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
Equations on this page are rendered with MathJax. Learn more.