Self-focusing

Self-focusing is a non-linear optical process induced by the change in refractive index of materials exposed to intense electromagnetic radiation. A medium whose refractive index increases with the electric field intensity acts as a focusing lens for an electromagnetic wave characterised by an initial transverse intensity gradient, as in a laser beam. The peak intensity of the self-focused region keeps increasing as the wave travels through the medium, until defocusing effects or medium damage interrupt this process. Self-focusing of light was discovered by Gurgen Askaryan.

Self-focusing is often observed when radiation generated by femtosecond lasers propagates through many solids, liquids and gases. Depending on the type of material and on the intensity of the radiation, several mechanisms produce variations in the refractive index which result in self-focusing: the main cases are Kerr-induced self-focusing and plasma self-focusing.

Kerr-induced self-focusing was first predicted in the 1960s and experimentally verified by studying the interaction of ruby lasers with glasses and liquids. Its origin lies in the optical Kerr effect, a non-linear process which arises in media exposed to intense electromagnetic radiation, and which produces a variation of the refractive index ${\displaystyle n}$ as described by the formula ${\displaystyle n=n_{0}+n_{2}I}$, where n₀ and n₂ are the linear and non-linear components of the refractive index, and I is the intensity of the radiation. Since n₂ is positive in most materials, the refractive index becomes larger in the areas where the intensity is higher, usually at the centre of a beam, creating a focusing density profile which potentially leads to the collapse of a beam on itself. Self-focusing beams have been found to naturally evolve into a Townes profile regardless of their initial shape.

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