Propagation of a Partially Coherent Bessel–Gaussian Beam in a Uniform Medium and Turbulent Atmosphere

In this paper, the coherent properties of partially coherent Bessel–Gaussian optical beams propagating through a uniform medium (free space) or a turbulent atmosphere are examined theoretically. The consideration is based on the analytical solution of the equation for the transverse second-order mutual coherence function of the field of partially coherent optical radiation in a turbulent atmosphere. For the partially coherent Bessel–Gaussian beam, the second-order mutual coherence function of the source field is taken as a Gaussian–Schell model. In this approximation, we analyze the behavior of the coherence degree and the integral coherence scale of these beams as a function of the propagation pathlength, propagation conditions, and beam parameters, such as the radius of the Gauss factor of the beam, parameter of the Bessel factor of the beam, topological charge, and correlation width of the source field of partially coherent radiation. It was found that, as a partially coherent vortex Bessel–Gaussian beam propagates through a turbulent atmosphere, there appear not two (as might be expected: one due to atmospheric turbulence and another due to the partial coherence of the source field), but only one ring dislocation of the coherence degree (due to the simultaneous effect of both these factors on the optical radiation). In addition, it is shown that the dislocation of the coherence degree that significantly affects the beam coherence level is formed only for beams, for which the coherence width of the source field is larger than the diameter of the first Fresnel zone.