Physical origin of Kerr effect I was wondering if someone could explain to me the physical (not mathematical) origin behind the Kerr effect and why it results in birefringence in materials.
Also, can the birefringence be introduced through the optical Kerr effect (achieved through high intensity linearly polarized light instead of through an application of a strong DC field).
Thank you very much
Nikolaos
 A: So, I can try to explain this more in a qualitative, descriptive way, rather than in a physical way, which perhaps will help you better understand what is happening. Also, this is highly simplified.
When light propagates through a crystalline dielectric material, it displaces the valence electrons within their potential wells, so we have 2 forces acting on them: the EM field pulling the electrons up the potential well, and the potential well, in turn, is making the electrons be pulled back towards the bottom, so a restitution force. The wells are well approximated by a parabola at the points where the electrons are. This movement of the electrons, same frequency as the propagating EM field, creates dipoles and in turn also generates an EM field which superimposes with that of the original, except is slightly phase shifted, which gives rise to the propagation of light through dielectrics.
But getting back to the electrons in their valence wells, as I said, the wells are well approximated by parabolas, and so the motion, for weak EM driving fields, is a harmonic motion, which mimics perfectly that of the EM driving field. See for example the picture below where I show a made up well and the parabolic approximation close to the bottom. Now, you need to understand that the wells are not 1D like I show below, but 3D. In every direction, the electron feels the restitution force and in every direction the well looks like I show. However, if the electrons can be moved "higher up" into the well in a direction, the well no longer resembles a parabola, or, in the case of a very weak EM driving field, for the DC effect, the parabolic approximation at the location of the electron is now different, than that at the resting point. This means that the phase shift and dipoles induced by the EM field are no longer the same between the resting point and the current electron point (for DC Kerr effect). Imagine an electron staying up the wall after a DC field is applied to the material. In a transversal direction, it is like no field is applied and it is just like the electron would be at the bottom of the well. This creates a birefringence: in one direction (same as DC) the electron is displaced from the bottom , and the induced dipole at that location, in the same direction of the DC field will have different properties to those excited in other transversal directions, which behave just like if the electron would be at the bottom!
Now, for the optical Kerr effect, just picture the electron swinging so high on the walls of the well that the motion is no longer harmonic, but has other frequency components as well: for example, in the picture below, as it goes higher on the well wall, it becomes easier for the field to keep pushing the electron up the well (the parabola would mean the needed "strength", or amplitude, to be exactly sine or co-sine, but as the well now is below that point, this means the electron can go up higher the well) which in turn means there are additional acceleration terms on the electron's motion, and if you know that an accelerating charge creates an EM field, you see that you are effectively generating new frequencies as the electrons swings high on the well.
I hope this is clear enough to understand where the effect comes from, in a simplified picture.
(I made the following picture in a hurry, not accurate, but shows what I want to illustrate)

