Propagation law and quasi-invariance properties of the truncated second-order moment of a diffracted laser beam

The propagation of the truncated second-order moment (i.e. integrated over a finite interval enclosing a constant fraction of the total power) of a diffracted beam is analyzed. An asymptotic analysis, supported by numerical simulations, shows that the propagation law becomes nearly perfectly parabolic as the power fraction increases. It is also demonstrated, on a general basis, that a parabolic propagation law implies the invariance of the infered beam-propagation factor.