Spreading of partially coherent Hermite-Gaussian beams in slant atmospheric turbulence

Based on the extended Huygens-Fresnel principle, the analytical expressions for the root mean square width and angular spread of partially coherent Hermite-Gaussian (H-G) beams propagating through slant atmospheric turbulence are derived, and are used to study the influence of propagation path and beam orders on the propagation of partially coherent H-G beams in atmospheric turbulence along a slant path. The relative width and relative angular spread are introduced to quantitatively describe the resistance of a beam to atmospheric turbulence. It is shown that under the same conditions the influence of atmospheric turbulence along a slant path on the partially coherent H-G beam propagation is smaller than that along a horizontal path. Therefore, the slant path is more beneficial to the beam propagation through atmospheric turbulence in comparison with the horizontal propagation. The larger the beam orders m, n are, the less the partially coherent H-G beams are affected by turbulence.