Strain-induced birefringence in GaAs

We present the results of density-functional calculations of the dielectric function and the photoelastic tensor---the susceptibility for strain-induced birefringence---in GaAs for photon frequencies below the direct band gap. These calculations were performed in the Kohn-Sham local-density approximation in a pseudopotential/plane-wave scheme which includes local-field effects and self-energy corrections. We find that traditional special-points integration methods are inadequate for performing the Brillouin-zone integrals involved in computing the photoelastic tensor. Very high resolution of the critical point at {ital k}=0 is needed to obtain even the correct {ital qualitative} behavior of the photoelastic tensor. Accurate expansions of the integrand in spherical harmonics for small {ital k} and plane waves elsewhere in the Brillouin zone were obtained and an integration approach which correctly integrates the expansions was used. Dramatic improvement in the qualitative frequency dispersion of the photoelastic tensor, in comparison with experiments, is obtained despite a large (50%) shift of the static value away from the measurement. We also present the result of a calculation of the internal strain relaxation associated with strains along the bonding [111] direction. These results are in excellent agreement with two previous {ital ab} {ital initio} calculations and with recent measurements.