Kerr lens

A beam's transverse intensity changes its own refractive index. For positive nonlinear index and a bright centre, the accumulated phase has the curvature of a converging lens. For $I(r)=I_0{e}^{-2r^2/w^2}$ over a short length $L$, the in-medium thin-lens approximation gives $1/f=4n_2{I}_{0}L/(n_0{w}^2)$. Negative $n_2$ instead produces self-defocusing.