Spatiotemporal flux breathing and topological sculpting in structured transverse orbital angular momentum lattices

Spatiotemporal optical vortices (STOVs) carrying transverse orbital angular momentum (OAM) have fundamentally expanded the degrees of freedom for structuring light. However, current generation paradigms are confined to isotropic, rigid-body geometries, effectively con- straining transverse OAM to a single scalar property and leaving the rich spatiotemporal dy- namics within the wave packet inaccessible. This rigidity stands in stark contrast to ubiquitous natural vortex systems such as quantum fluids and atmospheric cyclones, where non-uniform rotation and symmetry breaking are the norm. Here, we bridge this gap by exploiting the nonlinear mapping of the azimuthal phase gradient to break rotational symmetry, realizing a programmable spatiotemporal flux breathing effect. We theoretically clarify and experi- mentally verify that local variations in the phase gradient induce instantaneous group velocity anisotropy, compelling the local OAM density to spontaneously reorganize into stable, multi- lobed lattice structures while strictly preserving the global topological charge. Furthermore, we harness the modulation frequency of these structures as a robust degree of freedom for free- space information transfer, experimentally demonstrating high-fidelity encoding and decoding of spatiotemporal topological states. This work transitions STOVs from passive scalar objects to structured functional carriers, opening new avenues for high-dimensional optical communi- cations and ultrafast spatiotemporal field manipulation, while promising distinct applications in strong-field physics and high-dimensional quantum entanglement.