps, la pureté des modes fabriqués par la méthode d’holographie numérique a été étudiée, ainsi que le rôle que la pureté joue dans leur propagation. Ces modes ont été ensuite utilisés pour l’obtention une source d’atomes froids brillante. Depuis plus de 20 ans, des efforts considérables ont été faits pour obtenir des sources d’atomes froids les plus brillantes et les plus compactes possibles. Un piège magnéto-optique à deux dimensions (2D-MOT) est couramment utilisé pour obtenir une source continue d’atomes froids avec un flux important de l’ordre de 1010 atomes/s. Toutefois, le jet atomique ainsi obtenu présente une divergence d’environ 40 mrad ce qui contraint l’utilisateur à travailler près de la sortie mais avec un accès optique limité ou bien loin où il a un bon accès optique mais au prix d’une densité atomique plus faible. Une alternative est présentée, dans laquelle un mode de Laguerre-Gauss est utilisé pour canaliser les atomes à la sortie d’un 2D-MOT. Le mode de Laguerre-Gauss réalise un piégeage dipolaire qui confine les atomes sont le centre noir du mode, ce qui présente l’intérêt de limiter le chauffage dû à l’absorption/émission de la lumière. Ainsi, puisque les modes de Laguerre-Gauss gardent leur forme au cours de leur propagation, les atomes sont canalisés sur une distance de plusieurs décimètres. Nous avons étudié le fonctionnement de ce système pour différents ordres du mode de Laguerre-Gauss et différentes fréquences, et nous avons montré que ce système est efficace et permet d’atteindre un gain en densité d’un facteur 200 par rapport au cas d’un 2D-MOT conventionnel. Un cas particulier est aussi présenté, dans lequel la fréquence du mode de Laguerre-Gauss est choisie pour effectuer non seulement la canalisation des atomes mais aussi leur repompage, ce qui conduit à une simplification importante du système. D’un autre côté, les modes de Laguerre-Gauss sont d’un grand intérêt dans le domaine de l’information et la cryptographie quantique car ils peuvent être utilisés pour encoder et enregistrer l’information. Pour cela, il est indispensable de pouvoir les détecter de façon non-équivoque. Dans ce contexte, nous nous sommes intéressés à la détermination de ces modes. Jusqu’à maintenant, les techniques de détection ont permis de mesurer l’indice azimutal mais peu d’entre elles mesurent l’indice radial. Si on est capable de mesurer aussi l’indice radial, il peut être utilisé comme une nouvelle variable pour le codage et l’enregistrement de l’information. Sous cette motivation, une technique basée sur la transformation du mode de Laguerre-Gauss par un système astigmatique a été mise au point pour déterminer les deux indices qui le caractérisent. Nous avons montré que cette technique peut aussi être utilisée pour optimiser expérimentalement la fabrication des modes de Laguerre-Gauss d’ordre élevé les plus purs possibles
Laguerre-Gaussian modes of light are one of the solutions to the propagation equation of light in the paraxial approximation in cylindrical coordinates. These modes are characterized by two indices (azimuthal and radial) and present particular properties: ring-shaped structure and a helical phase. These properties have been put to use in several applications going from microscopy to astronomy. This work has been devoted to the study of these modes and their application in the cold atom domain. Initially, the purity of such modes generated by numerical holography was studied, as well as the role played by the purity in their propagation. These modes were then used to obtain a bright source of cold atoms. For more than 20 years, considerable efforts have been made to create sources of cold atoms as bright and compact as possible. A two dimensional magneto-optical trap (2D-MOT) is currently used to obtain a continuous source of cold atoms with high flux of the order of 1010 atomes/s. Nevertheless, the source of cold atoms thereby achieved show a divergence of about 40 mrad which constrains the user to work by output but with a limited optical access or far from the output but at the cost of lower density. An alternative is presented, in which a Laguerre-Gaussian mode of light is used to channel the atoms at the output of a 2D-MOT. The Laguerre-Gaussian mode of light carries out a dipole trapping that confines the atoms in the black center of the mode, which has the advantage of limiting the heating due to absorption/emission of light. Thus, since the Laguerre-Gaussian modes of light keep their ring-shape along their propagation, the atoms are channeled over a distance of several decimeters. We studied the functioning of this system for different orders of the Laguerre-Gaussian mode and at different frequencies, and we showed that this system is efficient and allows to achieve a density gain of a factor 200 compared to a conventional 2D-MOT. A particular case is also presented, in which the frequency of the Laguerre-Gaussian mode of light is chosen to carry out not only the channeling of the atoms, but also their repumping, which leads to an important simplification of the system. Laguerre-Gaussian modes of light are also of great interest in the domain of quantum information and quantum cryptography because they can be used to encode and store information. In order to do that, it is crucial to be able to detect them in an unequivocal way. In this context, we are interested in the determination of these modes. Until now, different detection techniques have measured the azimuthal index, but few of them have been able to measure the radial index. If we are able to measure the radial index, it can be used as a new variable to encode and store information. Under this motivation, a technique based on the transformation of a Laguerre-Gaussian mode of light by an astigmatic system has been extended to determine the two indices characterizing them. We showed that this technique can also be used to experimentally optimize the generation of the purest possible Laguerre-Gaussian modes of high order

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Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG
In this work we present a classification of the Laguerre minimal surfaces with flat curvature lines. We introduce three classes of hypersurfaces that generalize the Laguerre minimal surfaces with the prescribed Gaussian normal application. The first class is associated to biharmonic applications and is related by a Legendre transformation to hypersurfaces that in the isotropic model has harmonic isotropic mean curvature. As an application, we classify the hypersurfaces of rotation and we present examples of these hypersurfaces parameterized by flat curvature lines. We obtain a characterization of the other two classes of hypersurfaces, we study the rotation ones and we present examples.
