Fig. 3: Optical setup for synthesizing and characterizing vectoral spatiotemporal skyrmion wavepackets.

The apparatus comprises three components: (i) a 2D vectorial ultrafast holographic pulse shaper that incorporates a diffraction grating, a cylindrical lens, and an SLM, modulating only the x-polarization while leaving the y-polarization unaffected to control the amplitude ratio and phase difference between the x- and y-polarizations, thereby enabling polarization distribution control; (ii) a pulse compression system employing a parallel grating pair; and (iii) a time delay line system for fully reconstructing the 3D profile of the generated spatiotemporal wavepacket. Spatiotemporal holography used here must achieve accurate complex amplitude modulation in the zeroth order to ensure precise coaxial alignment between the x- and y-polarizations. The synthesized computer-generated hologram (CGH) enables complex-amplitude modulation of x-polarization, where the grating phase depth and delay regulate the amplitude and phase of the x-polarization component of incident beam, respectively^52,53,67. The CGH embedded in the SLM consists of three components: (1) the phase distribution of a spatial-spectral LGst₀₁ mode; (2) a GDD phase for managing the pre-chirp of the input pulse and balancing diffraction and dispersion; and (3) a phase-only diffraction grating with a phase depth modulated by the magnitude of Eq. (2) (see Methods). The 2D images of the composite CGH is placed in the bottom-right corner. BS beam splitter, HWP half-wave plate, QWP quarter-wave plate, P polarizer, L lens, M mirror, G grating, CL cylindrical lens, SLM spatial light modulator