Weierstrass Institute , Germany

We present our recent results related to the controversy on the all-optical Kerr effect and the actual intensity dependence of the nonlinear refractive index.Using a Kramers-Kronig type relation between nonlinear refraction and absorption enables us to calculate the nonlinear refraction coefficients of noble gases and wide bandgap solids, which is in remarkable agreement with literature values for the lowest order coefficient $n_2$. In addition, we point out the importance of ab-initio numerical methods and possible approaches to obtain conclusive results on the current debate.