Polarization fluctuations of partially coherent Hermite–Gaussian beams in a slant turbulent channel

The propagation of a partially coherent Hermite–Gaussian beam in a slant turbulent channel is studied. The analytical formula for the quantum degree of polarization of a partially coherent Hermite–Gaussian beam is derived based on the quantum Stokes operators and the generalized Huygens–Fresnel principle. It is shown that the zenith angle slightly affects the polarization degree of partially coherent Hermite–Gaussian beams, and the changes of polarization degree are affected by the coherence length, the detection photon-number and the ground refractive index structure parameter. Furthermore, the numerical simulations show that a partially coherent Hermite–Gaussian beam with bigger coherence length, higher photon-number level, lower beam order, shorter wavelength is less affected by the turbulence. These results indicate that one can choose the partially coherent Hermite–Gaussian beam with bigger coherence length, lower beam order, shorter wavelength, higher detection photon-number and set the size of transmitting aperture w0w0 as about 0.065 m to improve the performance of a polarization-encoded free-space quantum communication system.