The dielectric function for metals with low absorption can be defined as:

The contribution to the dielectric function from the total electric potential is assumed to average out, so that only the potential at wave vector k contributes.

The optical dielectric function is given by the fundamental expression:

This result is same as the classical dielectric function.

Therefore the dielectric function for the incident photon energy below the band gap exist!

This screening yields a dielectric function .

Below the plasma frequency, the dielectric function is negative and the field cannot penetrate the sample.

For the position of the dynamical image plane, it decreases with increasing dielectric function and is typically on the order of 0.2 Å.

The oscillations can be described as an instability in the dielectric function of a free electron gas.

This can be converted into a wavevector-dependent dielectric function: