The second-order moment statistics of a twisted electromagnetic Gaussian Schell-model propagating in a uniaxial crystal

Under the help of extended Huygens-Fresnel integral, we acquire the analytic expressions of second-order moments of the Wigner distribution function (WDF) for a twisted electromagnetic Gaussian Schell-model (TEGSM) beam propagating in a uniaxial crystal. Moreover, we obtain the formulae for propagation factor, the effective radius of curvature and Rayleigh range in which we studied the properties of the TEGSM beam numerically. It is found that the initial beam parameters and the uniaxial crystal parameters play a decisive role in the TEGSM beam propagating in a uniaxial crystal. The TEGSM beam with smaller absolute deviation of coherence width δxx and δyy is less affected by anisotropic diffraction in a uniaxial crystal, which is much different from the evolution properties of an EGSM beam in a uniaxial crystal. The Rayleigh range will decreases while the crystal parameter e increases. Thus, the propagation properties of a TEGSM beam could be controlled in a uniaxial crystal by changing the initial beam parameters and the uniaxial crystal parameters where it is necessary.