Criticality in optical properties of the Drude and Drude-Sommerfeld metals around the plasma frequencies for high carrier concentrations

We have analytically determined the attenuation constant of the Drude metal for the entire range of frequency ($0<\omega <\mathrm{\infty }$) of an electromagnetic (plane) wave incident on it within a single framework of classical electrodynamics. Here, by the Drude metal, we mean an electrical conductor that obeys the Drude model for the conduction electrons. We further consider the conductor to have linear dielectric and magnetic properties (i.e. permittivity $\epsilon >{\epsilon }_0$ and permeability $\mu >{\mu }_0$) due to the bound charges and bound currents in the background. Interestingly, for such a conductor with a high carrier concentration (${\omega }_p\tau \gg 1$), we have obtained a simple form of the attenuation constant $k_{-}\simeq +\sqrt{\frac{\mu \epsilon }{2}}\sqrt{{\omega }_p^2-{\omega }^2+\mathrm{\mid }{\omega }_p^2-{\omega }^2\mathrm{\mid }}$ for a wide range of high frequencies below and above plasma frequency ${\omega }_p$. Such a result gives rise to criticality in the conductor’s optical properties, such as – the attenuation constant, group velocity, and complex dielectric constant near around $\omega ={\omega }_p$. We have obtained the critical exponents for these quantities. We also have obtained a quantum correction to the optical properties within the Drude-Sommerfeld model with the Thomas-Fermi screening.