High-harmonic spin-orbit angular momentum generation in crystalline solids preserving multiscale dynamical symmetry.

Symmetries essentially provide conservation rules in nonlinear light-matter interactions and facilitate control and understanding of photon conversion processes or electron dynamics. Since anisotropic solids have rich symmetries, they are strong candidates for controlling both optical micro- and macroscale structures, namely, spin angular momentum (circular polarization) and orbital angular momentum (spiral wavefront), respectively. Here, we show structured high-harmonic generation linked to the anisotropic symmetry of a solid. By strategically preserving a dynamical symmetry arising from the spin-orbit interaction of light, we generate multiple orbital angular momentum states in high-order harmonics. The experimental results exhibit the total angular momentum conservation rule of light even in the extreme nonlinear region, which is evidence that the mechanism originates from a dynamical symmetry. Our study provides a deeper understanding of multiscale nonlinear optical phenomena and a general guideline for using electronic structures to control structured light, such as through Floquet engineering.