<p dir="ltr">This thesis deals with optical cavity-coupled two-dimensional (2D) materials. First, we describe a new theoretical approach to model the properties of cavity-coupled plasmons in 2D conductors. Next, we propose an optical cavity architecture for enhanced light-matter interaction with potential for performance and functionality beyond that of traditional approaches and describe an initial investigation of one example of such a system. Finally, we provide a thorough description of the fabrication techniques used to produce the previously mentioned optical cavities.</p><p dir="ltr">The advent of 2D materials has opened exciting possibilities for controlling light-matter interactions at the nanoscale. The first major contribution of this work is the investigation of coupling between patterned 2D Van der Waals materials and Fabry-Perot cavities, focusing on how system parameters like pattern shape and material properties influence these interactions. Using a quasistatic eigenmode expansion approach, we develop a theoretical framework to predict and manipulate optical behavior in these systems. Our work opens new pathways for engineering light-matter interactions within patterned 2D material platforms, paving the way for the engineering of novel optical phenomena.</p><p dir="ltr">The second major contribution of this work is the development of a versatile platform for light-matter coupling experiments in Van der Waals materials. It is well-known that light-matter interaction can be used to realize unprecedented functionality in the coupled materials. However, few---if any---approaches to date utilize this phenomenon to its fullest extent. We have provided a platform that can be used to realize light-matter coupling efficiencies beyond what is possible in conventional systems, can be easily integrated with 2D materials, and provides new opportunities to engineer the photonic environment of the coupled material. In particular, we focus on silicon dielectric bowtie cavities (DBCs) coupled to few-layer flakes of $\rm WSe_2$. This approach leverages topology-optimized cavity architectures to achieve simultaneous spatial and spectral confinement, yielding Purcell factors exceeding 2500, mode volumes as small as $\sim10^{-3}(\lambda/2n)^3$, and quality factors up to $\sim200$---performance metrics limited only by material losses. The lithographically defined DBCs enable deterministic emission hotspot placement and tunability across a broad wavelength range with minimal performance impact. Photoluminescence imaging and spectroscopy reveal comparable $\rm WSe_2$ exciton emission enhancement to plasmonic structures. This platform surpasses the limitations of conventional cavity architectures by enabling unprecedented coupling efficiencies and unique functionality while maintaining sufficient mechanical robustness for 2D material transfer.</p><p dir="ltr">The final chapter outlines the fabrication process for the cavities described in the previous chapter. The fabrication involves advanced nanolithography techniques to define patterns with high resolution, addressing challenges such as proximity effects and process blur. Techniques such as proximity effect correction (PEC) are used to enhance pattern accuracy, while careful optimization of exposure and development parameters ensures minimal distortion. The process utilizes high-anisotropy reactive ion etching to transfer the patterns onto the substrate, where precise optimization of the etching parameters has been performed to achieve high resolution and selectivity. The final optimized process yields structures with a minimum feature size of approximately 20 nm and minimum radius of curvature of approximately 10 nm, allowing for the repeatable fabrication of complex inverse-designed cavities.</p>

The dissertation thesis is focused on research and development in the field of microfabrication by the technology of electron beam lithography. In the first part of this work, the extensive study is conducted in the field of technology of electron beam lithography in terms of physical principles, writing strategies and resist materials. This is followed with description of physical principles of etching for the transfer of relief structures into substrates. The thesis describes innovative techniques in modelling, simulation, data preparation and optimization of manufacturing technology. It brings new possibilities to record deep binary or multilevel microstructures using electron beam lithography, plasma and reactive ion etching technology. Experience and knowledge in the large area of microlithography, plasma and anisotropic wet-etching of silicon have been capitalized to the design process of manufacturing of nano-patterned membranes. It was followed with practical verification and optimization of the microfabrication process.