Nonlinearity Assisted Mie Scattering from Nanoparticles

Scattering by nanoparticles is an exciting branch of physics to control and manipulate light. More specifically, there have been fascinating developments regarding light scattering by sub-wavelength particles, including high-index dielectric and metal particles for their applications in optical resonance phenomena, detecting the fluorescence of molecules, enhancing Raman scattering, transferring the energy to the higher order modes, sensing, and photodetector technologies. This research area has recently gained renewed attention with the study of near-field effects at the nanoscale in advanced regimes of operation, including nonlinear effects and the time-varying parametric modulation of local material properties. When the particle size is comparable to or slightly bigger than the incident wavelength, Mie solutions to Maxwell's equations describe these electromagnetic scattering problems. The addition and excitation of nonlinear effects in these high-indexed sub-wavelength dielectric and plasmonic particles holds promise to improve the existing performance of the system or provide additional features directed toward novel applications. This dissertation explores Mie scattering from dielectric and plasmonic particles in the presence of nonlinear effects, more specifically second and third order nonlinear effects. For numerical analysis, an in-house Rigorous Coupled Analysis (RCWA) method has been developed in a Matlab environment and validated based on designing metasurfaces and comparing them with established results. For dielectrics, this dissertation presents a numerical study of the linear and nonlinear diffraction and focusing properties of dielectric metasurfaces consisting of silicon microcylinder arrays resting on a silicon substrate. Upon diffraction, such structures lead to the formation of near-field intensity profiles reminiscent of photonic nanojets and propagate similarly. The results indicate that the Kerr nonlinear effect i.e. third order nonlinear effect enhances light concentration throughout the generated photonic jet with an increase in the intensity of about 20% compared to the linear regime for the power levels considered in this work. The transverse beamwidth remains subwavelength in all cases, and the nonlinear effect reduces the full width. On the other hand, plasmonic structures give rise to localized surface plasmons and excitations of the conduction electrons within metallic nanostructures. These aren't propagating but instead confined to the vicinity of the nanostructure, interacting with the electromagnetic field. These modes emerge from the scattering between small conductive nanoparticles with an oscillating electromagnetic field. This dissertation introduces a novel mechanism to transfer energy from excited dipolar mode to such higher-order subradiant localized mode. Recent advancements in time-varying structures that help relax photon energy conservation constraints and a newly proposed plasmonic parametric resonance pave the way for this work. With the help of the second-order nonlinear wave mixing process and parametric modulation of the dielectric permittivity in a medium surrounding metal particles, we have introduced a way to accomplish the otherwise nearly impossible task to selectively couple energy into specific high order modes of a nanostructures. This work further shows that the oscillating mode amplitude reaches a steady state, and the steady state establishes the ideal modulation conditions that enhance the amplitude of the high-order mode.