Optical Third-Order Mixing in GaAs, Ge, Si, and InAs

Nonlinear optical difference mixing of C${\mathrm{O}}_{2}$ laser radiation is studied in the semiconductors GaAs, Ge, Si, and InAs. The fourth-rank electric susceptibility tensor receivers independent contributions from the bound or valence electrons, ${\ensuremath{\chi}}^{b}$, and, in $n$-type material, from the conduction electrons ${\ensuremath{\chi}}^{n}$. These two contributions are separated and measured in GaAs. ${\ensuremath{\chi}}^{b}$ is found to be anisotropic and ${\ensuremath{\chi}}^{n}$ to be isotropic for carrier concentrations $nl~5\ifmmode\times\else\texttimes\fi{}{10}^{16}$. The relative signs of the susceptibilities are determined. ${\ensuremath{\chi}}^{b}$ in Ge and GaAs and ${\ensuremath{\chi}}^{n}$ in GaAs and InAs all have the same sign for the particular frequency combination studied. Theoretical and experimental evidence indicate that this sign is positive. At room temperature, ${\ensuremath{\chi}}^{n}$ in GaAs is a liner function of $n$ for $nl~{10}^{16}$. The value of the slope $\frac{\ensuremath{\partial}{\ensuremath{\chi}}^{n}}{\ensuremath{\partial}n}$ is a direct measure of the nonparabolicity of the conduction band in GaAs. It is shown to be inconsistent with Kane's model for small direct-band-gap semiconductors, and in agreement with Cardona's indirect measurements of the nonparabolicity in GaAs.