Twist phase-induced characteristic changes of a radially polarized partially coherent beam in a uniaxial crystal

We derived analytical formula for the cross-spectral density matrix of a radially polarized partially coherent twist (RPPCT) beam in a uniaxial crystal orthogonal to the optical axis with the help of the extended Huygens-Fresnel integral formula and unified theory of coherence and polarization. Furthermore, we explore the evolution properties of a RPPCT beam in a uniaxial crystal. It is found that the RPPCT beam becomes an anisotropic RPPCT beam and the beam is rotating with beam propagation in uniaxial crystal. Its evolution properties change with twist factor and the ratio of extraordinary index to ordinary refractive index. The twist factor affects their rotation orientation angles, and the ratio of extraordinary index to ordinary refractive index has an effect on their twisted levels.