Correlation singularities of a partially coherent radially polarized beam in non-Kolmogorov turbulence

We have investigated the correlation singularities of a partially coherent radially polarized beam propagating through non-Kolmogorov turbulence. An analytical expression for the radius of a ring dislocation is derived. It is shown that the dependence of the radius of a ring dislocation on spatial coherence width in non-Kolmogorov turbulence is quite different from that in free space. The relation between spatial coherence width and beam width affects the change trends of the radius of a ring dislocation versus spatial coherence width. For different value ranges of the power law, the change of the radius of a ring dislocation with power law has an opposite trend. It is also found that the propagation distance plays an important role in determining the change of the radius of a ring dislocation. Our results will be useful in measuring the statistical properties of a random medium or a random field.