Whereas the linear optical properties of plasmonic nanostructures are typically well described using, e.g., the measured dielectric function or the Drude model, only little knowledge is presently available regarding the origin of the nonlinear optical response of metallic nanostructures. We plan to develop an approach that is capable of describing the linear and nonlinear optoelectronic properties of metallic nanostructures on a fully microscopic quantum-mechanical basis.

So far, we performed time-dependent density-functional (TDDFT) calculations for metal slabs and computed SHG and developed a discontinuous Galerkin time-domain Maxwell solver and analyzed SHG from split ring resonators using a hydrodynamic description of the electron density. It is planned to proceed by developing a self-consistent analysis of the light-matter interaction by coupling the TDDFT calculations to a Maxwell solver and to analyze the origin of optical nonlinearities by comparing these results to hydrodynamic simulations. We furthermore plan to set up Bloch-type equations for the material dynamics that are based on the electronic band structure and corresponding wave functions as obtained from ab initio calculations. This equation-of-motion approach will provide a detailed microscopic description of ultrafast processes on the nanoscale, and it allows to incorporate dephasing and relaxation arising from scattering effects.

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