Dispersion of nonlinear optical susceptibilities of InAs, InSb, and GaAs in the visible region

We have measured the dispersion of $\left|{\chi }^{\mathrm{}\left(2\right)\mathrm{}}\right(2\mathrm{}\omega \left)\right|$ for the III-V semiconductors InAs, InSb, and GaAs at 80 and 300 K, with $\hslash \omega$ between 2.0 and 2.7 eV. Large dispersion in $\left|{\chi }^{\mathrm{}\left(2\right)\mathrm{}}\right(2\mathrm{}\omega \left)\right|$ is found for all three semiconductors, while the results for the two temperatures are similar. We compare the observed structures in ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}$ with those in ${\chi }^{\mathrm{}\left(1\right)\mathrm{}}\left(\omega \right)$ and ${\chi }^{\mathrm{}\left(1\right)\mathrm{}}\left(2\mathrm{}\omega \right)$, and derive Miller's $\Delta$ from our experimental values. We also compare our measured ${\chi }^{\mathrm{}\left(2\right)\mathrm{}}\left(2\mathrm{}\omega \right)$ with recent theoretical results obtained from empirical pseudopotential calculations.