Academic literature on the topic 'Bessel–Gauss beams'

The generation and propagation of harmonics in an atomic gas are described for the case of an incident Bessel-Gauss beam. Theoretical expressions are derived for the far-field amplitude of the harmonic field by solving the propagation equation using an elaborate integral formalism. We establish simple rules which determine the optimum Bessel-Gauss beam with respect to phase-matching as a function of the medium properties, such as the dispersion and the gas density. Target depletion due to photoionization and refractive index variations originating from both free electrons and dressed linear atomic susceptibilities are taken into account. The intensity-dependent complex atomic dipole moment is calculated using nonpertur- bative methods. Numerical propagation calculations for hydrogen, xenon and argon are presented. For hydrogen we consider the third harmonic of a 355-nm, 15-ps pump beam up to 3 X 10(^13) W/cm(^2) intensity, similarly for xenon, but at lower intensities. For argon we consider the 17th and 19th harmonic of a 810-nm, 30-fs pump beam around 10(^14) W/cm(^2) intensity. We compare conversion efficiencies and both spatial and temporal far-field profiles for an optimized Bessel-Gauss beam with respect to a Gaussian beam of same power and/or peak focal intensity. For the case of hydrogen, we investigate the effect of an ac-Stark-shift induced atomic resonance. We find all results in good agreement with our theoretical predictions. We conclude from our studies that Bessel-Gauss beams can perform better in terms of conversion efficiency than a comparable Gaussian beam. We find this to originate essentially from the more flexible phase-matching conditions for Bessel-Gauss beams. Bessel-Gauss beams also allow for spatial separation of the harmonic and the incident field in the far-field region, owing to the conical shape of their spatial far-field profile. Both features make Bessel-Gauss beams an attractive alternative to Gaussian beams in a limited but substantial number of experimental conditions.

In this work, we develop a new technique to determine the topological charge of a light beam with orbital angular momentum. Our technique is based on the diffraction by a triangular aperture. By performing numerical simulations, for Laguerre-Gaus beams and Bessel beams with different values of l, we found tha the diffraction pattern contains the signature of the topological charge of the beam. Our theoretical predictions for a triangular aperture were experimentally verifiel, demonstrating the the diffraction pattern reveals the topological charge of the light beam.
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Neste trabalho, desenvolvemos uma nova técnica para determinar a carga topológica de um feixe de luz com momento angular orbital. Nossa técnica é baseada na difração por uma abertura triangular. Através da realização de simulações numérica, para feixes Laguerre-Gauss e feixes Bessel com diferentes valores de l, descobrimos que o padrão de difração contém a assinatura da carga topológica do feixe. Nossas previsões teóricas para uma abertura triangular foram verificadas experimentalmente, demonstrando que o padrão de difração revela a carga topológica do feixe de luz. Esta técnica torna possível a determinação do módulo e do sinal da carga topológica de um feixe de luz de uma maneira simples e direta.

Thesis (PhD (Physics))--University of Stellenbosch, 2010.
