Opto-criticality in Drude metals near the plasma frequency

Abstract

Within a simple unified framework of classical electrodynamics that incorporates background bound charges and currents, we have analytically determined the attenuation constant, phase constant, and reflectivity of Drude metals across the full frequency spectrum ($0<\omega <\infty$).Our result for reflectivity agrees well with existing experimental data for both plasmas and seawater. Notably, for highly conductive Drude metals (${\omega }_p\tau \gg 1$), the attenuation constant simplifies to $k_{-}\simeq \sqrt{\frac{\mu \epsilon }{2}}\sqrt{{\omega }_p^2-{\omega }^2+|{\omega }_p^2-{\omega }^2|}$ across a broad high-frequency range spanning the plasma frequency ${\omega }_p$. The branch-point singularity at $\omega ={\omega }_p$ in this relation reveals opto-critical behavior near $\omega ={\omega }_p$ in properties such as the attenuation constant, group velocity, and complex dielectric constant, for which we have determined the corresponding opto-critical exponents. Furthermore, we have incorporated quantum corrections into these optical properties via the Drude-Sommerfeld model with Thomas-Fermi screening.

arXiv comment8 pages, 2 figures