Optical properties of liquid carbon measured by femtosecond spectroscopy

A comprehensive report of femtosecond time-resolved reflectivity and transmission of graphite and diamond following optical excitation above critical melting fluences ${\mathit{F}}_{\mathit{m}}$ of 0.13 and 0.63 J/${\mathrm{cm}}^{2}$, respectively, is presented. Normal- and oblique-incidence reflectivity has been measured with 100-fs resolution at wavelengths ranging from 700 to 310 nm. Within 1 ps following excitation above ${\mathit{F}}_{\mathit{m}}$, probe reflectance increases sharply at visible frequencies, remains nearly unchanged at near-ultraviolet frequencies, and depends weakly on excitation fluence. These optical changes are interpreted as an ultrafast melting transition from crystalline graphite or diamond to a common, more reflective liquid state. During the first picosecond following excitation, electron and lattice temperatures substantially equilibrate, and the lattice melts, before heat conducts out of the absorbing volume or the surface hydrodynamically expands. A Drude model of the reflectance spectrum 1 ps after excitation reveals a strongly damped plasma (plasma frequency-relaxation time product ${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$\ensuremath{\tau}\ensuremath{\sim}1), in contrast to liquid silicon (${\mathrm{\ensuremath{\omega}}}_{\mathit{p}}$\ensuremath{\tau}\ensuremath{\sim}5). Inferred electron mean free paths approach the average interatomic spacing (2 \AA{}), implying electron localization. Optically determined dc resistivities up to 625\ifmmode\pm\else\textpm\fi{}75 \ensuremath{\mu}\ensuremath{\Omega} cm agree with measurements at kilobar ambient pressure, but significantly exceed resistivities measured and calculated at low pressure. Thus, the attribution ``metal'' is questionable for fluid carbon under these conditions. The results demonstrate that femtosecond lasers can extend condensed-matter thermophysics measurements to temperature-pressure regimes inaccessible by other methods.