Diagonalization and symmetrization of anisotropic twisted Gaussian Schell-model beams

On the basis of the Wigner distribution function and second-order moments matrix methods, the diagonalization and symmetrization of anisotropic twisted Gaussian Schell-model (TGSM) beams are studied. The synthesis procedure for anisotropic TGSM beams is described and illustrated with numerical examples. It is shown that an anisotropic TGSM beam can be transformed into an aligned simple astigmatic (ASA) beam by four steps and then transformed into a stigmatic beam with twist by subsequent two steps.