Advances in photonics and laser physics render possible the generation of electromagnetic fields with spatio-temporally shaped phase and polarization states, both in the near and far field. The talk addresses the distinctive features of the interaction of matter with optical vortices, vector fields, and optical skyrmions. Emphasis is put on the strongly non-linear, spin-dependent quantum dynamics and the consequences of geometry and topology of the driving fields on the generated charge and spin densities and currents. The potential of polarization and phase engineering of the light wave for fundamental and applied research is illustrated by examples from condensed matter and atomic physics.
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