Making precise predictions of the Casimir force between metallic plates via a weighted Kramers-Kronig transform

The possibility of making precise predictions for the Casimir force is essential for the theoretical interpretation of current precision experiments on the thermal Casimir effect with metallic plates, especially for submicron separations. For this purpose it is necessary to estimate very accurately the dielectric function of a conductor along the imaginary frequency axis. This task is complicated in the case of ohmic conductors because optical data do not usually extend to sufficiently low frequencies to permit an accurate evaluation of the standard Kramers-Kronig integral used to compute epsilon(i xi). By making important improvements to the results of a previous paper by the author, it is shown that this difficulty can be resolved by considering suitable weighted dispersion relations, which strongly suppress the contribution of low frequencies. The weighted dispersion formulas presented in this paper permit us to estimate accurately the dielectric function of ohmic conductors for imaginary frequencies, on the basis of optical data extending from the IR to the UV, with no need for uncontrolled data extrapolations toward zero frequency that are necessary with standard Kramers-Kronig relations. Applications to several sets of data for gold films are presented to demonstrate the viability of the dispersion formulas presented in this paper.