Topological high-harmonic spectroscopy

Abstract

Linearly polarized vector beams are structured lasers whose topology is characterized by a well-defined Poincaré index, which is a topological invariant during high-order harmonic generation. As such, harmonics are produced as extreme-ultraviolet vector beams that inherit the topology of the driver. This holds for isotropic targets such as noble gases, but analogous behaviour in crystalline solids is still open to discussion. Here, we demonstrate that this conservation rule breaks in crystalline solids, in virtue of their anisotropic non-linear susceptibility. We identify the topological properties of the harmonic field as unique probes, sensitive to both the microscopic and macroscopic features of the target’s complex non-linear response. Our simulations, performed in single-layer graphene, show that the harmonic field is split into a multi-beam structure whose topology encodes information about laser-driven electronic dynamics. Our work promotes the topological analysis of the high-order harmonic field as a spectroscopic tool to reveal the nonlinearities in the coupling of light and target symmetries.