The scattering of acoustic waves by boundary discontinuities in waveguides is analyzed using the Method of Matched Asymptotic Expansions (MAE). Existing theories are accurate only for very low frequencies. In contrast, the theory developed in this thesis is valid over the entire range of frequencies up to the first cutoff frequency. The key to this improvement lies in recognizing the important physical role of the cutoff cross-modes of the waveguide, which are usually overlooked. Although these modes are evanescent, they contain information about the interaction between the local field near the discontinuity and the far-field. This interaction has a profound effect on the far-field amplitudes and becomes increasingly important with frequency. The cutoff modes also present novel mathematical problems in that current asymptotic techniques do not offer a rational means of incorporating them into a mathematical description. This difficulty arises from the non-Poincare form of the cross-modes, and its resolution constitutes the second new result of this thesis. We develop a matching scheme based on block matching intermediate expansions in a transform domain. The new technique permits the matching of expansions of a more general nature than previously possible, and may well have useful applications in other physical situations where evanescent terms are important. We show that the resulting theory leads to significant improvements with just a few cross-mode terms included, and also that there is an intimate connection with classical integral methods. Finally, the theory is extended to waveguides with slowly varying shape. We show that the usual regular perturbation analysis of the wave regions must be completely abandoned. This is due to the evanescent nature of the cross-modes, which must be described by a WKB approximation. The pressure field we so obtain includes older results. The new terms account for the cutoff cross-modes of the variable waveguide, which play a central role in extending the dynamic range of the theory. / Ph. D.

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MSc / Thesis (MSc (Physics))--University of Stellenbosch, 2009. / The propagation of electromagnetic radiation in homogeneous or periodically modulated media can be described by the coupled mode equations. The aim of this study was to derive analytical expressions modeling the solutions of the coupled-mode equations, as alternative to the generally used numerical and transfer-matrix methods. The path integral formalism was applied to the coupled-mode equations. This approach involved deriving a path integral from which a generating functional was obtained. From the generating functional a Green’s function, or propagator, describing the nature of mode propagation was extracted. Initially a Green’s function was derived for the propagation of modes having position independent coupling coefficients. This corresponds to modes propagating in a homogeneous medium or in a uniform grating formed by a periodic variation of the index of refraction along the direction of propagation. This was followed by the derivation of a Green’s function for the propagation of modes having position dependent coupling coefficients with the aid of perturbation theory. This models propagation through a nonuniform inhomogeneous medium, specifically a modulated grating. The propagator method was initially tested for the case of propagation in an arbitrary homogeneous medium. In doing so three separate cases were considered namely the copropagation of two modes in the forward and backward directions followed by the counter propagation of the two modes. These more trivial cases were used as examples to develop a rigorous mathematical formalism for this approach. The results were favourable in that the propagator’s results compared well with analytical and numerical solutions. The propagator method was then tested for mode propagation in a periodically perturbed waveguide. This corresponds to the relevant application of mode propagation in uniform gratings in optical fibres. Here two case were investigated. The first scenario was that of the copropagation of two modes in a long period transmission grating. The results achieved compared well with numerical results and analytical solutions. The second scenario was the counter propagation of two modes in a short period reflection grating, specifically a Bragg grating. The results compared well with numerical results and analytical solutions. In both cases it was shown that the propagator accurately predicts many of the spectral properties of these uniform gratings. Finally the propagator method was applied to a nonuniform grating, that is a grating for which the uniform periodicity is modulated - in this case by a raised-cosine function. The result of this modulation is position dependent coupling coefficients necessitating the use of the Green’s function derived using perturbation theory. The results, although physically sensible and qualitatively correct, did not compare well to the numerical solution or the well established transfer-matrix method on a quantitative level at wavelengths approaching the design wavelength of the grating. This can be explained by the breakdown of the assumptions of first order perturbation theory under these conditions.

