Broadband control of topological–spectral correlations in space–time beams

The synthesis of ultrashort pulses with simultaneously tailored spatial and temporal properties opens new horizons in multimode photonics, especially when the spatial degree of freedom is controlled by robust topological structures. Current methods to shape space–time beams with correlations between their topological charges and spectral components have yielded fascinating phenomena. However, shaping is currently limited to narrow topological and/or spectral bands, greatly constraining the breadth of achievable spatiotemporal dynamics. Here we introduce a Fourier space–time shaper for ultrabroadband pulses, covering nearly 50% of the visible spectrum and carrying a wide range of topological charges with values up to 80. Instead of relying on a conventional grating with linear geometry, our approach employs a diffractive axicon with circular geometry that allows to impart azimuthal phase modulations to beams carrying orbital angular momentum. We retrieve the spatiotemporal field by introducing a characterization technique based on hyperspectral off-axis holography. The tailoring of linear topological–spectral correlations enables the control of several properties of wave packets, including their chirality, orbital radius and number of intertwined helices, whereas complex correlations allow us to manipulate their dynamics. Our space–time beams with broadband topological content will enable a host of novel applications in ultrafast light–matter excitations, microscopy and multiplexing.