Analytical far-field divergence angle of a truncated Gaussian beam

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. (C) 2000 Optical Society of America OCIS codes: 050.1960, 050.1220, 000.4430, 260.0260.