Propagation of focused vector laser beams in turbulent atmosphere

By adopting a combination of beam coherence-polarization matrix and extended Huygens–Fresnel integral formula, analytical formulae are derived for the average intensity, the degree of polarization and the RMS (Root-Mean-Square) beam width of focused vector laser beams propagating in a turbulent atmosphere, and the propagation of focused vector laser beams is studied in detail. The spreading properties of vector laser beams and fundamental Gaussian beams are studied comparatively. It reveals that the focused vector laser beam evolves into Gaussian profile in shorter distance compared with collimated vector laser beams, and that destroying of polarization structure of focused ones is more severe. The spreading properties of the focused vector laser beams become the same as that of fundamental Gaussian beams faster. The propagation properties of focused vector laser beams are closely related to the parameters of the beam and the structure constant of the atmospheric turbulence. The results can provide useful reference in designing fiber laser system.