Lowest-Order Optical Nonlinearity in InSb: Theory of Dispersion near the Band Gap

A model for the lowest-order optical nonlinearity in InSb is presented. A method for ensuring the cancellation of sizeable contributions throughout the Brillouin zone is incorporated in the model. A calculation, based on the band structure of InSb at $k=0\mathrm{}$, successfully accounts for the dispersion of the optical nonlinearity near the band gap, measured by a second-harmonic-generation (SHG) experiment in InSb. General results are also presented on the interpretation of SHG measurements in absorbing media, with special attention devoted to interference experiments. From a comparison of the experimental dispersion with the theory, values are obtained for momentum matrix elements near $k=0\mathrm{}$.