Pressure and stress dependence of the refractive index of transparent crystals.

The pressure derivative of the refractive index (dn/dP) and the elastooptic constants (P(ij)) in the transparent frequency regime of semiconducting and ionic crystals are investigated theoretically. The electronic contribution to dn/dP of semiconductors is obtained by carrying out pseudopotential calculations of the band structure as a function of hydrostatic pressure, and the results compared with experiment. The lattice contribution to dn/dP is obtained by relating dn/dP to changes in the effective ionic charge and the phonon spectrum as functions of pressure. As for the P(ij), we perform a detailed application of the theory of Humphreys and Maradudin to calculate these for a variety of cubic crystals as functions of frequency in the transparent regime. The parameters required in the calculation are determined from improved prescriptions, which relate various microscopic functions to experimental data on the pressure dependence of phonon frequencies. The theoretical results are checked employing a relatio between dn/dP and the P(ij). Overall, one finds that frequency dispersion is most important for the ionic materials and is generally negligible for the more highly covalent materials.