prof. Ing. Miloslav Čapek, Ph.D.

Theory of characteristic modes presents one of the leading approaches to efficient analysis, synthesis and design of electrically small antennas for variety of potential applications as for example broad-band antennas, multi-band antennas, or MIMO antennas. A lot of fresh new findings related to characteristic modes have been published in recent years and deserve further investigation and deeper understanding. Many others are still awaiting their discovery. This broad research topic deals with both analytical and numerical advancement of characteristic modes theory, and will also demand investigation into topics of model order reduction and operator theory. Publications: elmag.fel.cvut.cz/CEM Supervisor(s): capek.elmag.org, elmag.fel.cvut.cz/profile-main/163

Topic deals with a utilization of optimization techniques, both convex and heuristic, in conjunction with modal and structural decomposition to design optimal electrically small antennas and scatterers. The framework aspiring to utilize the mixture of all these techniques is called Source Concept. Source Concept is capable of representing all antenna parameters and quantities solely in terms of electric and/or magnetic currents and important part of this work is focused on its generalization New perspectives of the Source Concept will also be studied together with practical application, code implementation and verification. Publications: elmag.fel.cvut.cz/CEM Supervisor(s): capek.elmag.org, elmag.fel.cvut.cz/profile-main/163

Most of the existing electrically small antennas are single port antennas. Such designs almost exclusively employs the dominant TM (electric dipole-like) mode which performance is however far from the fundamental bounds. On the other hand, the combination of the TM and TE (magnetic dipole-like) modes, promises valuable improvements in terms of most relevant antenna parameters (i.e., directivity, efficiency, bandwidth). Unfortunately, it turns out that such a combination cannot be fed by a single port, consequently multiport antennas should be utilized. Usage of multi-port antennas introduces new problems of interpreting parameters like quality factor Q, but also calls for robust optimization routines determining optimal combination of radiator’s shape, feeding position and feeding complex amplitudes. Publications: elmag.fel.cvut.cz/CEM Supervisor(s): capek.elmag.org, elmag.fel.cvut.cz/profile-main/163

The focal point of this dissertation is the exploration of machine learning's potential within the realm of electromagnetism. Specifically, it aims to develop algorithms to automate and expedite electromagnetic inverse design and optimization processes. Presently, existing topology optimization algorithms demand an extensive computational load. Any alteration in the optimization problem—such as changes in frequency, optimization domain, or objective—necessitates performing the entire process anew. Additionally, the resulting shapes often exhibit irregularities, posing challenges in precise manufacturing. These shortcomings could potentially be addressed through the application of machine learning techniques. The exploration begins with an in-depth characterization of current algorithms, encompassing state-of-the-art methodologies pioneered by the CEM group at CTU [1]. Subsequently, this dissertation proposes specific techniques to enhance the optimization process's speed and implements them in practical scenarios.

Modern antennas are subjects of strict, often contradictory, requirements ranging from compact electrical size to high-gain, low-loss, and high information capacity. To fulfill these requirements simultaneously requires a precise control of all levels of antenna design. This thesis aims at the development of antenna design framework unifying optimal radiating shape, based predominantly on modal methods, and optimal excitation, based on solutions to convex optimization problems. An indispensable part is a careful consideration of an environment affecting the performance of an antenna, e.g., an antenna operates in the vicinity of a large conducting platform. Developed antenna designs should offer extended functionalities such as reconfigurability, beam steering, or multiple polarization states. A relationship between characteristic mode decomposition and its port-mode counterpart should be found and utilized as the main design tool. All antenna designs will be compared with fundamental limitations on performance. The constraint on a prescribed input impedance will be incorporated into existing techniques determining the fundamental bounds. An important point to be considered is the integration of the radiating part of an antenna and of the matching circuit. It is expected that the novel co-simulation technique generates promising antenna designs, which will be manufactured, measured, and their performance will be compared with corresponding virtual models.

The fundamental bounds on electrically small antenna performance are already well-known, however, they are described in terms of optimal free-space current densities. Such currents cannot be supported with any conducting platform when only realistic number of feeding positions (typically only one) is demanded. The major task is thus a synthesis of conducting supports performing close to the principal bounds. At the current level of understanding such task is an NP hard problem accessible solely to heuristic algorithms. That means that new problem parametrizations and advanced algorithms are needed together with deeper understanding of the optimization problem. The effective solution can reside in the realm of machine or deep learning. Notice that the problem of topology and shape optimization is still considered as open problem in practically all areas of engineering. Publications: elmag.fel.cvut.cz/CEM Supervisor(s): capek.elmag.org, elmag.fel.cvut.cz/profile-main/163