Changes in the characteristics of a Gaussian beam weakly diffracted by a circular aperture.

A Gaussian beam weakly diffracted by a circular aperture can be approximated in the far field by another Gaussian beam with slightly different characteristics. Equations giving the intensity, the divergence, and the radius of the modified beam are derived in simple practical form for experimentalists. These approximated formulas show that, even in the case of negligible power losses through the aperture, the diffracted beam characteristics may appreciably differ from those of the incident beam. In a first approximation, diffraction effects may be ignored only if the ratio a/r(0) of the aperture radius a to the l/e intensity beam radius r(0) in the aperture plane is larger than 3.