Thesis (PhD) -- Stellenbosch University, 2001. / Some digitised pages may appear illegible due to the condition of the original hard copy. / ENGLISH ABSTRACT: A new technique for the design of multimode devices in overmoded waveguide is presented. The technique applies the principle of growth-based design and uses a conceptual functional block representation of the design structure to provide necessary flexibility to the design algorithms. Two growth based design strategies are proposed and evaluated. The first uses a generalized synthesis-oriented scanning technique, and the second uses an evolutionary strategy. The techniques provide reliable solutions to a variety of multimode design problems. In order to facilitate sufficiently fast numerical analysis, novel enhancements of the mode matching technique are developed and the use of surrogate models is investigated. In addition, to allow physical evaluation of the finished devices, original techniques of measuring multimode devices are formulated and utilised. Two practical problems are used to evaluate the performance of the design procedures. The first is the design of overmoded waveguide chokes for microwave heating facilities, and the second is the design of multimode horns for antenna and spatial power combining applications. Various examples of each type of problem are presented with measurements of manufactured solutions. / AFRIKAANSE OPSOMMING: ’n Nuwe tegniek vir die ontwerp van multimodusstelsels binne multimodus golfleier word voorgestel. Die tegniek maak gebruik van die beginsel van groei-georienteerde ontwerp en ontgin ’n konsepsuele funksionele module-voorstelling van die ontwerpstruktuur om die nodige buigsaamheid aan die ontwerpsalgoritmes te verleen. Twee groei-georienteerde ontwerpstrategiee word aangebied en geevalueer. Die eerste is gebasseer op ’n veralgemeende sintese-georienteerde skandeertegniek, en die tweede maak gebruik van ’n evolusie-strategie. Die tegniek verskaf betroubare oplossings vir ’n verskeidenheid van multimodusontwerpsprobleme. Ten einde ’n numeriese analise-tegniek daar te stel wat vinnig genoeg is, word oorspronklike verbeterings van die modal-pas metode ontwikkel en surrogaatmodelle is ook ondersoek. Verder, vir fisiese evaluasie, word oorspronklike meettegnieke vir multimodusstelsels geformuleer en gebruik. Twee praktiese probleme word gebruik om die ontwerpprosedures te evalueer. Die eerste is die ontwerp van multimodus golfleierdrywingsdempers vir mikrogolfverhitting, en die tweede is die ontwerp van multimodus horings vir antenna- en ruimtelike drywingskombineerdertoepasings. Verskeie voorbeelde van elke tipe probleem word gegee met metings van gei'mplementeerde oplossings.

Thesis (MScEng (Electrical and Electronic Engineering))--Stellenbosch University, 2008. / The nite element method (FEM) is a powerful tool for the computational analysis of a wide range of electromagnetic problems. As the complexity of the problems is increased so are the demands in terms of the computational resources required to obtain a su ciently accurate solution. In an attempt to obtain a desired accuracy at a lower computational cost adaptive and higher order methods are often employed. These methods generally entail re ning the solution only in the areas where greater complexity is required, thus decreasing the total computational demand. The adaptive nite element method is implemented and used to analyse the transverse electric cuto eigenmodes of 2D waveguiding structures. The higher order hierarchical vector basis functions that form part of this implementation are automatically generated to very high orders, with the results presented in excellent agreement to analytical ones where applicable. Accuracy to the order of numeric precision is attained. Using these adaptive methods, it is also possible to achieve improved cost e ciency of the error metrics considered with respect to storage requirements and computational cost.

Thesis (MScEng (Electrical and Electronic Engineering))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: An investigation into the cause of undesired sidelobes in the 3D radiation pattern of slotted waveguide arrays is conducted. It is hypothesized that the cross-polarization of the antenna is at fault, along with the possibility that an error is made when designing a linear array. In investigating and finding a solution to the problem, the “Z-slot ” is introduced in conjunction with polarizer plates. The base components are used by a custom optimization algorithm to design reference and solution antennas. Results of the antennas are then compared to ascertain the cause and possible solutions for the unwanted sidelobes. The generic nature of the process may be used to characterize other arbitrary aperture configurations and to design larger antennas. / AFRIKAANSE OPSOMMING: ‘n Ondersoek om die oorsaak van ongewensde sylobbe in die 3D uitstraalpatroon van golfleier-antennas vas te stel. Die hipotese is dat die probleem ontstaan uit die kruis-polarisasie van die antenna, tesame met ‘n verkeerdelikke aanname dat die opstelling liniêr is. Die “Z-Gleuf” tesame met polariseringsplate word voorgestel as hulpmiddel om die moontlikke oorsake te ondersoek. ‘n Gespesialiseerde optime erings-algoritme benut hierdie basiskomponente om beide verwysings- en oplossing-antennas te ontwerp. Resultate van die ontwerpde antennas word dan vergelyk om die oorsaak van die ongewensde sylobbe te vas te stel. Die generiese aard van die proses kan toegepas word op enige gleuf-konfigurasie en om groter antennas mee te ontwerp.

