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 closedform 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.
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