Neste trabalho apresentamos uma classificação das superfícies mínimas de Laguerre com linhas de curvatura planas. Introduzimos três classes de hipersuperfícies que generalizam as superfícies mínimas de Laguerre com aplicação normal de Gauss prescrita. A primeira classe está associada a aplicações biharmônicas e está relacionada por uma transformação de Legendre a hipersuperfícies que no modelo isotrópico tem curvatura média isotrópica harmônica. Como aplicação, classificamos as hipersuperfícies de rotação e apresentamos exemplos destas hipersuperfícies parametrizadas por linhas de curvatura planas. Obtemos uma caracterização das outras duas classes de hipersuperfícies, estudamos as de rotação e apresentamos exemplos.

Cette thèse porte sur la conception, la réalisation et l'étude expérimentale d'une source laser bifréquence de haute cohérence émettant à 1 µm en vue d'obtenir par photomélange un émetteur THz. Nous nous intéressons plus particulièrement aux lasers à semiconducteur émettant par la surface en cavité externe verticale (VeCSEL), l'objectif étant d'obtenir un fonctionnement laser bifréquence robuste en régime continu, basé sur la coexistence simultanée de deux modes transverses de Laguerre-Gauss. La sélection de seulement deux modes transverses est réalisée grâce à des masques de pertes insérés intracavité dans le plan transverses. Les caractéristiques du laser bifréquence, telles que l'équilibre entre les puissances des deux modes, le caractère monofréquence de chacun des deux modes, l'accordabilité de l'écart de fréquence, la simultanéité de l'émission et la cohérence du battement THz obtenu, sont étudiées. Enfin, la génération THz par photomélange est effectuée grâce au VeCSEL bifréquence et à une photodiode UTC commerciale
This work focuses on the design, realization and experimental study of highly coherent dual-frequency laser sources emitting at 1 µm for THz radiation generation by photomixing. We are particularly interested in vertical-external-cavity surface-emitting laser (VeCSEL), the aim being to obtain a robust dual-frequency continuous wave operation, based on simultaneous coexistence of two Laguerre-Gaussian transverse modes. We design intracavity transverse selective losses mask to select only the two Laguerre-Gaussian modes. The stable and simultaneous dual-frequency operation, the beat-frequency tunability range and the temporal coherence was specifically studied. We demonstrated THz emission by seeding a uni-travelling-carrier photodiode by an optically-pumped dual-frequency vertical-external-cavity surface-emitting

Thesis (PhD)--Stellenbosch University, 2014.
