Beam spreading and M2-factor of electromagnetic Gaussian Schell-model beam propagating in inhomogeneous atmospheric turbulence

The main purpose of this paper is to study the beam spreading and M2-factor of electromagnetic Gaussian Schell-model (EGSM) beam through inhomogeneous atmospheric turbulence. The analytical formulas for the root-mean-square (rms) spatial width, rms angular width, M2-factor of EGSM beam in turbulence are derived by using the second-order moments of the Wigner distribution function and extended Huygens-Fresnel integral. Our results show that the relative M2-factor of EGSM beam decreases with decreasing of zenith angle, initial coherence lengths and initial degree of polarization and with increasing of beam widths and inner scale. It is also shown that as the zenith angle is equal to π/6, the saturated propagation distances of the relative rms angular width, the relative rms spatial width, and the relative M2-factor are about 0.3 km, 3 km and 20 km, respectively. And it also can be found that the relative M2-factor becomes small when the initial degree of polarization closes to 0.