Effect of a external EM field on a dielectric

Question

If an external EM field (a laser, for example) act on a dielectric (a glass, for example) what will be the effect of this field on the dielectric constant and on the refractive index of the material? How, mathematically speaking, could I explain what is happen?

Answer 1

In linear electrodynamics (i.e. low intensities), the dielectric constant and refractive index remain unchanged. A different thing is nonlinear optics (applying to ED in general as well), for more theory see e.g. here. But this happens only for materials with strong non-linear parameters (usually $\chi^{(2)}$ or $\chi^{(3)}$) and for rather high field intensities. This usually yields effect such as the second harmonic generation, but there is also the effect of self-focusing among others, which stems from the dependence of the refractive index on the field amplitude.