ENGLISH ABSTRACT: High-dimensional quantum entanglement offers an increase in information capacity per photon; a highly desirable property for quantum information processes such as quantum communication, computation and teleportation. As the orbital angular momentum (OAM) modes of light span an infinite-dimensional Hilbert space, they have become frontrunners in achieving entanglement in higher dimensions. In light of this, we investigate the potential of OAM entanglement of photons by controlling the parameters in both the generation and measurement systems. We show the experimental procedures and apparatus involved in generating and measuring entangled photons in two-dimensions. We verify important quantum tests such as the Einstein, Podolsky and Rosen (EPR) paradox using OAM and angle correlations, as well as a violation of a Bell-type inequality. By performing a full state tomography, we characterise our quantum state and show we have a pure, highly entangled quantum state. We demonstrate that this method can be extended to higher dimensions. The experimental techniques used to generate and measure OAM entanglement place an upper bound on the number of accessible OAM modes. As such, we investigate new methods in which to increase the spiral bandwidth of our generated quantum state. We alter the shape of the pump beam in spontaneous parametric down-conversion and demonstrate an effect on both OAM and angle correlations. We also made changes to the measurement scheme by projecting the photon pairs into the Bessel-Gaussian (BG) basis and demonstrate entanglement in this basis. We show that this method allows the measured spiral bandwidth to be optimised by simply varying the continuous radial parameter of the BG modes. We demonstrate that BG modes can be entangled in higher dimensions compared with the commonly used helical modes by calculating and comparing the linear entropy and fidelity for both modes. We also show that quantum entanglement can be accurately simulated using classical light using back-projection, which allows the study of projective measurements and predicts the strength of the coincidence correlations in an entanglement experiment. Finally, we make use of each of the techniques to demonstrate the effect of a perturbation on OAM entanglement measured in the BG basis. We investigate the self-healing property of BG beams and show that the classical property is translated to the quantum regime. By calculating the concurrence, we see that measured entanglement recovers after encountering an obstruction.
AFRIKAANSE OPSOMMING: Hoë-dimensionele kwantumverstrengeldheid bied ’n toename in inligtingskapasiteit per foton. Hierdie is ’n hoogs wenslike eienskap vir kwantum inligting prosesse soos kwantum kommunikasie, berekening en teleportasie. Omdat die orbitale hoekmomentum (OAM) modusse van lig ’n oneindig dimensionele Hilbertruimte beslaan, het dit voorlopers geword in die verkryging van verstrengeling in hoër dimensies. In die lig hiervan, ondersoek ons die potensiaal van OAM verstrengeling van fotone deur die parameters in beide die generering en meting stelsels te beheer. Ons toon die eksperimentele prosedures en apparaat wat betrokke is by die generering en die meet van verstrengelde fotone in twee dimensies. Ons verifieer kwantumtoetse, soos die Einstein, Podolsky en Rosen (EPR) paradoks vir OAM en die hoekkorrelasies, sowel as ’n skending van ’n Bell-tipe ongelykheid. Deur middel van ’n volledige toestand tomografie, karakteriseer ons die kwantum toestand en wys ons dat dit ’n suiwer, hoogs verstrengel kwantum toestand is. Ons toon ook dat hierdie metode uitgebrei kan word na hoër dimensies. Die eksperimentele tegnieke wat tydens die generasie en meet van OAM verstrengeling gebruik is, plaas ’n bogrens op die aantal toeganklik OAM modusse. Dus ondersoek ons nuwe metodes om die spiraal bandwydte van ons gegenereerde kwantum toestand te verhoog. Ons verander die vorm van die pomp bundel in spontane parametriese af-omskakeling en demonstreer die uitwerking daarvan op beide OAM en die hoekkorrelasies. Ons het ook veranderinge aan die meting skema gemaak deur die foton pare op die Bessel-Gauss (BG) basis te projekteer. Ons wys dat hierdie metode die gemeetde spiraal bandwydte kan optimeer deur eenvoudig die kontinue radiale parameter van die BG modes te verander. Ons demonstreer dat BG modusse verstrengel kan word in hoër dimensies as die heliese modusse, wat algemeen gebruik word, deur berekeninge te maak en te vergelyk met lineêre entropie en vir beide modusse. Ons wys ook dat kwantumverstrengling akkuraat nageboots kan word, met behulp van die klassieke lig terug-projeksie, wat die studie van projeksie metings toelaat en voorspel die krag van die saamval korrelasies in ’n verstrengeling eksperiment. Ten slotte, gebruik ons elk van die tegnieke om die effek van ’n storing op OAM verstrengling wat in die BG basis gemeet is, te demonstreer. Ons ondersoek die self-genesingseienskap van BG bundels en wys dat die klassieke eienskap vertaal na die kwantum-gebied. Deur die berekening van die konkurrensie (concurrence), sien ons dat die gemeetde verstrengeling herstel word nadat ’n obstruksie ondervind is.

