Shape synthesis (also called topological synthesis or inverse design in other disciplines) has the potential to provide antenna engineers with a useful addition to their design tools. Transmitarray antennas, which consist of a feed antenna plus a printed planar structure that emulates a lens, are able to provide high directivity antenna performance, and have been the subject of sustained research over the past ten years. The transmitarray lens consists of a lattice of cells, with each cell occupied by an element that includes conductors of specific shape. The feed field incident on each element on the input surface side of the transmitarray is transformed by each element into a field of different amplitude and phase on the output surface side of each element, providing some desired aperture distribution on the output surface. In this thesis we develop a technique, and the overall computational tool to implement it, that fundamentally allows the electromagnetics to dictate how the conducting portions of a 3-layer element must be shaped in order to obtain some specific transmission coefficient. Such shape synthesis of the elements offers the possibility of obtaining elements that have properties not obtainable using conventional elements. These techniques were applied to the shape synthesis of dual-band elements (18 GHz and 24 GHz). A transmitarray using these elements was designed and fabricated, its performance measured and compared to simulated results. An in-depth discussion of the outcome experimentally validates the shape synthesis procedure.

Antennas are an important component of wireless ("without wires") communications, regardless of their use. As these systems have become increasingly complex, antenna design requirements have become more demanding. Conventional antenna design consists of selecting some canonical radiator structure described by a handful of key dimensions, and then adjusting these using an optimization algorithm that improves some performance-related objective function that is (during optimization) repeatedly evaluated via a full-wave computational electromagnetics model of the structure. This approach has been employed to great effect in the enormously successful development of wireless communications antenna technology thus far, but is limiting in the sense that the "design space" is restricted to a library of canonical (or regular near-canonical) shapes. As increased design constraints and more complicated placement requirements arise such an approach to antenna design could eventually become a bottleneck. The use of antenna shape synthesis, a process also referred to as inverse design, can widen the "design space", and include such aspects as occupancy and fabrication constraints, the presence of a platform, even weight constraints, and much more. Dielectric resonator antennas (DRAs) hold the promise of lower losses at higher frequencies. This thesis uses a three-dimensional shape optimization algorithm along with a characteristic mode analysis and a genetic algorithm to shape synthesize DRAs. Until now, a limited amount of work on such shape synthesis has been performed for single-feed fixed-beam DRAs. In this thesis we extend this approach by devising and implementing a new shaping methodology for significantly more complex problems, namely directivity-maximized multi-port fixed-beam DRAs, and multi-port DRAs capable of the beam-steering required to satisfy certain spherical coverage constraints, where the location, type and number of feed-ports need not be specified prior to shaping. The approach enables even low-profile enhanced-directivity DRAs to be shape synthesized.

Many microwave (RF) circuit designs require passive distributed sub-components with prescribed scattering parameters. These sub-components have typically been realised by cascading building-block configurations (eg. transmission lines of specific lengths, bends in transmission lines, coupled lines, and so on) of standard shape, and then adjusting the dimensions of selected prescribed features of these building-blocks. The problem with this approach is that the resulting sub-component may take up more "real-estate" on the overall circuit board than can be tolerated, may require tolerances that are too tight and hence be more costly than product developers can allow, can lead to less-than-best performance because we select the building-blocks (that we think are needed) ahead of time, and so on. The research in this thesis contributes to the shape synthesis approach of physical microstrip circuit design. The shape synthesis process is usually contrasted to traditional design by recognizing that it does not merely adjust the dimensions of a set of prescribed geometrical features on pre-selected shapes, but allows the electromagnetic physics to tell us what the sub-component layout needs to be (and it can be unconventional) in order to obtain the required performance. Existing shape synthesis techniques are based on the discrete- or continuous-pixelation method. Each of these approaches, however, have disadvantages (eg. too many degrees of freedom required to achieve the geometrical resolution necessary; the need for arbitrary decisions to fix material properties) that have prevented shape synthesis from being accepted for widespread use in design practice. In this thesis we develop, implement and apply a completely new shape synthesis approach, called the subtractive approach, that overcomes many of the above-mentioned disadvantages of pixelation-based methods It reduces the number of variables (degrees of freedom) needed in spite of the fact that the "design space" is significantly broadened by this approach. The latter is confirmed by the fact that it produces physical circuit geometries that we would not have come up with using traditional design methods. Examples are provided of the application of the new subtractive shape synthesis method. This new method involves continuous variables directly related to the physical circuit geometry, and thus could be used with surrogate modelling, unlike some existing shape synthesis procedures.

Characteristic modes (CMs) provide deep insight into the electromagnetic behaviour of any arbitrarily shaped conducting structure because the CMs are unique to the geometry of the object. We exploit this very fact by predicting a perhaps surprising number of important antenna metrics such as resonance frequency, radiation efficiency and antenna Q (bandwidth) without needing to specify a feeding location. In doing so, it is possible to define a collection of objective functions that can be used in an optimizer to shape-synthesize antennas without needing to define a feed location a priori. We denote this novel form of optimization “feedless” or “excitation-free” antenna shape synthesis. Fundamentally, we are allowing the electromagnetics to dictate how the antenna synthesis should proceed and are in no way imposing the physical constraints enforced by fixed feeding structures. This optimization technique is broadly applied to three major areas of antenna research: electrically small antennas, multi-band antennas and reflectarrays. Thus, the scope of applicability ranges from small antennas, to intermediate sizes and concludes with electrically large antenna designs, which is a testament to the broad applicability of characteristic mode theory. Another advantage of feedless electromagnetic shape synthesis is the ability to synthesize antennas whose desirable properties approach the fundamental limits imposed by electromagnetics. As an additional benefit, the feedless optimization technique is shown to have greater computational efficiency than traditional antenna optimization techniques.

