  Vortex crystals are geometric arrays of vortices found in various physics
fields, owing their regular internal structure to mutual interactions within a
spatially confined system. In optics, vortex crystals may form spontaneously
within a nonlinear resonator but their usefulness is limited by the lack of
control over their topology. On the other hand, programmable devices used in
free space, like spatial light modulators, allow the design of nearly arbitrary
vortex distributions but without any intrinsic dynamics. By combining
non-Hermitian optics with on-demand topological transformations enabled by
metasurfaces, we report a solid-state laser that generates vortex crystals with
mutual interactions and actively-tunable topologies. We demonstrate 10x10
coherent vortex arrays with nonlocal coupling networks that are not limited to
nearest-neighbor coupling but rather dictated by the crystal's topology. The
vortex crystals exhibit sharp Bragg diffraction peaks, witnessing their
coherence and high topological charge purity, which we resolve spatially over
the whole lattice by introducing a parallelized analysis technique. By
structuring light at the source, we enable complex transformations that allow
to arbitrarily partition the orbital angular momentum inside the cavity and to
heal topological charge defects, making these resonators a robust and versatile
tool for advanced applications in topological optics.