La génération d’harmoniques d’ordre élevé est un processus d’interaction lumière-matière hautement non-linéaire permettant la synthèse d’impulsions sub-femtosecondes, dites attosecondes (1 as = 10⁻¹⁸ s). Mes travaux de thèse portent sur l’étude du transfert de moment angulaire lors de ce processus, afin de contrôler les caractéristiques spatiales et de polarisation du rayonnement émis dans l’extrême ultraviolet. Comme pour la matière, le moment angulaire de la lumière peut être séparé en une composante de spin, associée à l’état de polarisation du faisceau, et une composante orbitale, reliée à la forme du front d’onde. La maitrise complète du moment angulaire des harmoniques nécessite de recourir à des schémas de génération à deux faisceaux non-colinéaires, créant un réseau de diffraction dans le milieu générateur. Nous avons montré que, bien que les règles de transfert obéissent à des lois de conservation du moment angulaire, la description fine du phénomène requiert une analyse précise du champ laser dans le milieu de génération. Ces travaux ouvrent des perspectives de mise en forme avancée des impulsions attosecondes
High-order harmonic generation is a highly nonlinear laser-matter interaction process which allows the synthesis of sub-femtosecond pulses, also called attosecond (1 as = 10⁻¹⁸ s) pulses. My PhD is centered around the study of angular momentum transfer during this process, in order to control spatial and polarization features of the radiation which is emitted in the extreme ultraviolet. As for matter, the angular momentum of light can be divided into a spin component, associated with the beam’s polarization, and an orbital component, related to the shape of the wavefront. The control of high harmonics’ angular momentum requires generating schemes involving two crossing beams, thus creating a diffraction grating in the generating medium.We have shown that, although the transfer rules obey conservation laws of the angular momentum, the fine description of the phenomenon requires an accurate analysis of the laser field in the generation medium. This work opens the road for advanced shaping of attosecond pulses

Dans ce travail nous avons résolu deux problèmes principaux de la mise en forme topologique de faisceau paraxial pour les composants plans : la modalité et le polychromatisme.Nous les résolvons en introduisant de nouveaux concepts d’éléments optiques à interaction spin orbite,à savoir la “q-plate modale” et la “q-plate Bragg-Berry”. D’un côté, la q-plate modale convertit un faisceau gaussien incident en un faisceau de Laguerre-Gauss pour un indice radial et un indice d’azimut donnés, ce qui par conséquent dépasse les capacités des q-plates conventionnelles qui ne modifient que le degré de liberté azimutal, c.à.d. le moment orbital angulaire de la lumière. À des fins expérimentales, deux approches ont été développées : une basée sur des lames de verres nanostructurées artificiellement, l’autre sur des défauts topologiques de cristaux liquides auto-organisés naturellement. D’un autre côté, la q-plate Bragg-Berry consiste en une fine couche inhomogène de cristaux liquides chiraux (cholestériques) devant un miroir, ce qui fournit une mise en forme de faisceau spin-orbite pleinement efficace sur une large bande spectrale du faisceau incident, contrairement au q-plates conventionnelles qui ne sont fabriqués que pour une longueur d’onde donnée. Par ailleurs, nous obtenons une mise en forme de faisceau spin-orbite ultra-large bande en induisant une modulation de la structure supramoléculaire torsadée des cristaux liquides cholestériques selon la direction de propagation de la lumière. Nous montrons également que la présence du miroir derrière permet un puissant contrôle spatio-temporel des propriétés vectorielles de la polarisation du champ lumineux générées par la q-plate Bragg-Berry
It is well-known that paraxial coherent electromagnetic fields can be completelycharacterized in terms of their radial and azimuthal spatial degrees of freedom in the transverse planethat add to the polarization degree of freedom and wavelength. In this work we address two mainissues of paraxial beam shaping that are the modality and the polychromaticity in the context of flatopticsthat we address by introducing novel concepts of spin-orbit optical elements. Namely, the‘modal q-plate’ and the ‘Bragg-Berry q-plate’. On the one hand, modal q-plate converts an incidentfundamental Gaussian beam into a Laguerre-Gaussian beam of given radial and azimuthal indices,hence going beyond the capabilities of conventional q-plates that only control the azimuthal degreeof freedom, i.e. the orbital angular momentum content of light. Towards experimental realization ofmodal q-plates, two approaches are developed: one based on artificially nanostructured glasses andanother based on naturally self-organized liquid crystal topological defects. On the other hand,Bragg-Berry q-plate consist of mirror-backed inhomogeneous thin film of chiral liquid crystal(cholesteric) that provides fully efficient spin-orbit beam shaping over broad spectral range of theincident beam, in contrast to the conventional q-plates that are designed for single wavelength.Furthermore, ultra-broadband spin-orbit beam shaping is achieved by inducing an extra modulationof the supramolecular twisted structure of the cholesteric liquid crystal along the propagationdirection. We also show that the presence of a back-mirror allows a powerful spatio-temporal controlof the polarization vectorial properties of the light fields generated by Bragg-Berry q-plate

