| Abstract: | Symmetries and their associated selection rules are extremely useful in all fields of science. In nonlinear optics, it has been shown that the symmetries of both matter and light's time-dependent polarization determine the allowed/forbidden processes (i.e. selection rules). I will present a general theory for selection rules in high harmonic generation that accounts for both microscopic and macroscopic (i.e. multi-scale) symmetries of the light-matter interaction. I will show our experimental result of selection rules of new symmetries, including elliptical dynamical symmetry and selection rules from light with discrete multi-scale symmetries. I will also present theoretical examples, including multi-scale twisted light and aperiodic electromagnetic vector fields that brings together all the DOF of light to form polarized space-time quasicrystals of light. This work paves the way for novel spectroscopic techniques in multi-scale systems as well as for imprinting complex structures in EUV-X-ray beams, attosecond pulses, or in the interacting medium itself. |
