Based on diffraction integral formula and selfreproducing principle,diffraction integral equation for transverse modes in a circular symmetric resonator with an aperture diaphragm was disintegrated to finitesum matrix equation,and field distributions of transverse modes in the resonator were calculated by solving matrix for eigenvalues and eigenvectors.

Based on the Huygens-Fresnel integral and the expansion of the hard aperture function into a finite sum of Gaussian functions,the approximation analytical expression of the high-order Bessel-Gaussian beam passing through a paraxial ABCD optical system with a circular aperture is derived.

By contrast when using circular apertures to shape CW laser, we must combine it with spatial filter to get the .

Theoretical analyses of the reverse mode suppression using diaphragm for symmetric confocal unstable ring resonator;