Beam quality factor of a twisted Gaussian Schell-model elliptical vortex beam carrying the cross-phase propagating through a turbulent atmosphere

We derive the analytical expressions for the beam quality factor (M2-factor) of a twisted Gaussian Schell-model elliptical vortex beam carrying the cross phase (TCGSMEV beam) in atmospheric turbulence. Based on these expressions, we have meticulously studied the variations in the propagation factor of the TCGSMEV beam in turbulence. Our outcomes reveal that the M2-factor of the TCGSMEV beam with large twist factor and cross factor increases in atmospheric turbulence, indicating that beam quality obviously becomes worse during propagation. However, the larger the twist factor, cross factor and topological charge are, or the smaller the ellipticity and initial coherence length are, the smaller the relative M2-factor of the TCGSMEV beam is, which means that the TCGSMEV beam can reduce the turbulence-induced degradation of beam quality more significantly than the Gaussian Schell-model beam. These findings may provide a new way to improve beam quality in free-space optical communications.