Self-Focusing

Abstract

In the last decade, with the availability of high-power laser beams, a large number of interesting nonlinear optical phenomena have been studied, among which the self-focusing of intense laser beams occupies an important place because of its relevance to other nonlinear effects. The self-focusing effect arises primarily due to the dependence of the refractive index of a material on the intensity of the propagating electromagnetic wave. This nonlinear dependence may arise, among others, from the following mechanisms:

• 1. Electrostriction. In the presence of an inhomogeneous electric field, dielectrics are subject to a volume force; this phenomenon is known as electrostriction. Because of this volume force, the material tends to be drawn into the high-field region, which affects the density of the material. The refractive index changes due to density variations and one obtains a dependence of the refractive index on the intensity of the beam. For a quantitative analysis of the phenomenon, see, e.g., Panofsky and Phillips (1962) and Sodha et al. (1974).

• 2. Thermal effects. When an intense electromagnetic wave (having an intensity distribution along its wavefront) propagates through an absorbing medium, a transverse temperature gradient is set up. This temperature gradient leads to a variation of the refractive index that causes either focusing or defocusing of the beam.

• 3. Kerr effect. If a liquid molecule (like CS₂) possesses anisotropic polarizability, then the electric field of an intense laser beam will tend to orient these anisotropically polarized molecules such that the direction of maximum polarizability is along the electric vector. This results in a nonlinear dependence of the dielectric constant on the electric field. For weak fields the dielectric constant varies linearly with the intensity; however, for strong fields all the molecules will get aligned and the dielectric constant attains a saturation value (see Problem 9.7).