Changes in the spectral degree of polarization of a partially coherent dark hollow beam in the turbulent atmosphere for on-axis and off-axis propagation point

We report analytic formulas for the elements of the 2 × 2 cross spectral density matrix of a partially coherent dark hollow beam (DHB) with circular symmetry propagating through the turbulent atmosphere. In this paper, from these formulas changes in the spectral degree of polarization of partially coherent DHB for on-axis and off-axis propagation point and for near and far fields are determined for different source conditions.