Design, fabrication and characterization of metamaterials for slow wave devices in the MHz and GHz regimes
Keywords: split ring resonator
numerical modeling
metamaterials
additive manufacturing
analytical modeling

This thesis investigates the coupling mechanisms and dispersion characteristics of discrete and coalesced resonators operating in the MHz and GHz regimes. We employ an analytic model taking into account both magnetic and electric couplings between resonators, aiming to develop novel ways of dispersion control. The study places particular emphasis on the fabrication aspect, with the development of a novel method based on liquid metal injection which was used for the realization of 3D resonant structures. The resonators studied can communicate using their magnetic fields via the law of induction; a time-varying current in one, induces a current in another. In an array of resonators, the induced currents propagate along the line like waves. These waves have been named magnetoinductive waves due to the magnetic coupling between elements.
The coupling mechanisms are analyzed in two planar scenarios; a discrete arrangement, where the resonators are in close proximity but not in contact, and a coalesced arrangement, where the resonators are touching and sharing one side. While arrangements of discrete resonators have been extensively studied, configurations of coalesced resonators have been overlooked in the literature. Arrays of resonators with one, three and four gaps are considered. While the resonators are not in contact (discrete case), it is found that the number of gaps has no effect on the total coupling coefficient, which is negative. The main contribution comes from the magnetic coupling while the electric coupling coefficient is near zero. When the resonators are connected so that they share one side (coalesced case), it is shown that the coupling coefficient can change drastically depending on the number of gaps. In particular, when the shared side is capacitively loaded, the total coupling coefficient switches to positive values, allowing for forward waves to propagate on the structure. This change is due to the electric coupling increasing in magnitude, as shown from the analytic model used to extract the magnetic and electric coupling coefficients. Based on these findings, an optimisation procedure for setting up numerical simulations to match the experimental data is proposed. This approach aims to reduce computational resource requirements while ensuring the reliability of the simulations. The simulations provided significant insight on the electric coupling's behaviour, which was crucial in the development of a tunable capacitor metamaterial array for dispersion control.
Despite recent advances in additive manufacturing, the fabrication of truly 3D conductive structures still remains a challenge. To address this issue, a novel method based on liquid metal injection is proposed. During the process, dielectric moulds with hollow paths are created using a 3D printer. Subsequently, the paths are injected with liquid Field's metal, a metal alloy which solidifies at room temperature. The metal fills the paths and conforms to their shape, allowing for the realisation of 3D conductive structures inside a dielectric medium. The method shows great potential to be incorporated into standard 3D printing setups, as the filling process can be performed using a custom-made Field's metal filament loaded on a commercially available 3D pen. Initial characterization of the method involves determining the minimum feature size of paths that can be achieved on our setup and conducting resistance measurements of filled tracks. The value of 3.6\,MS/m is, to the best of our knowledge, the most reliable measurement for Field's metal conductivity in the literature. Using this method, square and spiral resonators are fabricated. Even though the square resonators exhibit higher losses compared to similar geometries made with conventional methods such as printed circuit board, the spiral resonators demonstrate exceptionally high quality factors. It is shown that the operating frequency and quality factor of the spirals can be tuned by adjusting the number of turns. After testing various dielectric materials for their suitability and electromagnetic properties, the study reveals that the most favourable material for use in Field's metal fabrication is high impact polystyrene. Using the spiral resonators, a 3D metamaterial cube is constructed and the different couplings present in the structure are investigated. Field's metal fabrication paves the path for the creation of 3D circuits, allowing the miniaturization of devices. This is demonstrated with the fabrication of a thermometer circuit.
The work presented in this thesis further explores the physics behind coupled resonators and wave propagation of magnetoinductive waves, while carrying important technological implications with the development of a novel method for 3D conductive structures.