High-Frequency Franz-Keldysh Effect

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 $\hslash \Omega$ approximating the energy gap of the material is found to be modulated at a basic frequency of $2\omega$, where $\omega$ is the frequency of the applied field. Components of the current associated with these transitions have frequencies of $\Omega \pm 2n\omega$ and $\mathrm{}(2n+1)\mathrm{}\omega$. 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.