Characteristic modes (CMs) provide deep insight into the electromagnetic behaviour of any arbitrarily shaped conducting structure because the CMs are unique to the geometry of the object. We exploit this very fact by predicting a perhaps surprising number of important antenna metrics such as resonance frequency, radiation efficiency and antenna Q (bandwidth) without needing to specify a feeding location. In doing so, it is possible to define a collection of objective functions that can be used in an optimizer to shape-synthesize antennas without needing to define a feed location a priori. We denote this novel form of optimization “feedless” or “excitation-free” antenna shape synthesis. Fundamentally, we are allowing the electromagnetics to dictate how the antenna synthesis should proceed and are in no way imposing the physical constraints enforced by fixed feeding structures. This optimization technique is broadly applied to three major areas of antenna research: electrically small antennas, multi-band antennas and reflectarrays. Thus, the scope of applicability ranges from small antennas, to intermediate sizes and concludes with electrically large antenna designs, which is a testament to the broad applicability of characteristic mode theory. Another advantage of feedless electromagnetic shape synthesis is the ability to synthesize antennas whose desirable properties approach the fundamental limits imposed by electromagnetics. As an additional benefit, the feedless optimization technique is shown to have greater computational efficiency than traditional antenna optimization techniques.

Characteristic modes (CMs) provide deep insight into the electromagnetic behaviour of any arbitrarily shaped conducting structure because the CMs are unique to the geometry of the object. We exploit this very fact by predicting a perhaps surprising number of important antenna metrics such as resonance frequency, radiation efficiency and antenna Q (bandwidth) without needing to specify a feeding location. In doing so, it is possible to define a collection of objective functions that can be used in an optimizer to shape-synthesize antennas without needing to define a feed location a priori. We denote this novel form of optimization “feedless” or “excitation-free” antenna shape synthesis. Fundamentally, we are allowing the electromagnetics to dictate how the antenna synthesis should proceed and are in no way imposing the physical constraints enforced by fixed feeding structures. This optimization technique is broadly applied to three major areas of antenna research: electrically small antennas, multi-band antennas and reflectarrays. Thus, the scope of applicability ranges from small antennas, to intermediate sizes and concludes with electrically large antenna designs, which is a testament to the broad applicability of characteristic mode theory. Another advantage of feedless electromagnetic shape synthesis is the ability to synthesize antennas whose desirable properties approach the fundamental limits imposed by electromagnetics. As an additional benefit, the feedless optimization technique is shown to have greater computational efficiency than traditional antenna optimization techniques.

L’objet principal de cette thèse est de proposer des méthodes pour la synthèse de formes qui soient contrôlables et permettent d’imprimer les résultats obtenus. Les imprimantes 3D étant désormais plus faciles d’accès que jamais, les logiciels de modélisation doivent maintenant prendre en compte les contraintes de fabrication imposées par les technologies de fabrication additives. En conséquence, des algorithmes efficaces doivent être développés afin de modéliser les formes complexes qui peuvent être créées par impression 3D. Nous développons des algorithmes pour la synthèse de formes par l’exemple qui prennent en compte le comportement mécanique des structures devant être fabriquées. Toutes les contributions de cette thèse s’intéressent au problème de génération de formes complexes sous contraintes géométriques et objectifs structurels. Dans un premier temps, nous nous intéressons à la gestion des contraintes de fabrication, et proposons une méthode pour synthétiser des structures de support efficaces qui sont bien adaptées aux imprimantes à filament. Dans un deuxième temps, nous prenons en compte le contrôle de l’apparence, et développons de nouvelles méthodes pour la synthèse par l’exemple qui mélangent astucieusement des critères sur visuels, et des contraintes sur le comportement mécanique des objets. Pour finir, nous présentons une méthode passant bien à l’échelle, afin de contrôler les propriétés élastiques des structures imprimées. Nous nous inspirons des méthodes de synthèse de texture procédurales, et proposons un algorithme efficace pour synthétiser des microstructures imprimables et contrôler leurs propriétés élastiques / The main goal of this thesis is to propose methods to synthesize shapes in a controllable manner, with the purpose of being fabricated. As 3D printers grow more accessible than ever, modeling software must now take into account fabrication constraints posed by additive manufacturing technologies. Consequently, efficient algorithms need to be devised to model the complex shapes that can be created through 3D printing. We develop algorithms for by-example shape synthesis that consider the physical behavior of the structure to fabricate. All the contributions of this thesis focus on the problem of generating complex shapes that follow geometric constraints and structural objectives. In a first time, we focus on dealing with fabrication constraints, and propose a method for synthesizing efficient support structures that are well-suited for filament printers. In a second time, we take into account appearance control, and develop new by-example synthesis methods that mixes in a meaningful manner criteria on the appearance of the synthesized shapes, and constraints on their mechanical behavior. Finally, we present a highly scalable method to control the elastic properties of printed structures. We draw inspiration from procedural texture synthesis methods, and propose an efficient algorithm to synthesize printable microstructures with controlled elastic properties