Research on the coherence of partially coherent radially polarized beam during propagation

Based on the generalized Huygens theory and the unified theory of coherence and polarization, study is made on the module value of complex degree of coherence of partially coherent radially polarized beam (PCRPB) which changes with transmission distance at different reference point. Results show that the module value distribution of the complex degree changing with the transmission distance is different for different reference point while PCRPB propagates in a free space. When the reference point is at the origin, with the increase of the transmission distance, mu(xx) and mu(xy) hold a symmetric distribution, and the distribution range increases. When the reference point is confined on the x-axis, mu(xx) changes from single peak to three peaks, and the two valleys lie symmetrically; and mu(xy) changes from two peaks to four peaks, and the four valleys lie symmetrically. The transmission distance of the evolution is related to the distance between the reference point and the origin: the closer the distance between the reference point and the origin, the shorter the transmission distance is needed to achieve the evolution process. When the reference point lies on the y-axis, mu(xx) holds a symmetric distribution, its distribution range increases, and mu(xy) changes from two peak values to four peaks and four valleys which are in symmetric form. The transmission distance is related to the spacing between the reference point and the origin, the closer the distance between the reference point and the origin: the shorter the transmission is needed to achieve the evolution process. In addition, when the reference point lies at other positions on the observation plane, the module value distribution of mu(xx) and mu(xy) is obtained by combining the distribution rules of reference point at x-axis and y-axis: i.e., when the reference point lies at other positions of the observation plane, the module values mu(xx) and mu(xy) can be composed of three peaks and four peaks with the increase of transmission distance, respectively.