The Franz-Keldysh effect revisited: Electroabsorption including interband coupling and excitonic effects

We study the linear optical absorption of bulk semiconductors in the presence of a homogeneous constant (dc) electric field with an approach suitable for including excitonic effects while working with many-band models. The absorption coefficient is calculated from the time evolution of the interband polarization excited by an optical pulse. We apply the formalism to a numerical calculation for GaAs using a 14-band $\textbf{k} \cdot \textbf{p}$ model, which allows us to properly include interband coupling, and the exchange self-energy to account for the excitonic effects due to the electron-hole interaction. The Coulomb interaction enhances the features of the absorption coefficient captured by the $\textbf{k} \cdot \textbf{p}$ model. We consider the dependence of the enhancement on the strength of the dc field and the polarization of the optical field.