Propagation of Partially Coherent Hollow Gaussian Beam in Inhomogeneous Atmospheric Turbulence

Based on the Huygens-Fresnel principle and the definition of the Wigner distribution function, the analytical expression of the beam width and the far-field divergence angle for partially coherent Hollow Gaussian beam in inhomogeneous atmospheric turbulence have been derived. The propagation of PCHGB in inhomogeneous atmospheric turbulence was quantitatively analyzed and discussed. The results show that the beam width of PCHGB depends on the waist width, beam order, wavelength, coherence width, inner scale of the turbulence and the zenith angle in inhomogeneous turbulence. Similarly, the far-field divergence angle of PCHGB depends on the zenith angle, inner scale of the turbulence, coherence width and wave number in inhomogeneous turbulence. We also found that the saturation propagation distances (SPDs) of the far-field divergence angle of PCHGB in inhomogeneous turbulence with a zenith angle of π/3 are about 0.3 km.