Theoretical Investigations of Mie Scattering and Virtual Excitations in Nanophotonics

Nanophotonics represents a dynamic and rapidly expanding area of research focused on investigating fundamentals of light-matter interactions and developing cuttingedge nanoscale devices for high-speed computation, medicine, different kinds of sensors, and renewable energy. To effectively address these technological and social challenges, nanophotonics necessitates a robust and efficient platform. Historically, plasmonics, a branch of nanophotonics harnessing the tightly confined optical resonances in metallic nanoparticles, emerged as a compelling option for both applications and fundamental investigations, but plasmonics suffers from unwanted energy dissipation. In recent years, a novel approach rooted in Mie resonances in dielectric nanostructures has gained attention, offering the prospect of high quality factors and tunable resonances accompanied by negligible losses, in contrast to plasmonics. This paradigm shift, termed ”Mie-tronics,” has brought significant advancements, including photonic bound states in the continuum, supercavity modes, optical anapoles, superscattering, and perfect absorption, giving rise to groundbreaking technologies like nanolasers, Huygens metasurfaces, and metalenses, among others. Thus, further investigations of Mie resonances in connection to other research topics, such as optical levitodynamics and extreme electromagnetic field confinement, are significantly relevant. Moreover, combining Mie resonances with complex frequency excitation, namely, virtual absorption and gain, presents a promising avenue for theoretical studies that can potentially result in new energy-efficient nanophotonic devices. This thesis investigates approaches provided by Mie resonances and virtual excitations to boost optical trapping, low-loss electromagnetic field confinement, Purcell effect, and tunability of optical properties. The thesis is a collection of the research papers produced during the PhD studies, and, therefore, it consists of a broad introduction including the most central theoretical background and the papers. First, a comparative study of the emission rate enhancement in plasmonic and dielectric nanostructures is carried out. Second, the tunability of nanophotonic structures composed of phase-change materials and photochromatic materials coupled to Mie resonances is explored. Based on these explorations, a tunable phase-change core-shell nanoparticle capable of reversibly switching between nanolaser and cloaking regimes is designed. In addition, a reconfigurable Fano resonance in a hydrogen-rich silicon Mie nanoparticle coupled to a photochromatic material that can change the refractive index when exposed to intense ultra-violet and visible light is proposed. Third, capabilities of dielectric metasurfaces, such as quality factor and spatial localization of light, are extended through the photonic bound states in the continuum and antiferromagnetic order of magnetic Mie resonances. Fourth, Mie-resonant nanoparticles are shown to master optical levitodynamics by enhancing the gradient optical forces induced by counterpropagating gaussian beams. Finally, the impact of virtual excitations on light scattering and optical forces in Mie-resonant nanoparticles is investigated. It is revealed that signals with complex frequencies, i.e., exponentially growing or decaying temporal profiles, can induce pulling optical force or increase pushing force in Mie-resonant nanoparticles. This observation challenges the conventional understanding of the optomechanical interaction of plane wave signals with photonic structures. Also, a significant improvement of optical Kerker, anti-Kerker, and transverse Kerker effect under the complex frequency excitation is uncovered, revisiting the optical theorem in the complex frequency plane. These groundbreaking fundamental results can pave the way for nanophotonic devices beyond the existing constraints, improve their tunability and sensitivity.