Propagation of an elliptic Gaussian laser beam in a medium with saturable nonlinearity

We present an analysis for self-focusing of an elliptic Gaussian laser beam in a saturable nonlinear medium. It is shown that stationary self-trapped propagation is forbidden in a saturable medium. Though self-trapped propagation does not occur, a virtual threshold power for self-focusing can be defined. Above this threshold power value, but not far from it, the beam focuses. Below this threshold the beam defocuses. It is also shown that the effective beam radius never reaches zero, which is a property of a Gaussian laser beam.