Frequency-dependent criticality in optical properties of the Drude metals, including plasmas and seawater

Abstract

We have analytically determined attenuation constant, phase constant, and reflectivity of Drude metals over the entire frequency range ($0<\omega<\infty$) for an incident electromagnetic (plane) wave, within a single framework of classical electrodynamics, taking into account bound charges and currents in the background. We have compared our result with existing experimental data for the reflectivity of plasmas and that of seawater in this regard. Interestingly, for the Drude metal with a high carrier concentration ($\omega_p\tau\gg1$), we have obtained a simple form of attenuation constant $k_-\simeq+\sqrt{\frac{\mu\epsilon}{2}}\sqrt{\omega_p^2-\omega^2+|\omega_p^2-\omega^2|}$ for a wide range of high frequencies below and above plasma frequency $\omega_{p}$. Such a result gives rise to criticality in conductors' optical properties, such as attenuation constant, group velocity, and complex dielectric constant, \textit{etc} near around $\omega_{p}$. We have obtained critical exponents for these quantities. We have also obtained a quantum correction to the optical properties within the Drude-Sommerfeld model with the Thomas-Fermi screening.