  Multiple-degrees-of-freedom free-space communication combining polarization
and high-order spatial modes promises high-capacity communication channel.
While high-order spatial modes have been widely exploited for dense coding and
high-dimensional quantum information processing, the properties of polarization
preservation of high-order spatial beams propagating in turbulent atmosphere
have not been comprehensively investigated yet. Here we focus on the properties
of polarization preservation of partially coherent Hermite-Gaussian beams
propagating along different atmospheric turbulence paths. The analytical
expressions for the polarization of partially coherent Hermite-Gaussian beams
propagating through atmospheric turbulence along different paths have been
derived. It is shown that the larger the coherence length is, and the larger
the beam order m, n are, the less the polarization is changed. We find that the
evolution properties of the polarization in slant-down paths through turbulent
atmosphere are similar to the case in free space if the condition zenith angle
{\xi}<{\pi}/4 is satisfied. While at a long propagation distance, evolution
properties of polarization in horizontal paths of turbulent atmosphere differs
much from that in free space and in slant paths. The results may allow one to
choose the optimal propagation path in terms of specific applications, which is
helpful for future experimental implementation of multiple-degrees-of-freedom
free-space communication.
