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, ${\chi }^b$, and, in $n$-type material, from the conduction electrons ${\chi }^n$. These two contributions are separated and measured in GaAs. ${\chi }^b$ is found to be anisotropic and ${\chi }^n$ to be isotropic for carrier concentrations $n<~5\times {10}^{16}$. The relative signs of the susceptibilities are determined. ${\chi }^b$ in Ge and GaAs and ${\chi }^n$ 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, ${\chi }^n$ in GaAs is a liner function of $n$ for $n<~{10}^{16}$. The value of the slope $\frac{\partial {\chi }^n}{\partial n}$ 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.