Hagen-Rubens relation beyond far-infrared region

An extension of Hagen-Rubens relation beyond the far-infrared region is proposed by taking into account inertial effects due to charge carriers. The influence of inertia is described by introducing a finite relaxation time τ for the current density in the framework of a generalized Ohm's law. A closed formula for τ as a function of metallic permittivity and radiation frequency is derived. Our approach is applied to aluminum for which it is found that τ~6.91 fs at room temperature. It is also shown that the behavior of the observed absorptivity by that metal is in excellent agreement with our formulation up to the near-infrared region. The macroscopic approach proposed here is totally independent of other microscopic formulations such as Drude's theory of metallic conduction. Applications of our theory to related problems can lead to progress in extending the classical theory for the optics of metals.