Partially coherent sources whose coherent modes are spatiotemporal optical vortex beams

We analyze three non-stationary partially coherent sources whose coherent modes are spatiotemporal optical vortex (STOV) beams. Using spatiotemporal (ST) Bessel-Gauss and Laguerre-Gauss beams (STOV-carrying solutions to the space-time paraxial wave equation) as eigenfunctions in the coherent-modes representation of the mutual coherence function, we derive the ST versions of J ₀-Bessel-correlated, I _n -Bessel-correlated, and twisted Gaussian Schell-model beams. We model, in simulation, these ST random beams via their coherent-modes expansions, compare and contrast the simulated results to theory, and analyze/discuss their free-space propagation characteristics. The work presented in this paper will be useful for simulating or physically generating these ST beams for use in applications or future studies.