Linear and Nonlinear Optical Properties in Plasmonic and Dielectric Nanoparticle Lattices

Abstract

This dissertation investigates plasmonic and dielectric lattice resonances with the goal of enhancing second harmonic generation (SHG) in such periodic structures. We employ analytic models coupled with numerical simulations to gain important insights into the underlying physical principles and mechanisms that drive the enhancement of SHG via the manipulation of lattice resonance properties. The analytic coupled dipole-quadrupole model is used to understand the resonant behaviors of periodic spherical particle arrays and guide their design and optimization. To study the nonlinear response, a full 3D finite-difference time-domain (FDTD) Maxwell solver with a hydrodynamic nonlinear Drude model is implemented to simulate SHG in the vicinity of optimized linear lattice resonances. We show that suitably designed linearmultipole resonant coupling can significantly enhance SHG in metasurfaces. For arbitrary-shaped particles, the multipole decomposition method is used to break down complex electromagnetic fields into individual multipole components. We extend analytic formulas to include both electric and magnetic octupoles and demonstrate the applicability of multipole decomposition near lattice resonances. Relatively few multipoles obtained from the spherical harmonics expansion can produce accurate results, even with strong multipole coupling. This provides a powerful tool for understanding and predicting resonant behavior. Finally, the dissertation explores the study of bound states in the continuum (BICs), which are localized states that exist in the spectral continuum of periodic structures. It highlights a novel type of BIC and quasi-BIC that arise from the mutual coupling between electric and magnetic multipole resonances in a periodic lattice of plasmonic nanoparticles. By breaking the inversion symmetry of the structure, additional multipole coupling is introduced, which creates high-Q bound and quasibound states. Strong absorption at the quasi-BIC enhances SHG in the lattice.