Les ondes gravitationnelles sont des perturbations de l'espace-temps qui pourraient être détectées par un interféromètre de Michelson avec cavités Fabry-Perot. Plusieurs interféromètres sont à présent en opération: LIGO, Virgo, GEO. Ces instruments ont atteint leur sensibilité nominale et ont accompli plusieurs acquisitions de données scientifiques. Aucune détection n'a été reportée. Advanced Virgo, Advanced LIGO et LCGT sont les projets d'amélioration de sensibilité des détecteurs actuels d'un ordre de grandeur. Ces instruments, dont la construction est en cours, permettront la première détection directe des ondes gravitationnelles. Une ultérieure troisième génération d'instrument offrant une encore plus grande sensibilité est à l'étude. La sensibilité des détecteurs futurs sera limitée par le bruit thermique des miroirs. Cette thèse porte sur deux thèmes liés à la réduction de ce bruit. Le premier concerne la conception optique des cavités stable de Advanced Virgo. Leurs propriétés sont présentées, les arguments en faveur de leur utilisation sont discutés. Une procédure est établie pour achever leur conception optique. Plusieurs configurations sont examinées, conduisant à la sélection de l'une d'entre elles dont on discute les performances optiques. Le deuxième thème concerne l'utilisation des modes de Laguerre-Gauss (LG). On présente les résultats d'une expérience testant la génération d'un mode LG33 avec une optique diffractive et une cavité Fabry-Perot. Ce mode est utilisé dans un interféromètre de Michelson pour démontrer la faisabilité de mesures interférométriques avec des faisceaux non-Gaussiens. L'utilisation des modes LG dans les détecteurs futurs est discutée.

Thesis (M.S.)--University of Wisconsin--Madison, 1997.
Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leav 54).

碩士
國立臺灣師範大學
物理學系
105
It has been more than fifty years that laser was invented, because of the properties of laser are not common with the general light. By the rapid development of technology not only the laser has a great applications in many other fields but also more thorough and wide we know about laser than before. Laser has many different kinds of properties like coherent, polarization, distribution of intensity and concentrated energy. We focus on the laser modes, superposed modes and both the distribution of polarization in this topic. Using the method of numerical simulation to create the grating what we plan to study. Entering the grating into spatial light modulator and assisted by interferometer and other optical instruments to build the Gaussian laser mode which under the cylindrical coordinate we called Laguerre-Gaussian mode. Also we use the same method to build the superposed Laguerre-Gaussian mode, because of the complex composition and symmetry we called it flower type mode. In addition we employ quarter wave plate to adjust the distritubion of polarization to generate the spatilly inhomogeneous beam, not common with the general spatilly homogeneous beam. Finally we analyze the spatilly inhomogeneous beam and distribution of intensity by high order Poincaré sphere.

碩士
國立臺灣師範大學
物理學系
102
The laser cavity system mentioned in the thesis is different from the traditional solid state laser. We can manipulate the pump offset to generate a variety of the laser beams with complex spatial structures. We investigate the geometric beams generated from a c-cut Nd:YVO4 laser. The Nd:YVO4 acts as a birefringence crystal. In this work, we focused on six spots of the circular geometric mode. In the far field, the structured laser beam is left-handed circularly polarized and right-handed circularly polarized at the same time. This particular property has many applications, like cold atom system. The phase retardation (δ) of a stable geometric mode can be derived by the birefringence theory. According to the birefringence property of Nd:YVO4, the effective refractive index neff can be calculated by the coefficient ne and no. It leads to get the refraction angle θ of the geometric mode. In the numerical simulation, we fit twelve orders of six spots of circular geometric modes and get the patterns. In the experiment we use the quarter-wave plate (QWP) and the linear plate(LP) to detect the laser polarization. Experimental results reveal that a geometric mode possesses circularly polarized states in opposite directions at the same time and the superposition of orthogonally polarized geometric beams can be generated systematically by controlling the off-axis magnitude. The numerical results have a good agreement with the experimental results. The research may make some contributions for the application of structured beams.

