Nonparaxial properties of partially coherent Lorentz-Gauss vortex beam propagating in free space

The analytical formulae of nonparaxial propagation, paraxial propagation and far field propagation for the partially coherent Lorentz-Gauss vortex beam have been derived, the propagation properties of nonparaxial, paraxial and far field propagation are analyzed using the derived formulae. One finds that the paraxial propagation can be seen as a special case of the nonparaxial propagation at the propagation distance of the Rayleigh length, and the far field propagation can also be regarded as special case of the nonparaxial propagation at the longer propagation distance.