Fig. 1. (a) Schematic of generating EUV skyrmions with HHG. A synthesized two-color (800nm+400nm) CVVB field is employed to generate HHG with non-trivial spatial spin distribution. The red and blue arrows represent the instantaneous electric field vectors of 800- and 400-nm incident fields, respectively, and the accompanied pseudocolor maps show their angular phase structures. We control the beam width of the incident 800-nm field that is twice that of the 400-nm field, so the focal distributions of intensities of 800- and 400-nm CVVBs are the same. We note here that if they are not the same, one cannot generate the skyrmions presented in this work. Here, we show the EUV skyrmionic fields can be generated, and the 13th harmonic spins down at the beam center and spins up at the surrounding. The inset illustrates the coordinates in the incident plane and focal plane, respectively. (b) The distributions of intensity (upper panel) and normalized z-direction SAM density (bottom panel) of 800- and 400-nm CVVBs in the focal plane individually. (c) The focal electric field structure of the two-color synthesized CVVB. The pseudocolor map indicates the intensity distribution of the driving beam. The overlapped Lissajous figures illustrate the local polarization states, in which the red profiles show the sixfold spatial symmetry of the two-color synthesized field.

Fig. 2. Spatio–spectral signatures of HHG driven by the CVVBs. (a)–(c) High harmonic spectra. (d)–(f) Spatial intensity distributions of logarithmic scales. (g)–(i) Spatial distributions of normalized SAM densities along the z-direction. The HHG drivers are (a), (d), (g) the 800-nm CVVB, (b), (e), (h) 400-nm CVVB, and (c), (f), (i) their synthesized two-color CVVB. The harmonic orders marked by black arrows in (a)–(c) correspond to each column in (d)–(i).

Fig. 3. Characterization of the EUV skyrmions in HHG. (a) Unit Poincaré sphere defined by the normalized Stokes parameters, S=(S1,S2,S3). At the north and south poles of the Poincaré sphere, polarizations are spin-up and spin-down, respectively. (b) The projection of Stokes parameters of 13th and 14th harmonics in the S1−S3 plane as a function of radial distance (upper panel) and the projection in the S1−S2 plane as a function of azimuthal angle (lower panel). (c), (d) Spatial distributions of Stokes vectors for the 13th and 14th harmonics in the focal plane, in which the color scheme of the Stokes vector is encoded by the value of S3. (e), (f) Physical picture of generating skyrmions in HHG.

Fig. 4. Control over the topological texture of EUV skyrmions. (a), (b) HyOPSP formed by an 800-nm Poincaré beam (ℓω1=−1 and ℓω1′=0) and a 400-nm Poincaré beam (ℓω2=0 and ℓω2′=1). The varying colors on the spheres are used to show the qualified combination of two-color Poincaré beams. Points A and B on the HyOPSP indicate the positions of two-color Poincaré beams, which can generate (c), (d) a Bloch-type EUV skyrmion and (e) a Néel-type EUV skyrmion in HHG. (f) If selecting the point A in the 800-nm sphere and A′ in the 400-nm sphere, the generated EUV field reveals a non-skyrmion structure. (g), (h) Formation of anti-skyrmion and third-order skyrmion, respectively. In each diagram, the lower panel shows the projection of Stokes vectors in the S1-S2 plane as a function of azimuthal angle. The harmonic orders are 13th for (c) and 14th for (d)–(f).