Far-field encircled radius of truncated Gaussian beams: a scaling law for arbitrary encircled power ratios

In order to evaluate the far-field encircled radius of Gaussian beam propagation, we construct the scaling law from both theoretical and numerical aspects. First, we derived the theoretical formula of the far-field encircled radius for aperture-truncated Gaussian beams at different encircled power ratios. Then, the scaling law based on a theoretical formula considering jitter and aberration effects is further proposed. Finally, the scaling law is validated against wave-optics simulations. The results show that the scaling law we proposed can effectively predict the far-field encircled radius of Gaussian beams under different effects. It is hoped that the result can provide researchers and engineers with a predictive tool for laser applications ranging from laser systems to directed energy technologies.