碩士
逢甲大學
光電學系
103
The purpose of this thesis is to construct a selective generation of radically (RP) and azimuthally polarized (AP) Laguerre-Gaussian beam by using a diode-end-pumping Nd:YAG laser and a spot-defect cavity. The spot defect can suppress the generation of Hermite-Gaussian modes. The thermal induced bifocusing of Nd:YAG can help to select RP and AP beams at different pump power. Two Cr coated spot-defects, 50 and 100 μm in diameter, were used. A flat/flat cavity resonated at 1.06 μm was constructed and the cavity length was kept around 2 cm. At 5.64 W diode pump power, an unpolarized LG beam with 1.5 W output power was obtained. Adopting 100 μm spot-defect, the degree of polarization (DOP) could achieve 89.7% for RP beam, and an output power of 0.2 W was obtained at 1.05 W diode pump power. Adopting 50 μm spot-defect, the DOP could achieve 77.2% for AP beam, and an output power of 1.1 W was obtained at 5.22 W diode pump power.

碩士
國立臺灣師範大學
物理學系
103
In 1993 M. W. Beijersbergen and L. Allen found when Hermite-Gaussian modes pass through a pair of cylindrical lens which can change the phase of light, Laguerre-Gaussian modes would be generated. We combined hemi-spherical cavity and a pair of cylindrical lens to set up a hemi-cylindrical cavity. In our experiment, we verified that astigmatic Hermite-Gaussian modes can be generated from hemi-cylindrical cavity, and can convert to Laguerre-Gaussian modes by using an extra-cavity cylindrical lens. In degenerate hemi–cylindrical cavity, by controlling the pump offset and the pump size, we observed the unique patterns experimentally. From degenerate cavity theory, we understand that special patterns are superposed by a set of high order Laguerre-Gaussian modes with the same degenerate frequency. Because these unique pattern look like flowers in nature, so we call them flower type modes. When we use the a-cut Nd:YVO4, the directions of polarization of experimental results are parallel to the c-axis of the crystal. In recent research, the polarized property of c-cut Nd:YVO4 has attracted much attention in laser field. Therefore we change the gain medium from a-cut to c-cut one, and observed the polarization of patterns. Finally, in simulation analysis we use the Huygens integral and ABCD law to clearly demonstrate the transformation of modes along the propagation directions after they passing through the extra-cavity cylindrical lens.

This thesis will outline studies performed on the fluorescence dynamics of phenyl-benzo- [c]-tetrazolo-cinnolium chloride (PTC) in alcoholic solutions with varying viscosity using time-resolved fluoro-spectroscopic methods. Furthermore, the properties of femtosecond Laguerre-Gaussian (LG) laser pulses will be investigated with respect to their temporal and spatial features and an approach will be developed to measure and control the spatial intensity distribution on the time scale of the pulse. Tetrazolium salts are widely used in biological assays for their low oxidation and reduction thresholds and spectroscopic properties. However, a neglected feature in these applications is the advantage that detection of emitted light has over the determination of the absorbance. To corroborate this, PTC as one of the few known fluorescent tetrazolium salts was investigated with regard to its luminescent features. Steady-state spectroscopy revealed how PTC can be formed by a photoreaction from 2,3,5-triphenyl-tetrazolium chloride (TTC) and how the fluorescence quantum yield behaved in alcoholic solvents with different viscosity. In the same array of solvents time correlated single photon counting (TCSPC) measurements were performed and the fluorescence decay was investigated. Global analysis of the results revealed different dynamics in the different solvents, but although the main emission constant did change with the solvent, taking the fluorescence quantum yield into consideration resulted in an independence of the radiative rate from the solvent. The non-radiative rate, however, was highly solvent dependent and responsible for the observed solvent-related changes in the fluorescence dynamics. Further studies with the increased time resolution of femtosecond fluorescence upconversion revealed an independence of the main emission constant from the excitation energy, however the dynamics of the cooling processes prior to emission were prolonged for higher excitation energy. This led to a conceivable photoreaction scheme with one emissive state with a competing non-radiative relaxation channel, that may involve an intermediate state. LG laser beams and their properties have seen a lot of scientific attention over the past two decades. Also in the context of new techniques pushing the limit of technology further to explore new phenomena, it is essential to understand the features of