Gaussian cooling

In my experiments at school I do laser cooling of Mg atoms. For this we use a Gaussian beam (that is a beam that has the intensity shape of a 2D Gaussian in the direction of the beam) to get a good distribution of light on the atoms. But I wonder what would happen if we had non-Gaussian beams? See the pictures here to see how Gaussian and non-Gaussian beams look like (the Gaussian beam is the TEM00 one).