Propagation of Correlation Singularities of a Partially Coherent Field

We investigate the structure of correlation singularities for the Laguerre–Gauss beam of order n=0 and m=2 in the transverse plane during the propagation of the beam in the beam-wander model. We explicitly derive analytical expressions for the cross-spectral density of the corresponding beam order and the analytic expressions representing the singular behavior. We also verify that the singular points disappear at certain z values and reappear at other z values as shown in the previous numerical study. We investigate the dependence of the absolute value of the complex degree of coherence μ on the parameter δ of the beam-wander model during the propagation of the Laguerre–Gauss beam in the corresponding order. The complex degree of coherence depends not only on δ but also on the relative positions of two transverse observation points ρ1 and ρ2, as well as on the propagation variable z for the fixed values of the beam waist and the wavelength of the Laguerre–Gauss beam. Experiments on μ can demonstrate the range of the applicability of the beam-wander model in the turbulent atmosphere. Finally, we examine the orbital angular momentum flux density of the beam and confirm that the general behaviors of the previous studies also hold for m=2.