this beam class and check the consistency of the findings with theoretical knowledge. The mode conversion of a Hermite-Gaussian (HG) mode into a LG mode with the help of a spiral phase plate (SPP) was investigated with respect to its space-time characteristics. It was found that femtosecond LG and HG pulses of a given temporal duration share the same spectrum and can be characterized using the same well-established methods. The mode conversion proved to only produce the desired LG mode with its characteristic orbital angular momentum (OAM), that is conserved after frequency doubling the pulse. Furthermore, it was demonstrated that temporal shaping of the HG pulse does not alter the result of its mode-conversion, as three completely different temporal pulse shapes produced the same LG mode. Further attention was given to the sum frequency generation of fs LG beams and dynamics of the interference of a HG and a LG pulse. It was found that if both are chirped with inverse signs the spatial intensity distribution does rotate around the beam axis on the time scale of the pulse. A strategy was found that would enable a measurement of these dynamics by upconversion of the interference with a third gate pulse. The results of which are discussed theoretically and an approach of an experimental realization had been made. The simulated findings had only been reproduced to a limited extend due to experimental limitations, especially the interferometric stability of the setup
Die vorliegende Arbeit wird eine Übersicht über die durchgeführten Studien, die die Fluoreszenzdynamiken von Phenyl-Beno-[c]-Tetrazolo-Cinnolinum Chlorid (PTC) in alkoholischen Lösungsmitteln verschiedener Viskosität mit Hilfe von zeitaufgelöster Fluoreszenzspektroskopie untersuchen, liefern. Des weiteren werden die Eigenschaften von Laserpulsen mit Laguerre-Gauss (LG) strahlprofilen in Hinblick auf ihre räumlichen und zeitlichen Charakteristika beleuchtet und ein Ansatz entwickelt, die räumliche Intensitätsverteilung zu messen und auf der Zeitskala der Pulse zu kontrollieren. Tetrazoliumsalze sind aufgrund ihrer niedrigen Oxidations- und Reduktionspotentiale und ihrere spektroskopischen Eigenschaften weit verbreitet in biologischen Assays. Allerdings wird in diesen Anwendungen der Vorteil, den Messungen der Lichtesmission gegenüber der Lichtabsorption haben, vernachlässigt. Um das zu ergründen wurde PTC, als eines der wenigen bekannten Tetrazoliumsalze welches fluoresziert, im Hinblick auf seine lichtemittierenden Eigenschaften untersucht. Statische Spektroskopie wies nach, wie PTC aus einer Photoreaktion aus 2,3,5-Triphenyl-Tetrazoliumchlorid (TTC) erzeugt werden konnte und wie sich die Fluoreszenzquantenausbeute in alkoholischen Lösungsmitteln mit unterschiedlicher Viskosität verhält. In den gleichen Lösungsmitteln wurden zeitkorreliertes Einzelphotonen Zählen (TCSPC) durchgeführt und der Fluoreszenzzerfall untersucht. Die globale Analyse der Ergebnisse hat gezeigt, das die Dynamiken sich in den verschiedenen Lösungsmitteln unterscheiden, die Konstante, welche die Hauptemission beschreibt, sich in den unterschiedlichen Lösungsmitteln zwar verändert, aber wenn die Fluoreszenzquantenausbeute auch berücksichtigt wird, zu Raten der Lichtemission führte, die unabhängig vom Lösungsmittel sind. Die nichststrahlende Rate allerdings hängt stark vom Lösungsmittel ab und ist auch verantwortlich für die unterschiedlichen Dynamiken in den verschiedenen Lösungen. Weitere Studien, die mit der höheren zeitlichen Auflösung der Fluoreszenzaufkonversionsmethode durchgeführt wurden, ergaben, dass die Hauptfluoreszenz unabhängig von der Anregungsenergie ist, aber die Relaxationsprozesse, welche vor der Lichtaussendung stattfinden, mit höherer Anregungsenergie länger dauern. Die Ergebnisse mündeten in ein denkbares Photoreaktionsschema, das durch einen strahlenden Zustand gekennzeichnet ist und einen konkurrierenden nichtstrahlenden Zerfallspfad besitzt, welcher einen kurzlebigen Zwischenzustand besitzen könnte. Laguerre-Gauss Laserstrahlen und ihre Eigensachften haben in den letzten zwei Jahrzehnten viel wissenschaftliche Aufmerksamkeit erhalten. Auch im Hinblick auf neue Methoden, die die technologische Machbarkeitsgrenze verschieben, um neue Phänomene zu erforschen, ist es notwendig, das Verständnis über diese Strahlklasse zu erweitern und die Konsistenz der Resultate mit dem theoretischen Wissen abzugleichen und in Einklang zu bringen. Die Konversion einer Hermite-Gauss (HG) Mode in eine LG Mode, mit Hilfe einer spiralen Phasenplatte (SPP), wurde im Hinblick auf ihre räumlich-zeitlichen Charakteristika untersucht. Es wurde herausgefunden, dass Femtosekunden HG und LG Pulse einer bestimmten zeitlichen Dauer das gleiche Spektrum besitzen und durch die gleichen etablierten Methoden charakterisiert werden können. Es