ENGLISH ABSTRACT: There are many applications where a Gaussian laser beam is not ideal, for example, in areas such as medicine, data storage, science, manufacturing and so on, and yet in the vast majority of laser systems this is the fundamental output mode. Clearly this is a limitation, and is often overcome by adapting the application in mind to the available beam. A more desirable approach would be to create a laser beam as the output that is tailored for the application in mind – so called intra-cavity laser beam shaping. The main goal of intra-cavity beam shaping is the designing of laser cavities so that one can produce beams directly as the output of the cavity with the required phase and intensity distribution. Shaping the beam inside the cavity is more desirable than reshaping outside the cavity due to the introduction of additional external losses and adjustment problems. More elements are required outside the cavity which leads to additional costs and larger physical systems. In this thesis we present new methods for phase and amplitude intra– cavity beam shaping. To illustrate the methods we give both an analytical and numerical analysis of different resonator systems which are able to produce customised phase and intensity distributions. In the introduction of this thesis, a detailed overview of the key concepts of optical resonators is presented. In Chapter 2 we consider the well–known integral iteration algorithm for intra–cavity field simulation, namely the Fox–Li algorithm and a new method (matrix method), which is based on the Fox–Li algorithm and can decrease the computation time of both the Fox–Li algorithm and any integral iteration algorithms. The method can be used for any class of integral iteration algorithms which has the same calculation integrals, with changing integrants. The given method appreciably decreases the computation time of these algorithms and approaches that of a single iteration. In Chapter 3 a new approach to modeling the spatial intensity profile from Porro prism resonators is proposed based on rotating loss screens to mimic the apex losses of the prisms. A numerical model based on this approach is presented which correctly predicts the output transverse field distribution found experimentally from such resonators. In Chapter 4 we present a combination of both amplitude and phase shaping inside a cavity, namely the deployment of a suitable amplitude filter at the Fourier plane of a conventional resonator configuration with only spherical curvature optical elements, for the generation of Bessel–Gauss beams as the output. In Chapter 5 we present the analytical and numerical analyses of two new resonator systems for generating flat–top–like beams. Both approaches lead to closed form expressions for the required cavity optics, but differ substantially in the design technique, with the first based on reverse propagation of a flattened Gaussian beam, and the second a metamorphosis of a Gaussian into a flat–top beam. We show that both have good convergence properties, and result in the desired stable mode. In Chapter 6 we outline a resonator design that allows for the selection of a Gaussian mode by diffractive optical elements. This is made possible by the metamorphosis of a Gaussian beam into a flat–top beam during propagation from one end of the resonator to the other. By placing the gain medium at the flat–top beam end, it is possible to extract high energy in a low–loss cavity.
AFRIKAANSE OPSOMMING: Daar is verskeie toepassings waar ʼn Gaussiese laser bundel nie ideaal is nie, in gebiede soos mediese veld, stoor van data, vervaardiging en so meer, en tog word die meeste laser sisteme in die fundamentele mode bedryf. Dit is duidelik ’n beperking, en word meestal oorkom deur aanpassing van die toepassing tot die beskikbare bundel. ’n Beter benadering sou wees om ʼn laser bundel te maak wat afgestem is op die toepassing - sogenaamde intra-resonator bundel vorming. Die hoofdoel van intra-resonator bundel vorming is om resonators te ontwerp wat direk as uitset kan lewer wat die gewenste fase en intensiteits-distribusie vertoon. Vorming van die bundel in die resonator is voordeliger omdat die vorming buite die resonator tot addisionele verliese asook verstellings probleme bydra. Meer elemente word benodig buite die resonator wat bydra tot hoër koste en groter sisteme. In hierdie tesis word nuwe fase en amplitude intra-resonator bundelvormings metodes voorgestel. Om hierdie metode te demonstreer word analitiese en numeriese analises vir verskillende resonator sisteme wat aangepaste fase en intensiteit distribusies produseer, bespreek. In die inleiding van die tesis word ʼn detailleer oorsig oor die sleutel konsepte van optiese resonators voorgelê. In hoofstuk 2 word die bekende integraal iterasie algoritme vir intraresonator veld simulasie, naamlik die Fox-Li algoritme, en ʼn nuwe metode (matriks metode), wat gebaseer is op die Fox-Li algoritme, en die berekeningstyd van beide die Fox-Li algoritme en