Space-time singularities in spatially-chirped Laguerre-Gaussian beams of any order

The electric field distributions and space-time singularity curves are computed for ultrashort pulsed Laguerre-Gaussian laser beams having spatial chirp. Due to the breaking of cylindrical symmetry by the spatial chirp, the singularities trace complicated curves in space-time, which also vary for different combinations of radial and vortical orders. Analytical solutions are mostly presented along with a recipe for numerically calculating higher orders. The behavior of the singularities upon propagation is also shown, along with a discussion of the extension towards few-cycle pulses. These results are an example of how a simple physical scenario can result in highly complicated singular behavior in space-time.