Modeling of electromagnetic wave propagation in terms of Gaussian beams (GBs) has been considered in recent years. The incident radiation is expanded in terms of GBs by means of the point matching method. The simultaneous equations can be solved directly to produce excitation coefficients that generate the approximate pattern of a known antenna. Two different types of antenna patterns have been approximated in terms of GBs: a truncated antenna pattern and a hyperbolic antenna pattern. The influence of the Gaussian beam parameters on the approximation process is clarified.

Although the Maxwell equations govern the propagation of EM waves at all frequencies, the methods required to generate, direct, analyse and detect radiation differ from band to band. This thesis is concerned with the development and demonstration of 'Quasi-optical' techniques for millimetre wavelengths, which involve the propagation of Gaussian profiled beams a few wavelengths across, and the realization of a general circuit approach to mm-wave measurement. Gaussian beam-mode analysis, which is used in later chapters to understand propagation of quasi-optical beams, is reviewed in chapter 1. Chapter 2 outlines the design, manufacture and testing of corrugated feed horns which generate fundamental Gaussian beam-modes. The design and manufacture of lenses which control the spreading of the beams and directional couplers which provide desirable signal processing functions in quasi-optical circuits is discussed in chapter 3. Chapter 4 traces the development of a Faraday isolator which operates in free-space and can suppress unwanted reflections in quasi-optical circuits. Chapter 5 discusses a reusable circuit board upon which systems can be easily and quickly constructed. A null reflectometer built using quasi-optical components is outlined in chapter 6 and reflection measurements from lenses and horns presented. Chapter 7 describes a corrugated feed horn/lens antenna used in a balloon-borne nw-wave cosmic background experiment. Finally, Chapter 8 demonstrates the use of quasi-optical components in a 115 GHz receiver circuit.

The topic of antenna pattern synthesis, in the context of beam shaping, is considered. One approach to this problem is to use the method of point matching. This method can be used to approximate antenna patterns with a set of uniformly spaced sources with suitable directivities. One specifies a desired antenna pattern and approximates it with a combination of beams. This approach results in a linear system of equations that can be solved for a set of beam coefficients. With suitable shifts between the matching points and between the source points, a good agreement between the assumed and the reproduced antenna patterns can be obtained along an observation line. This antenna modelling could be used in the program NERO to compute the field at the receiver antenna for a realistic 2D communication link. It is verified that the final result is not affected by the details of the antenna modelling.

Please read the abstract on page i of this thesis / Thesis (PhD)--University of Pretoria, 2009. / Electrical, Electronic and Computer Engineering / unrestricted

Propagation of a Gaussian beam in a layered periodic structure is studied analytically, numerically, and experimentally. It is demonstrated that for a special set of parameters the acoustic beam propagates without diffraction spreading. This propagation is also accompanied by negative refraction of the direction of phase velocity of the Bloch wave. In the study of two-dimensional viscous phononic crystals with asymmetrical solid inclusions, it was discovered that acoustic transmission is nonreciprocal. The effect of nonreciprocity in a static viscous environment is due to broken PT symmetry of the system as a whole. The difference in transmission is caused by the asymmetrical transmission and dissipation. The asymmetrical transmission is caused solely by broken mirror symmetry and could appear even in a lossless system. Asymmetrical dissipation of sound is a time-irreversible phenomenon that arises only if both energy dissipation and broken parity symmetry are present in the system. The numerical results for both types of phononic crystals were verified experimentally. Proposed devices could be exploited as collimation, rectification, and isolation acoustic devices.