enige ander integraal iterasie algoritme verminder. Die metode kan gebruik word om enige klas van integraal iterasie algoritmes wat dieselfde berekenings integrale het, met veranderde integrante (waar die integrand die veld van die lig golf is in die geval van die Fox-Li algoritme, IFTA, en die skerm metode. Die voorgestelde metode verminder die berekeningstyd aansienlik, en is benaderd die van ʼn enkel iterasie berekening. In hoofstuk 3 word ʼn nuwe benadering om die modellering van die ruimtelike intensiteitsprofiel van Porro prisma resonators, gebaseer op roterende verliese skerms om die apeks-verliese van die prismas te benader, voorgestel. ʼn Numeriese model gebaseer op hierdie benadering wat die uitset van die transversale veld distribusie in eksperimentele resonators korrek voorspel, word voorgestel. In hoofstuk 4 word ʼn tegniek vir die generering van Bessel-Gauss bundels deur die gebruik van ʼn kombinasie van amplitude en fase vorming in die resonator en ʼn geskikte amplitude filter in die Fourier vlak van ʼn konvensionele resonator konfigurasie met optiese elemente wat slegs sferiese krommings het, voorgestel. In hoofstuk 5 word die analitiese en numeriese analises van twee nuwe resonator sisteme vir die generering van sogenaamde “flat–top” bundels voorgestel. Beide benaderings lei na ʼn geslote vorm uitdrukking vir die resonator optika wat benodig word, maar verskil noemenswaardig in die ontwerptegniek. Die eerste is baseer op die terug voortplanting van plat Gaussiese bundel, en die tweede op metamorfose van Gaussiese “flat-top” bundel. Ons toon aan dat beide tegnieke goeie konvergensie het, en in die gevraagde stabiele modus lewer. In hoofstuk 6 skets ons die resonator ontwerp wat die selektering van ʼn Gaussiese modus deur diffraktiewe optiese element moontlik maak. Dit word moontlik deur die metamorfose van ’n Gaussiese bundel na ʼn “flat-top” gedurende die voortplanting van die een kant van die resonator na die ander. Deur die wins medium aan die “flat–top” kant van die bundel te plaas word dit moontlik om hoë energie te onttrek in ʼn lae verlies resonator.

Cette thèse présente les contributions de l'auteur au domaine des ondes non-diffractives. Essentiellement, les ondes non diffractives sont des faisceaux électromagnétiques qui rayonnent une énergie localisée avec une variété d'applications pratiques potentielles. Le travail présenté dans cette thèse peut être divisé en deux parties. Dans la première partie, un nouveau concept de synthèse de lanceurs de faisceaux de Bessel/ondes X à profil spline a été proposé. Tout d'abord, un outil basé sur l'adaptation de mode est présenté. L'outil est capable d'évaluer les paramètres S, les diagrammes de rayonnement en champ proche et lointain de structures métalliques à symétrie azimutale. Ensuite, des lanceurs métalliques à faisceau de Bessel/ à impulsion sont synthétisés à l'aide de cet outil ad hoc. Le concept a été validé expérimentalement en fabriquant et en mesurant un lanceur pour fonctionner dans une gamme de fréquences de 75 à 105 GHz. Le lanceur est la première démonstration d'un lanceur d'ondes X à de telles fréquences. Dans la deuxième partie, nous avons étudié l'utilisation d'ondes non diffractives pour le transfert d'énergie sans fil. Tout d'abord, l'utilisation de faisceaux de Bessel-Gauss pour le WPT est étudiée. Les performances supérieures des faisceaux de Bessel-Gauss par rapport aux faisceaux de Bessel sont démontrées. Un lanceur Bessel-Gauss a été conçu pour valider cette affirmation. Le coefficient de transfert de puissance du lanceur dépasse 50 % pour les distances dépassant sa portée de non diffraction
This thesis present the author’s contributions to the field of non-diffractive waves. Essentially, non-diffractive waves are electromagnetic beams that radiate localized energy with a variety of potential practical applications. The work presented in this thesis can be divided into two parts. In the first part, a novel concept of synthesizing metallic spline profiled Bessel beam/X-wave launchers has been proposed. First, an ad-hoc tool based on mode matching is presented. The tool is capable of evaluating the S parameters, near-, and far-field radiation patterns of metallic structures with azimuthal symmetry. Then, metallic Bessel beam/X-wave launchers are synthesized using the ad-hoc tool. The concept has been experimentally validated by manufacturing and measuring an X-wave launcher operating in a 75-105 GHz frequency range. The fabricated launcher is the first experimental demonstration of an X-wave launcher at such frequencies. In the second part, we have investigated the use of non-diffractive waves for wireless power transfer. First, the use of Bessel-Gauss beams for WPT is investigated. The superior performance of Bessel-Gauss beams compared to Bessel beams is demonstrated. A Bessel-Gauss launcher has been designed for validating this claim. The power transfer coefficient of the launcher exceeds 50% for distances exceeding its non-diffractive range