Generation and control of extreme ultraviolet free-space optical skyrmions with high harmonic generation

Optical skyrmion serves as a crucial interface between optics and topology. Recently, it has attracted great interest in linear optics. Here, we theoretically introduce a framework for the all-optical generation and control of freespace optical skyrmions in extreme ultraviolet regions via high harmonic generation. We show that by employing full Poincare beams, the created extreme ultraviolet fields manifest as skyrmionic structures in Stokes vector fields, whose skyrmion number is relevant to harmonic orders. We reveal that the generation of skyrmionics structure is attributed to spatial-resolved spin constraint of high harmonic generation. Through qualifying the geometrical parameters of full Poincar\'e beams, the topological texture of extreme ultraviolet fields can be completely manipulated, generating the Bloch-type, Neel-type, anti-type, and higher-order skyrmions, etc. This work promotes the investigation of topological optics in optical highly nonlinear processes, with potential applications towards ultrafast spintronics with structured light fields.