Refractive index of dense materials

We show that applying the Lorentz-Lorenz transformation to the refractive index of metals and semiconductors allows for a less empirical modeling of this refractive index. The dielectric constant ε of an assembly of polarizable point particle is well described by the Clausius-Mossoti formula (ε-1) / (ε+2)=C ρ α where ρ is the density of particles α their polarizability and C a constant. Both ε and α are complex numbers and frequency dependent. In the optical domain this equation can be rewritten as (n²-1) / (n²+2) =C ρ α known as Lorentz-Lorenz formula. This formula has no basis for being applied to metals, but an empirical use reveals an interesting phenomenon. The most striking case is that of silver. The real and imaginary part of the so computed " polarizability " are shown in fig 1 as a function of the wavevector : Figure 1 : Real (top) and imaginary part of the polarizabilty calculated by application of the Lorentz-Lorenz formula to the refractive index of silver as a function of the wavevector (in cm-1