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<p><p>Microstrip structures became very attractive with the development of cost-effective dielectric materials. Among several techniques suitable to the analysis of such structures, the discrete mode matching method (DMM) is a full-wave approach that allows a fast solution to Helmholz equation. Combined with a full-wave equivalent circuit, the DMM allows fast and accurate analysis of microstrips lines on multilayered substrates.</p><p> </p><p>The knowledge of properties like dispersion and electromagnetic fields is essential in the implementation of such transmission lines. For this objective a MATLAB computer code was developed based on the discrete mode matching method (DMM) to perform this analysis.</p><p> </p><p>The principal parameter for the analysis is the utilization of different dielectric profiles with the aim of a reduction in the dispersion in comparison with one-layer cylindrical microstrip line, showing a reduction of almost 50%. The analysis also includes current density distribution and electromagnetic fields representation. Finally, the data is compared with Ansoft HFSS to validate the results.</p></p> / The German Aerospace Center has rights over the thesis work

Microstrip structures became very attractive with the development of cost-effective dielectric materials. Among several techniques suitable to the analysis of such structures, the discrete mode matching method (DMM) is a full-wave approach that allows a fast solution to Helmholz equation. Combined with a full-wave equivalent circuit, the DMM allows fast and accurate analysis of microstrips lines on multilayered substrates.   The knowledge of properties like dispersion and electromagnetic fields is essential in the implementation of such transmission lines. For this objective a MATLAB computer code was developed based on the discrete mode matching method (DMM) to perform this analysis.   The principal parameter for the analysis is the utilization of different dielectric profiles with the aim of a reduction in the dispersion in comparison with one-layer cylindrical microstrip line, showing a reduction of almost 50%. The analysis also includes current density distribution and electromagnetic fields representation. Finally, the data is compared with Ansoft HFSS to validate the results. / The German Aerospace Center has rights over the thesis work

Dielectric waveguides are important passive devices in optical communication systems. Circular-core fibers with slight ellipticity may lead to polarization-mode dispersion. A clear understanding of the propagation characteristics of the elliptical fibers thus becomes important for theoretical as well as practical purposes. Although mesh-dependent methods such as the finite-element method or finite-difference method, can be used to study such a complex structure, its computational task is very high. Strictly speaking, mesh-based solution does satisfy the Helmholtz equation and the solution only provided four to five significant digits. On the other hand, the highly accurate solution based on solving the Helmholtz equation of the elliptical coordinate system spend most its computational resources on computing the functional value and the zeros of the modified Mathieu functions of the first kind. Our method is based on linear combination of the exact mode-field solutions of the dielectric optical fiber. We apply the analytical continuity principle to obtain the simultaneous equation of the expansion coefficient vector. Since each basis solution satisfies the Helmholtz equation exactly, the overall solutions are very accurate and provide more than six significant digits for fibers with small elliptical eccentricity. In addition, only the Bessel functions are needed in our computation. Using cylindrical coordinate and symmetry, together with ACM principle, we simplify the problem of modal analysis of dielectric elliptical waveguides. This method also can be applied to some regular polygonal dielectric waveguides such as the large area VCESL.

Abstract Optical fiber communications have been become one of the most popular researches since 1970s. In this field, there are many studies on the coupling between semiconductor lasers and fibers and many conclusions are demonstrated. In this thesis we build a 2-D numerical model to simulate energy coupling between laser diodes (LDs) and tapered optical fibers. Our model is based on the spectral domain integral equation (SDIE) formulation which is derived from Maxwell equations and the principle of mode matching. Through this numerical model we will be able to show the field distribution in LD waveguide junctions. We may also use this tool to study the coupling parameters such as the separation distance and tapered fiber geometry.

The limit of current technology for mobile base station filters is the multimode filter, in which each cavity supports two (or possibly three) independent degenerate resonances. Shielded dielectric resonators with a rectangular cross-section are useful in this application. In the design of these filters, manufacturers are using software packages employing finite element or finite difference time domain techniques. However, for sufficient accuracy these procedures require large numbers of points or elements and can be very time consuming. Over the last decade research using the mode matching technique has been used to solve this kind of difficulty for various types of filter design and waveguide problems. In this thesis a mode matching method and computer program is developed to calculate the propagation coefficients and field patterns of the modes in a shielded rectangular dielectric rod waveguide. Propagating, complex, evanescent and backward wave modes are included and the work shows the presence of a dominant mode, and other fundamental modes, not previously identified. The effect of the shield proximity on the propagation characteristics and mode spectrum is investigated, together with the limitations on the accuracy of the mode matching method. In addition, the fields within the shielded rectangular dielectric rod waveguide, are used to calculate the attenuation coefficient of the dominant and fundamental modes. The influence on the attenuation coefficient of the proximity of the shield to the rod is also evaluated for these modes and limitations on accuracy are discussed. The calculated numerical results for the propagation and attenuation coefficient values are verified by measurement. The propagation coefficients results are typically within 2% of those measured. Verification of the attenuation coefficient results is achieved by comparing calculated and measured Q at the resonant frequencies of a number of shielded rectangular dielectric rod resonators. The difference between calculated and measured Q values is on average less than 4%. In the absence of a full solution of the shielded rectangular dielectric rod resonator, these results provide useful design information for this structure. In addition, the work reported in this thesis provides a basis for a full electromagnetic solution of this type of resonator. This would encompass the cubic dielectric resonator in a cubical cavity.

Finite-Difference (FD) based complex modes solver and Complex Mode Matching Method (CMMM) is one of the most popular combinations in modeling and simulation of opti- cal waveguides. This thesis covers the basic theories behind the approaches and impor- tant implementation details. Weighted Optical Path Distance is proposed to speed up convergence and improve numerical accuracy to deal with asymmetric structures. An improved formula is derived for Complex Mode Matching Method expansion process based on matrix optimization. The latter part applies the above approach in the mod- eling of bending structures and grating structures. Typical structures, including bend- ing structures, straight-bend-straight structures, long-period gratings, gratings with de- posited layer, gratings with deep corrugations, are investigated and analyzed. / Thesis / Master of Science in Electrical and Computer Engineering (MSECE)

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.

Microwave processing of ceramics has seen a growth in research and development efforts throughout the past decade. One area of interest is the exploration of improved heating control through experiments and numerical modeling. Controlled heating may be used to counteract non-uniform heating and avoid destructive phenomena such as cracking and thermal runaway. Thermal runaway is a potential problem in materials with temperature dependent dielectric properties. As the material absorbs electromagnetic energy, the temperature increases as does its ability to absorb more energy. Controlled processing of the material may be achieved by manipulating the applied field. The purpose of this research is to model the interaction of the EM-field with a thin ceramic fiber to investigate possible mechanisms that may affect the heating process. The fiber undergoes microwave heating in a single-mode resonant applicator. Maxwell's equations for the fields within the cavity are solved using mode-matching techniques taking into account the field interaction of the fiber and an arbitrarily shaped coupling aperture. Effects of varying the aperture shape on the field distribution are explored. The coupled nature of the electromagnetic solution with the material's temperature-dependent properties, including an analysis of non-uniform heating, is also discussed. / Master of Science

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.