An Evaluation of Inverse Reflectivity 1/|r|^2 as a Foundation of (w/wp) for (k/k_F ) = 0.005, 0.05 and 0.1 with rs = 0.3wp and 0.15 wp

Nonlocal effects in metal optics lead to rapidly varying longitudinal field near the surface but far from the surface only transverse electromagnetic field survive. This is true even at and above the plasma frequency, since the damping plasma wave is typically by a factor c/vp longer than that of the transverse waves. Within the very successful classical longer than that of the transverse waves. Within the very successful classical Fresnel optics, which consider only transverse field, all the optics properties of a clean metal surface are determined by the bulk dielectric function of the metal (and the adjacent medium) which is a function of frequency. It seems desirable to have a similar description of the nonlocal surface effect in term of one or two general function which depend only on frequency and allow to calculate all the optical properties