L’objectif de ce travail de thèse est d’enrichir la formulation du Lancer de Faisceaux Gaussiens (LFG) et de tester sa capacité à répondre à certains des besoins actuels en calculs de propagation dans le domaine du Radar terrestre. Le LFG est envisagé comme une alternative possible aux méthodes classiques (Equation Parabolique, méthodes de rayons) en environnement complexe urbanisé, en particulier en présence d’obstacles latéraux, avec une cible située en non visibilité. La méthode de LFG "de base", qui utilise des expressions analytiques obtenues par approximation paraxiale, permet des calculs de propagation rapides en environnements complexes, sans problèmes de caustiques. Elle conduit à des résultats de précision satisfaisante dans le domaine millimétrique, par exemple pour des calculs de champs intra-bâtiments. Aux fréquences plus basses comme celles utilisées en Radar terrestre, elle est limitée par une prise en compte trop approximative des effets de diffraction et par l’élargissement spatial des faisceaux gaussiens au regard des dimensions des obstacles. La théorie des frames est utilisée dans cette thèse pour dépasser ces limites. La théorie des frames fournit un cadre rigoureux pour la décomposition initiale du champ rayonné en faisceaux gaussiens, et permet de calibrer le nombre et les directions des faisceaux à lancer. Dans ce travail de thèse, l’emploi de frames de fenêtres gaussiennes pour décomposer des distributions de champs ou de sources équivalentes est généralisé aux distributions de champs incidents sur des plans ou des portions de plans, choisis en fonction des obstacles rencontrés et des distances parcourues. Les champs rayonnés à partir de ces plans sont alors obtenus par sommation des faisceaux gaussiens lancés depuis ces frames dits de "re-décomposition". Les transformations de faisceaux gaussiens par des obstacles de taille limitée sont ainsi traitées par redécomposition : les faisceaux incidents partiellement interceptés par des surfaces limitées sont "re-décomposés" successivement sur deux frames de re-décomposition, à fenêtres "étroites" puis "larges", définis dans les plans de ces surfaces. Le frame à fenêtres "étroites" permet de traiter les discontinuités physiques, tandis que le frame à fenêtres "larges" permet de propager les champs transformés sous la forme de faisceaux "collimatés". Dans cette thèse, nous présentons une formulation de ces re-décompositions permettant une mise en œuvre numériquement efficace, grâce à des expressions analytiques approchées des coefficients de frame pour la première décomposition, et des éléments de la matrice de changement de frame pour la seconde. Cette formulation est mise en œuvre numériquement, et l’influence de différents paramètres sur la précision des re-décompositions est analysée. Finalement, l’algorithme de LFG enrichi de ces re-décompositions successives est utilisé dans un scénario simplifié proche de situations rencontrées en propagation Radar terrestre. / In this work the Gaussian Beam Shooting (GBS) algorithm is complemented with new original formulations, and the ability of this "augmented" GBS algorithm to address specific problems encountered in electromagnetic field computations for ground-based Radar applications is tested. GBS is considered as an alternative to methods (Parabolic Equation, ray based methods) currently used for such computations in complex urban environments, especially when lateral obstacles and Non-Line-Of-Sight (NLOS) targets are involved. The "basic" GBS algorithm makes use of analytical expressions obtained through paraxial approximations. It allows to perform fast computations in complex environments, without suffering from any caustics problems. Reasonably accurate results have been obtained with this method in the millimetric range, e.g. for indoor field calculations. At lower frequencies, such as used in ground Radar systems, "basic" GBS cannot model diffraction effects accurately enough, and Gaussian beam width with respect to obstacle dimensions becomes a problem after some propagation distance. Frame theory is used in this PhD to overcome these limitations. Frame theory provides a rigorous framework for the initial decomposition of radiated fields into a set of Gaussian beams, providing flexible rules to adjust the number and directions of the launched beams. In this thesis, frame theory is used to discretize not only the source field distribution but also incident field distributions over planes or parts of planes of interest, according to encountered obstacles and propagation distances. The radiated fields are then obtained by summation of Gaussian beams launched from these frames called "reexpansion frames". Gaussian beam transformations by finite sized obstacles are addressed by this re-expansion scheme : the incident beams partially impinging on limited areas are successively "re-expanded" on two re-expansion frames, the first one composed of "narrow" windows and the second one of "wide" windows, both defined in the plane containing the limited area. Spatially narrow window frames allow to take into account abrupt transitions in space, and spatially wide window frames radiate in the form of collimated Gaussian beams. The re-expansion formulation proposed in this work is designed for efficient numerical implementation. Approximate analytical expressions are established for expansion coefficients on narrow window frames, and for frame change matrix elements. This formulation has been implemented, and the influence of frame parameters on re-expansion accuracy is analyzed. Finally, the GBS algorithm augmented with successive re-expansions is used to compute fields in simplified scenarios similar to situations encountered in ground-based Radar propagation problems.

