High Harmonic Generation with Spatiotemporal Optical Möbius Topology

We theoretically study the generation of extreme-ultraviolet (EUV) spatiotemporal optical Möbius strips via high harmonic generation (HHG) process. Using a synthesized two-color driving field that combines an optical vortex and an optical toroidal vortex and considering the selection rule imposed by angular momentum conservation, we show that the spatiotemporal phase structure of HHG forms optical twisted phase strips, representing a unification of optical knots, optical Hopfions, and optical Möbius strips. We further show that we can control the spatiotemporal Möbius topology of HHG and generate HHG Möbius phase strips with arbitrary twist numbers using two-color driving fields that contain Möbius phase strips with opposite twisting handedness. We find that the twist number is conserved throughout this highly nonlinear process. Moreover, we illustrate that the twisting handedness of HHG Möbius phase strips can be precisely tuned by adjusting the intensity ratio of the two-color driving fields. Our work reveals the capacity of HHG as a nonlinear toolkit for high-dimensional manipulation of light in the EUV regime and holds great promise for investigating topological light–matter interactions.