Average intensity of four-petal Gaussian beams through paraxial optical system in atmosphere turbulence

The propagation properties of four-petal Gaussian beams through the paraxial ABCD optical system in atmosphere turbulence are investigated by numerical examples. It is found that the beam propagating through ABCD optical system in atmosphere turbulence can keep its initial four-petal beam profile almost invariant for a short propagation distance, the beam will converted to Gauss-like beam with several small petals with the propagation increasing, and the beam loses its initial profile slower than the beam propagating in atmosphere turbulence.