stellte sich heraus, dass die Modenkonversion nur die gewünschte LG Mode mit ihrem charakeristischen orbitalen Drehimpuls (OAM), der bei Frequenzverdopplung erhalten bleibt, erzeugt. Außerdem wurde demonstriert, dass ein zeitlich geformter Femtosekunden HG Puls nicht das Resultat der Modenkonversion beeinflusst, da zeitlich völlig verschieden strukturierte Pulse die gleiche LG Mode erzeugen. Des weiteren wurde die Summenfrequenz von fs LG Strahlen und die Dynamik der Interferenz eines HG und eines LG Pulses beleuchtet. Es wurde gefunden, dass wenn beide entgegengesetzt gechirpt sind, die räumliche Intensitätsverteilung auf der Zeitskala der Pulse um die Strahlachse rotiert. Theoretisch wurde ein Vorgehen entwickelt, das eine Messung dieser Dynamik, durch die Aufkonversion der Interferenz mit einem dritten Gate-Puls, ermöglicht. Die Ergebnisse dieser Methode wurden auf theoretischer Ebende diskutiert und ein Versuch einer experimentellen Realisierung wurde unternommen. Allerdings konnten die gemessenen Resultate, aufgrund experimenteller Limitierungen insbesondere der interferometrischen Stabilität, die theoretischen Erwartungen nur bedingt demonstrieren

The subject of this thesis is the study of coherent interaction of light with matter (atoms) to improve the precision measurements and techniques. Special attention is drawn to get the narrow subnatural electromagnetically induced transmission (EIT), electromagnetically induced absorption (EIA) and nonlinear magneto-optic rotation (NMOR) caused by alkali atoms contained in a vapor cell. Subnatural polarization rotation introduces by a strong circularly polarized light in the absence of any external magnetic field was also studied. A detailed theoretical treatment, given in this dissertation, allows to associate each of the features of the spectra with a special physical mechanism. Many quantum phenomena related to interferences, coherences, optical pumping etc. experiments are studied using home-built diode lasers. This thesis also describes laser cooling and trapping of rubidium atoms using two techniques. Deflection of cold atoms horizontally from MOT using pushing beams are discussed in close consideration for the improvements in the precision measurements. This thesis is organized as follows. In Chapter 1, an introduction to the importance of sub-natural narrow resonance and simplified technique in the precision measurement will be discussed. In Chapter 2, an introduction to EIT, EIA and NMOR resonance are discussed. This chapter will provide a basic theoretical background of atom-field interactions, especially for Λ-type and N -type systems and its steady state solution using density matrix analysis and experimental tools. The most important notion of laser cooling of atoms, ions or molecule i.e., exchange of momentum between light and atoms combining with the Doppler effect will be discussed. In Chapter 3, the observation of subnatural EIT and subnatural EIA in closed and open degenerate two-level system using room temperature vapor cell filled with Rb will be presented. Physical mechanisms that contribute to EIT and EIA, and the contrast of our results from the coherent population trapping (CPT)–type resonances are discussed in detail in appendix A.2 according to our experimental results. In Chapter 4, the narrowing of subnatural EIT and subnatural EIA linewidth in closed and open systems again in degenerate two level transition, using the “Laguerre-Gaussian” control beam instead of generally studied Gaussian beam, will be discussed in detail. In Chapter 5, the conversion between subnatural EIT to subnatural EIA in a degenerate Λ system will be discussed. The physical mechanism created by the introduction of a coherent counter propagating control laser to the co-propagating probe and the control laser are studied. The effect of polarization and axial velocity Doppler averaging will also be studied. In Chapter 6, we will discuss the sensitive technique for precise measurement of small magnetic fields using the NMOR, by chopping the resonant laser beam. We will study the sensitivity and the potential application of this technique in the measurement of an atomic electric-dipole moment. In Chapter 7, we will be studying about the induced optical rotation by a circularly polarized control laser on the linearly polarized probe laser. The effect of the intensity of the control laser beam on the higher order optical rotation will also be studied. In Chapter 8, we will be studying about the cooling and trapping of 87Rb in magneto-optic trap. We will be studying two techniques of trapping of atoms in MOT. The cold cloud of atoms from the MOT are deflected horizontally by using different configuration of pushing beam are studied. A brief summary and outlook of my thesis work will be discussed at Chapter 9.