Figure 1

Calculated two-photon Franz-Keldysh effect in GaAs for $E_{\mathrm{dc}}=67$ kV/cm. (Blue or gray dotted) No dc field; (Red or gray dashed) ${\mathbf{E}}_{\mathrm{opt}}\perp {\mathbf{E}}_{\mathrm{dc}}$; (black solid) ${\mathbf{E}}_{\mathrm{opt}}\parallel {\mathbf{E}}_{\mathrm{dc}}$. (a) Two-photon absorption spectrum $\beta (\omega )$ using a model with two bands in the parabolic band approximation (PBA, thin lines) and an eight-band $\mathbf{k}·\mathbf{p}$ model (thick lines). The inset shows a close-up view of the absorption spectrum near the half band gap $\hslash {\omega }_g/2$, with the units on the two axes the same as the main plot. (b and c) Two-photon electroabsorption spectrum [$\beta (\omega )$ with a dc field minus $\beta (\omega )$ without a field]. (Red dashed) ${\mathbf{E}}_{\mathrm{opt}}\perp {\mathbf{E}}_{\mathrm{dc}}$; (black solid) ${\mathbf{E}}_{\mathrm{opt}}\parallel {\mathbf{E}}_{\mathrm{dc}}$. The half band gap is marked with an arrow. (b) Two-band PBA model. (c) Eight-band $\mathbf{k}·\mathbf{p}$ model.Reuse & Permissions