Theoretical studies on the dispersion of the nonlinear optical susceptibilities in GaAs, InAs, and InSb

The nonlinear optical susceptibilities, $\left|{\chi }_{14}^{\mathrm{}\left(2\right)\mathrm{}}\right(2\mathrm{}\omega \left)\right|$ for second-harmonic generation of GaAs, InAs, and InSb in the range $0.05\le \hslash \omega \le 3.0$ eV are calculated from the band structure obtained by the empirical pseudopotential method. The spin-orbit interaction has been taken into account, and the transitions from the top four valence bands to the bottom four conduction bands are included in the calculation. The calculated $\left|{\chi }_{14}^{\mathrm{}\left(2\right)\mathrm{}}\right(2\mathrm{}\omega \left)\right|$ with the $\overrightarrow{\mathrm{k}}$-dependent dipole matrix elements give much better agreement with the available experimental data than the results of constant matrix elements, which, in turn, show more structure than the ones calculated by Bell. In the case of InSb, there are two structures at 1.6 and 1.8 eV due to double resonances. A simplified model to predict structure in $\left|{\chi }_{14}^{\mathrm{}\left(2\right)\mathrm{}}\right(2\mathrm{}\omega \left)\right|$ from the linear spectrum is discussed.