Interplay of crystal symmetries and light topology in high harmonic spectroscopy

Abstract Structured ultrafast laser beams offer unique opportunities to explore the interplay of the angular momentum of light with matter at the femtosecond scale. Linearly polarized vector beams are paradigmatic examples of structured beams whose topology is characterized by a well-defined Poincaré index. It has been demonstrated that the Poincaré index is a topological invariant during high-order harmonic generation from isotropic targets, such as noble gases. As a result, harmonics are produced as extreme-ultraviolet vector beams with the same topology as the driver. In this work we demonstrate that high-order harmonic generation driven by vector beams from anisotropic crystalline targets, such as single-layer graphene, splits the harmonic field into a multibeam structure: a central vector beam that preserves the driver's topology, surrounded by a topological cluster of unitary vortices, where this symmetry is broken. We identify the target's non-linear anisotropic response as the vehicle of coupling the crystal symmetries with the driving field's topology. Our work opens the route towards using the topological analysis of the high-order harmonic field as a novel spectroscopic tool to reveal the role of symmetries in the non-linear response of matter.