Abstract
From the analytical properties of the third-harmonic generation susceptibility and from its asymptotic behaviour in the frequency variable, a set of eight Kramers - Kronig relations and nine sum rules are obtained. These universal constraints are used to generate a simplified model for the static limit of in insulating systems with inversion symmetry. The static limits of calculated within this model for silicon and germanium are shown to be in qualitative agreement with the experimental data.
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