Refractive index of the alkali halides.mI. Constant joint density of states model

Abstract

The electronic contribution to the imaginary part of the dielectric function of the alkali halides is assumed to be proportional to ${\mathrm{E}}^{\mathrm{\ensuremath{-}}2}$ above the onset of optical absorption, which is equivalent to the assumption of a constant joint density of states (CJDOS) model. In this approach the electronic contribution to the refractive index can be described by two parameters, the long-wavelength limit of the refractive index ${\mathrm{n}}_{\mathrm{\ensuremath{\infty}}}$ and the frequency of the onset of optical absorption ${\mathrm{E}}_{\mathrm{x}0}$ . Various fits of the corresponding model function to experimental dispersion data show that ${\mathrm{E}}_{\mathrm{x}0}$ is closely related to the frequency of the lowest exciton. Exciton absorption and interband transitions from the p valence bands to s and d conduction bands make the main contributions to the imaginary part of the dielectric function. The relative shifts of the s and d bands with respect to the p bands with density have different signs, and make different contributions to the photoelastic behavior. The CJDOS model is extended to account for the different behavior of s and d bands, and it is shown that the available literature data for the density dependence of the refractive index can be related to the energies of the s and d bands, derived from optical spectra and band-structure calculations. Shock data for LiF and NaCl are discussed, as well as low-pressure results for KCl, KBr, and KI. Recent high-pressure results for CsI show a strong nonlinear density dependence of the refractive index, in contrast to the almost linear behavior of the lighter alkali halides. Within the CJDOS model, this nonlinear behavior can be related to the closure of the band gap in CsI.