Propagation properties of three-dimensional TEMm,n-mode Hermite-Gaussian beams through an optical symmetric system

By using the second order moments method and generalized Huygens-Fresnel diffraction integral,the transformation properties of a three-dimensional TEMm,n-mode Hermite-Gaussian beam passing th rough an optical symmetrizing system are studied in detail. It is shown that the symmetrization is complete,because,not only the symmetrizing transformation is achieved in the second order moments sense,but also the output beam becomes a circular one,and then retains its shape unchanged upon propagation.