Two-photon absorption in Ge: Band effects

Calculations are reported of the two-photon absorption in germanium using a Kane band model. All bands within 10 eV of the valence-band edge are considered. The matrix elements are evaluated using $\overrightarrow{\mathrm{k}}·\overrightarrow{\mathrm{p}}$ theory to find the relevant wave functions. The spherical model of Baldereschi and Lipari is used to treat the distinction between the light-hole and heavy-hole bands properly. Detailed calculations are made to test various approximations that simplify the evaluation of these complicated nonlinear optical coefficients. For Ge it is essential that the split-off band be included as an intermediate state and that the nonparabolicity of the conduction band be treated correctly. The results of the most complete calculation are in good agreement with experimental results.