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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?

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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.

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Thank you so so much! That is exactly what I looking for! – Rodrigo Thomas May 13 '11 at 22:30

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