Self-focusing

Summary

Self-focusing is the narrowing of an intense light beam in a medium whose refractive index increases with intensity. This is the case of the optical Kerr effect with $n_2 > 0$. The beam is brightest at its centre, so the medium acts like a converging lens. Below a critical power, diffraction wins and the beam spreads; above it, the self-focusing wins and the beam collapses until other effects stop it. In the simplest model it is described by the two-dimensional focusing nonlinear Schrödinger equation, whose solutions can blow up in finite distance.