Resonant self-focusing of a cw intense light beam

A single pass of an intense cw light beam through a strongly absorbing medium can be characterized by two parameters, the input on-axis intensity normalized to the saturation value $I_{0,0}$, and the Fresnel number $F$ for an absorption length ${\alpha }^{-1\mathrm{}}$. For both large $I_{0,0}$ and $F$, propagation can be divided in two parts: At the very beginning, the transverse profile of the beam experiences an encoding. For a beam tuned exactly on resonance, encoding reduces to a stripping of the profile from the wings to the center, progressively, as the light beam goes further into the cell. For $F>>1\mathrm{}$ and $I_{0,0}>>1\mathrm{}$, and both of the same order of magnitude, this stripping can be modeled by a circular aperture placed at the end of the encoding region. Afterwards, the beam is assumed to propagate in free space, its profile exhibits Fresnel interferences and on-axis enhancement. Using a perturbative treatment, the width and the location of the aperture are analytically estimated, and the model is successfully compared with numerical predictions of on-resonance self-focusing. For $I_{0,0}\lesssim F$, the stripping and free-space propagation cannot be separated because near-axis stripping coexists with large diffraction effects on the wings. This case, the best for observing cw on-resonance enhancement, would gain in a more sophisticated model, taking into account diffraction by successive apertures.