Superconvergence and sum rules for the optical constants: physical meaning, comparison with experiment, and generalization

A physical interpretation of recently obtained sum rules for dielectric functions and for the index of refraction is provided in terms of the inertial properties of the linear dielectric response of material media. The superconvergent sum rules are then compared with experimental optical data for AgCl, Al, and Mo and shown to produce good agreement as well as a critical test of extrapolations and of the Kramers-Kronig relations. A straightforward extension to higher powers of the optical constants and their moments is briefly discussed.