Dispersion of phonon-assisted nonresonant third-order nonlinearities

An analysis of the dispersion of two-photon absorption and Kerr nonlinearity of indirect semiconductors below the indirect bandgap is presented. Similar to the case of linear absorption, third-order nonlinear processes are found to be mediated by phonon-assisted transitions. The Kerr coefficient n(2) is positive below the indirect gap, and the dispersion of the third-order non-linearities is reduced relative to direct semiconductors. The results are compared with existing experimental data in silicon.