Spreading and M2-factor based on second-order moments for partially-coherent anomalous hollow beam in turbulent atmosphere

The spreading and M2-factor of partially-coherent anomalous hollow (PCAH) beam in the turbulent atmosphere are studied in detail based on the extended Huygens – Fresnel principle. Analytical formulae of the root-mean-square (rms) spatial width, rms angular width, curvature radius of wave plane and propagation factor (M2-factor) of PCAH beam in turbulent atmosphere are obtained, respectively. It is found that the spatial and angular sizes of PCAH beam spreads rapidly in the strong turbulence than the weak turbulence and the free space. Beam spreadings and curvature radius of PCAH beam depend on initial beam widths, coherence length, wavelength and turbulence. The smaller M2-factor depends on the larger transverse coherence length, wavelength and inner scale of turbulence, and the weak turbulence.