In an attempt to mitigate the effects of the atmosphere on the coherence of an optical (laser) beam, interest has recently been shown in changing the beam shape to determine if a different power distribution at the transmitter will reduce the effects of the random fluctuations in the refractive index. Here, a model is developed for the field of a flattened Gaussian beam as it propagates through atmospheric turbulence, and the resulting effects upon the scintillation of the beam and upon beam wander are determined. A comparison of these results is made with the like effects on a standard TEM00 Gaussian beam. The theoretical results are verified by comparison with a computer simulation model for the flattened Gaussian beam. Further, a determination of the probability of fade and of mean fade time under weak fluctuation conditions is determined using the widely accepted lognormal model. Although this model has been shown to be somewhat optimistic when compared to results obtained in field tests, it has value here in allowing us to compare the effects of atmospheric conditions on the fade statistics of the FGB with those of the lowest order Gaussian beam. The effective spot size of the beam, as it compares to the spot size of the lowest order Gaussian beam, is also analyzed using Carter's definition of spot size for higher order Gaussian beams.

No description available.

Since the first detection of a Gravitational Wave, the LIGO-Virgo Collaboration has worked to improve the sensitivity of their detectors. This continuous effort paid off in the last scientific run, in which the collaboration detected an average of one gravitational wave per week and collected 74 candidates in less than one year. This result was also possible due to the Frequency Independent Squeezing (FIS) implementation, which improved the Virgo detection range for the coalescence between two Binary Neutron Start (BNS) of 5-8\%. However, this incredible result was dramatically limited by different technical issues, among which the most dangerous was the mismatch between the squeezed vacuum beam and the resonance mode of the cavities. The mismatch can be modelled as a simple optical loss in the first approximation. If the beam shape of squeezed vacuum does not match the resonance mode, part of its amplitude is lost and replaced with the incoherent vacuum. However, this modelisation is valid only in simple setups, e.g. if we study the effect inside a single resonance cavity or the transmission of a mode cleaner. In the case of a more complicated system, such as a gravitational wave interferometer, the squeezed vacuum amplitude rejected by the mismatch still travels inside the optical setup. This component accumulates an extra defined by the characteristics of the mismatch, and it can recouple into the main beam reducing the effect of the quantum noise reduction technique. This issue will become more critical in the implementation of the Frequency Dependent Squeezing. This technique is an upgrade of the Frequency Independent Squeezing one. The new setup will increase the complexity of the squeezed beam path. The characterisation of this degradation mechanism requires a dedicated wavefront sensing technique. In fact, the simpler approach based on studying the resonance peak of the cavity is not enough. This method can only estimate the total amount of the optical loss generated by the mismatch, but it cannot characterise the phase shift generated by the decoupling. Without this information is impossible to estimate how the mismatched squeezed vacuum is recoupled into the main beam, and this limits the possibility to foreseen the degradation of the Quantum Noise Reduction technique. For this reason, the Padova-Trento Group studied different techniques for characterising Mode Matching. In particular, we proposed implementing the Mode Converter technique developed by Syracuse University. This technique can fully characterise the mismatch of a spherical beam, and it can be the first approach to monitoring the mismatch. However, this method is not enough for the Frequency Dependent Squeezer source since it cannot detect the mismatch generated by the astigmatism of the incoming beam. In fact, the Frequency Dependent Squeezer Source case uses off-axis reflective telescopes to reduce the power losses generated by transmissive optics. This setup used curved mirrors that induce small astigmatic aberrations as a function of the beam incident angle. These aberrations are present by design, and the standard Mode Converter Technique will not detect them. To overcome this issue, I proposed an upgrade of the Mode Converter technique, which can extend the detection to this kind of aberration.

The ultrasonic nondestructive technique is mainly used to evaluate interior defect, material properties and outside dimensions by measuring the transmitting and reflecting sound waves. Generally, the evaluation of the ultrasonic testing depends on the amplitudes and delay time of the received signals; however, this research is focused on the analysis of the phase differences of the received signals. The leakage phenomenon of surface waves propagating at the liquid-solid interface has been studied for more than fifty years. The main characteristic of this phenomenon is the 180-degree phase difference between the reflected and leaky ultrasound when a bounded ultrasonic beam is incidented. And the null zone caused by the interference of these two waves is appearing in the reflected field. The phase difference is changed as the surface condition altered, including surface roughness and layered structures. The normal-mode theory is used at this research to analyze the analytical model of the leaky surface wave in thin layered structures. In experiments, the measurements of the reflected field are proceeded by the scanning system, so as to analyze the phase difference between the reflected and leaky ultrasound and calculate the layer thickness by the phase difference. As a result of the surface roughness of the thin layers, the leakage is more serious when the ultrasound propagates with lower frequency. For the consideration of locating the null-zone in the reflected field, this research prefers using lower frequency as an initial frequency at the beginning of the testing, then increasing the frequency to achieve a better sensitive of the thickness.