Measuring refractive indices of a uniaxial crystal by structured light with non-uniform correlation

We introduce an effective method for measuring the refractive indices of a uniaxial crystal based on the independent self-focusing property of non-uniformly correlated beams along the $x$ and $y$ directions. We demonstrate how the positions of the independent foci can be changed by adjusting coherence lengths to determine the characteristic coherence lengths of the beams in a uniaxial crystal, and how this information can be used to determine the refractive indices by relating the propagation characteristics of the beam in free space and in the crystal. Furthermore, it is demonstrated that, by choosing a high beam order, one can reduce the measuring error caused by CCD detection precision. These results present an example of how non-uniformly correlated beams can be used for applications in anisotropic materials.