Fast calculation of orbital angular momentum flux density of partially coherent Schell-model beams on propagation

Optical coherence has recently become a degree of freedom to modulate the orbital angular momentum (OAM) flux density of a partially coherent beam during propagation. However, the calculation of the OAM flux density for the partially coherent beam involves partial differential and four-dimensional integral operations, which poses drawbacks for its fast numerical calculations. In this paper, we present an efficient numerical protocol for calculating the OAM flux density of any partially coherent Schell-model beam propagating through a paraxial ABCD optical system by only adopting two-dimensional (2D) Fourier transforms. The general formalism is established in detail for the fast numerical calculation of the OAM flux density. It is found that the operation number in the developed algorithm is independent on the spatial coherence states of the beam. To demonstrate the validity of our algorithm, we calculate the OAM flux density of the partially coherent Laguerre-Gaussian beams during propagation with both the analytical and numerical methods. The obtained results are consistent well with each other. Moreover, the OAM flux density properties of two other classes of Schell-model beams, having no analytical solutions, are investigated as the specific examples. Our method provides a convenient way for studying the correlation-induced OAM density changes for any Schell-model beam propagation through a paraxial optical system.