Since in the medium there is a dispersion we can not neglect, the relationship between the electric field and its polarization is given by a convolution integral.
\tilde{E} (\mathbf{r},\omega - \omega_0) = \int\limits_{-\infty}^{\infty}\!\! E (\mathbf{r}, t ) e^{-i (\omega - \omega_0)t} dt .