In Optics, Self-Focusing is when a light beam (usually an intense laser light) focuses without the aid of a lens. Non-linear effects in the material that the light is passing through are responsible for the effect.
Self-Focusing is due to the dependance of the optical dielectric constant on the electric field of the incident field. This dependance is due to the fact that some molecules have an anisotropic polarizability. The molecular polarizability along the molecular axis of symmetry is different from the value at right angles to it. This causes the average dipolar energy of the applied field to be reduced by those molecules that have their axis of symmetry aligned in that particular way. The number of molecules aligned in this specific way can be given by:
Where N is the number of molecuals per unit volume, k is Boltzmann's constant, T is the temperature, a is the dielectric constant for the two orientations of the molecule, and E2 is the time average of the squared optical electric field. This number is proportional to the change in the dielectric constant. The dielectric constant can be written as:
= epsilon + epsilon2
Self-Focusing can be used in a variety of exotic optical experiments but as with most non-linear effects, it is typically seen as an undesirable effect.