Transverse effects on squeezing with atoms

We evaluate the squeezing of a probe beam with a transverse Gaussian structure interacting with an ensemble of two-level atoms in a cavity. We use the linear input-output formalism where the effect of atoms is described by susceptibility and noise functions, and show that the transverse structure is accounted for by averaging these atomic functions over the intensity profile. The results of the plane-wave and Gaussian-wave theories are compared. We find that, when a large squeezing is predicted, the prediction of the plane-wave model is not reliable outside the Kerr domain. We give an estimate of the squeezing degradation due to the Gaussian transverse structure.