Design and topological optimization of nanophotonic devices

Abstract

A central topic in the research of nanophotonics is the geometrical optimization of the nanostructures since the geometries are deeply related to the Mie resonances and the localized surface plasmon resonances in dielectric and metallic nanomaterials. When many nanostructures are assembled to form a metamaterial, the tuning of the geometrical parameters can bring even more profound effects, such as bound states in the continuum (BIC) with infinite quality factors (Q factors). Moreover, with the development of nanofabrication technologies, there is a trend of integrating nanostructures in the vertical direction, which provides more degrees of freedom for controlling the device performance and functionality. The main topic of this dissertation is to explore some of the abovementioned tuning possibilities to enhance the performance of nanophotonic devices. The dissertation contains two major parts: In chapters 2 and 3, the vertical integration of metalenses is studied. We discover a phenomenon similar to the Moiré effect in the bilayer Pancharatnam-Berry phase metalenses and reveal the role of geometrical imperfections on the focusing performance of reflective metalenses. Novel multifocal and reflective metalenses, with smaller

footprints and enhanced performance compared to their bulky conventional counterparts, are designed based on the theoretical findings. The study of geometrical imperfections also provides guidelines for analyzing and compensating the fabrication errors, which is vital for large scale production and commercialization of metalenses. In chapters 4 and 5, we use machine learning to harness the full tuning power of the complicated geometries, which is challenging with conventional design methods. Plasmonic metasurfaces with on-demand optical responses are designed by manipulating the coupling of multiple nanodisks using neural networks. An accuracy of ± 8 nm is achieved, which is higher than previous reports and close to the fabrication limits of nanofabrication technologies. We also demonstrate, for the first time, the control of multiple BIC states using freeform geometries with predefined symmetry. It is a new method to exploit the untapped potential of freeform photonics structures. The discoveries we have made in both dielectric and plasmonic nanophotonic devices could benefit applications such as imaging, sensing, and light-emitting devices.