High-Frequency Franz-Keldysh Effect

Abstract

Theoretical analysis of the electric-field perturbation of optical properties exhibited by a semiconductor in the spectral region near the energy gap is extended to the case of very high-frequency applied fields. The transition rate due to incident photons of energy $\ensuremath{\hbar}\ensuremath{\Omega}$ approximating the energy gap of the material is found to be modulated at a basic frequency of $2\ensuremath{\omega}$, where $\ensuremath{\omega}$ is the frequency of the applied field. Components of the current associated with these transitions have frequencies of $\ensuremath{\Omega}\ifmmode\pm\else\textpm\fi{}2n\ensuremath{\omega}$ and $(2n+1)\ensuremath{\omega}$. These may be regarded as sources for sidebands and harmonics of the applied radiations. The compatability of these results with both the low-frequency Franz-Keldysh effect and the two-photon absorption process is demonstrated; in addition, an example selected to lie in the intermediate range where neither of the latter explanations is appropriate is analyzed.