text: A useful way to study the interaction of an atom in a Gaussian beam is to look at the harmonic potential approximation of the intensity profile the atom experiences. In the case of the two-level atom, the potential experienced is related to its AC Stark Shift,
  where  is the natural line width of the excited state,  is the electric dipole coupling,  is the frequency of the transition, and  is the detuning or difference between the laser frequency and the transition frequency.
  The intensity of a gaussian beam profile is characterized by the wavelength , minimum waist , and power of the beam . The following formulas define the beam profile:
  To approximate this Gaussian potential in both the radial and axial directions of the beam, the intensity profile must be expanded to second order in  and  for  and  respectively and equated to the harmonic potential . These expansions are evaluated assuming fixed power.
  This means that when solving for the harmonic frequencies (or trap frequencies when considering optical traps for atoms), the frequencies are given as:
  so that the relative trap frequencies for the radial and axial directions as a function of only beam waist scale as: