When an intense laser beam passes through a material, the electric field of the beam can induce a change in the refractive index of the material that is proportional to the intensity of the beam. This nonlinear effect is called the Kerr effect. The total refractive index of the material is the sum of the refractive index, n0, with no laser beam present and the term n2 I, where n2 is the second-order nonlinear refractive index and I is the intensity of the beam.

n = n0 + n2 I

The change in refractive index can be positive or negative. Values of n2 are generally small (e.g. approximately 3 x 10-16 cm2 W-1 for silica), so that high beam intensities are required to have a significant effect. In the time domain, the Kerr effect by itself leads to a phase shift and frequency shift, but no self-focusing or de-focusing. However, if the refractive index change is positive, the Kerr effect combined with diffraction can lead to self-focusing of the laser beam since the center of the beam will have higher intensity and a higher refractive index change than the edges of the beam. The index changes are equivalent to having a positive gradient index lens.

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