Optical second-harmonic susceptibilities: Frequency-dependent formulation with results for GaP and GaAs.

A formula for frequency-dependent optical second-harmonic susceptibilities for insulating crystals, including local-field corrections, is presented. In analogy to a formula given previously for the static limit, the formula is analyzed in terms of ``virtual electron'' (ccv) and ``virtual hole'' (vvc) terms to obtain a numerically stable form. Numerical results for GaP and GaAs agree with most of the experimental values suggested in a recent review article by Roberts. Miller's ${\mathrm{\ensuremath{\Delta}}}_{\mathit{M}}$ is predicted to vary by 13% from the laser lines at 10.6 to 1.32 \ensuremath{\mu}m for GaP.