M²-factor of high-power laser beams through a multi-apertured ABCD optical system

Based on the generalized truncated second-order moments, an approximate analytical formula of the beam propagation factor M² of high-power laser beams passing through the optical system with multiple hard-edged apertures is deduced. Numerical examples of the beams passing through an aperture-spatial filter are enclosed, and the influences of amplitude modulations (AMs) and phase fluctuations (PFs) on the beam propagation quality of high-power laser beams passing through the multi-apertured ABCD optical system are considered and discussed. It is shown that PFs are able to degrade the beam propagation quality of laser beams more than AMs when the high-power laser beams passing through the aperture-spatial filter, furthermore, one or two aperture-lens optical systems configured appropriate aperture parameters are both able to upgrade the beam propagation quality of high-power laser beams. The M² factor of Gaussian beam passing through the multi-aperture optical system is a special case in this paper.