  The Artmann formula provides an accurate determination of the Goos-Haenchen
lateral displacement in terms of the light wavelength, refractive index and
incidence angle. In the total reflection region, this formula is widely used in
the literature and confirmed by experiments. Nevertheless, for incidence at
critical angle, it tends to infinity and numerical calculations are needed to
reproduce the experimental data. In this paper, we overcome the divergence
problem at critical angle and find, for Gaussian beams, a closed formula in
terms of modified Bessel functions of the first kind. The formula is in
excellent agreement with numerical calculations and reproduces, for incidence
angles greater than critical ones, the Artmann formula. The closed form also
allows one to understand how the breaking of symmetry in the angular
distribution is responsible for the difference between measurements done by
considering the maximum and the mean value of the beam intensity. The results
obtained in this study clearly show the Goos-Haenchen lateral displacement
dependence on the angular distribution shape of the incoming beam. Finally, we
also present a brief comparison with experimental data and other analytical
formulas found in the literature.
