Maxwell-TDDFT Nanoplasmonics and Structured Light Shaping

Abstract

Modern pump–probe spectroscopies increasingly exploit electromagnetic fields with tailored spatial and temporal structure. Attosecond techniques push pulse durations to the sub-femtosecond regime, enabling real-time tracking of electronic motion, while X-ray spectroscopies probe matter at angstrom-scale wavelengths, accessing core-level dynamics with atomic spatial resolution. At the same time, spatially structured light, such as twisted beams carrying orbital angular momentum (OAM), vector beams, and other engineered wavefronts, is emerging as a powerful tool for controlling and interrogating matter, with applications ranging from ultrafast imaging to chiral discrimination and quantum information processing. These advances expose the limitations of common theoretical approximations, particularly the electric-dipole approximation, which cannot capture field gradients, spatial textures, or the intrinsic angular momentum of structured light. In this thesis, we go beyond the dipole approximation and employ a full minimal-coupling framework that retains the complete spatial structure, gradients, and OAM content of the electromagnetic field. This approach allows us to explore the multiscale interaction of structured light with matter through a combination of classical electrodynamics and quantum-mechanical simulations, revealing regimes of control and spectroscopy that are inaccessible to conventional treatments. First, we demonstrate the generation of optical vortices from nanoplasmonic Archimedean spirals using real-time real-space electrodynamics simulations, where we resolve the emergence and temporal evolution of the local orbital angular momentum density. The resulting vortices manifest pronounced spatial structure owing to the angular momentum transfer. We validate the phase structuring of the beam by using classically described point charges as probes. The position dependence of the test charge trajectories across the beam highlights the necessity of accounting for the spatial dependence of OAM beams. We proceed to investigate high-harmonic generation in atomic hydrogen beyond the dipole approximation, employing the full minimal-coupling Hamiltonian to include magnetic, quadrupolar, and spatial-gradient effects without truncation. We confirm the existence of such effects with plane-wave lasers. Moreover, we observe that structured fields such as Bessel beams induce characteristic forms of nonlinear dipole motion and symmetry breaking, which are particularly visible in even harmonics. We tune the incident OAM number to show that beyond-dipole corrections in the electron trajectory are susceptible to this parameter. We expand this analysis to the molecular case. We investigate a benzene molecule subjected to a circularly polarized plane wave beam, and identify the modified, beyond dipole selection rules in the harmonic spectrum. We turn our focus to the forward-backward coupling of light-matter. We employ a Cherenkov wave packet traveling faster than the phase velocity of light in our numerical setup to demonstrate that not only the level of coupling, but also accounting for the back reaction of the matter to the electromagnetic field can have significant implications: We identify symmetry breaking in the electronic wave packet that is only visible when beyond dipole approaches are combined with the forward-backward coupling. To summarize, the results of this thesis highlight that the spatial structure of light, its angular momentum, and resulting symmetry breaking are not captured when accounting only for the temporal properties of the electromagnetic field. By combining classical and quantum descriptions, and by embracing the full description of the electromagnetic field by going beyond the electric dipole approximation, we study structured electromagnetic fields starting from plasmonic vortex generation, then move to high-harmonic emission and Cherenkov radiation. We provide a set of predictive simulations where the interaction of light and matter is sensitive to spatial structure and symmetry. Our results offer a basis for future studies involving structured electromagnetic fields and their effects on quantum systems.