Photonic Crystal structures have been heralded as a disruptive technology for the miniaturization of opto-electronic devices, offering as they do the possibility of guiding and manipulating light in sub-micron scale waveguides. Applications of photonic crystal guiding - the ability to send light around sharp bends or compactly split signals into two or more channels have attracted a great deal of attention. Other effects of this waveguiding mechanism have become apparent, and attracted much interest - the novel dispersion surfaces of photonic crystal structures allow the possibility of “slow light” in a dielectric medium, which as well as the possibility of compact optical delay lines may allow enhanced light-matter interaction, and hence miniaturisation of active optical devices. I also consider a third, more traditional type of photonic crystal, in the form of a grating for surface coupling. In this thesis, I address many of the aspects of passive photonic crystals, from the underlying theory through applied device modelling, fabrication concerns and experimental results and analysis. Further, for the devices studied, I consider both the relative merits of the photonic crystal approach and of my work compared to that of others in the field. Thus, the complete spectrum of photonic crystal devices is covered. With regard to specific results, the highlights of the work contained in this thesis are as follows: Realisation of surface grating couplers in a novel material system demonstrating some of the highest reported fibre coupling efficiencies. Development of a short “injecting” taper for coupling into photonic crystal devices. Optimisation and experimental validation of photonic crystal routing elements (Y-splitter and bend). Exploration of interfaces and coupling for “slow light” photonic crystals.

In this thesis I describe experimental work and present data on the guiding of Rubidium atoms along free-space propagating light beams as well as within hollow core glass fibres, namely photonic crystal fibres. I describe experiments, laser systems and vacuum trap assemblies designed to facilitate this guiding. These experiments are intended to aid progression within the field of cold atom guidance wherein narrow diameter, long distance hollow-fibre guides are a current goal. Realisation of these guides could lead to promising applications such as atom interferometers and spatially accurate, multi-source, atom depositors. Herein, guided fluxes are observed in free-space guiding experiments for distances up to 50mm and up to 10GHz red-detuning from resonance. Additionally hollow-core, Kagome structured, quasi- and true-photonic crystal fibres are characterised. Finally a number of detailed fibre-guiding magneto-optic traps are developed. Both cold atomic-beams and cold atomic clouds are reliably positioned above fibre entrance facets in conjunction with a guiding laser beam coupled into the fibre core. Issues regarding optical flux detection outwith fibre confinement appear to have hindered observation of guided atoms. A far more sensitive detection system has been developed for use in current, ongoing fibre-guide experiments.

This dissertation reports the application of nonlinear optical effects for the investigation of vibrational and electronic spectroscopy of molecules adsorbed on thin film metal oxide surfaces and metal oxide surfaces. The main emphasis of the experiments cited here is to introduce the recently developed multi-photon technique, Waveguide Surface Coherent anti-Stokes Raman Scattering Spectroscopy (WSCARS), to the scientific community. Planar optical waveguides have been utilized to generate large optical field enhancements on metal oxide surfaces. Guided waves have been employed to obtain the surface coherent anti-Stokes Raman scattering spectra of pyridine, phenol, benzene, methanol, CD₃OD, 2,4-pentadione, oxygen, ammonia and ND₃ adsorbed onto a ZnO (0001) surface. Vibrational spectra of transient species (O₂⁻) adsorbed on ZnO (0001) surface are also presented. Furthermore, the WSCARS has been used to monitor catalytic hydrogenation of ethylene adsorbed on ZnO (0001) surface. The WSCARS technique is compared with the other vibrational surface probes. Future directions and limitations of the technique are also discussed. Electronic spectra of surface bound species have been examined by resonantly enhanced surface second harmonic generation (SSHG). SHG spectra of trans-cinnamic acid adsorbed on optically cleaned fused silica have been obtained at room temperature and at 4 K. Surface second harmonic generation has been applied to study the adsorption of water and acetone onto thermally grown silicon dioxide/silicon surface. SSHG has been successfully applied to monitor photo-oxidation and photo-reduction of a rutile (110) surface. Experiments are described, data are presented, and surface-adsorbate binding modes are discussed.