Approximate, but accurate, analytical expressions for the far-field divergence angle of a Gaussian beam normally incident on a circular aperture are derived. A first equation is obtained based on the concept of Gaussian transform, in which the Bessel function present in the far-field diffraction integral is approximated by a Gaussian function. Refining this approach yields another simple, practical closed-form formula with such a level of accuracy that we propose that it can be used as an exact reference. All approximations hold for any combination of Gaussian beam width and aperture radius.
© 2000 Optical Society of America
(000.4430) General : Numerical approximation and analysis
(050.1220) Diffraction and gratings : Apertures
(050.1960) Diffraction and gratings : Diffraction theory
(260.0260) Physical optics : Physical optics
Emmanuel M. Drνge, Neal G. Skinner, and Dale M. Byrne, "Analytical Far-Field Divergence Angle of a Truncated Gaussian Beam," Appl. Opt. 39, 4918-4925 (2000)