Kramers-Kronig transform for the surface energy loss function

A new pair of Kramers-Kronig (KK) dispersion relationships for the transformation of surface energy loss function Im[−1/(ɛ + 1)] has been proposed. The validity of the new surface KK transform is confirmed, using both a Lorentz oscillator model and the surface energy loss functions determined from the experimental complex dielectric function of SrTiO3 and tungsten metal. The interband transition strength spectra (Jcv) have been derived either directly from the original complex dielectric function or from the derived dielectric function obtained from the KK transform of the surface energy loss function. The original Jcv trace and post-Jcv trace overlapped together for the three modes, indicating that the new surface Kramers-Kronig dispersion relationship is valid for the surface energy loss function.