Anisotropy of the Optical Constants and the Band Structure of Graphite

Abstract

Detailed experimental results have been obtained on the reflectivity of both natural and pyrolytic graphite single crystals in the visible and ultraviolet regions. Results have been taken for both $E\ensuremath{\perp}c$ and $E\ensuremath{\parallel}c$ at near-normal incidence, and as a function of angle of incidence for radiation having its electric vector both perpendicular and parallel to the plane of incidence. These latter results, used in conjunction with an analysis of the Fresnel relations for anisotropic materials, permit extremely accurate values of the optical constants to be obtained both parallel and perpendicular to the crystal planes. The results show that ${k}_{z}$, the absorption index perpendicular to the cleavage planes, is identically equal to zero at all energies below about 5 eV, as expected from the two-dimensional approximation of the energy bands in graphite. A three-dimensional calculation is performed to explain the above picture. The optical constants here obtained explain the electron-energy-loss experiments on graphite and require the absence of the low-energy plasmon along the $c$ axis. The newly developed Fresnel analysis presented here can find general application to all highly anisotropic materials.