Two-photon resonant effect of hyper-Raman scattering in the vicinity of the direct forbidden gap in a rutile crystal

A two-photon resonance effect of the hyper-Raman scattering from optic phonons was investigated in a rutile crystal at 30 K near the direct forbidden energy gap ${\mathit{E}}_{\mathit{g}}$. The scattering efficiency of the allowed modes in the 90° scattering geometry was found to increase remarkably, as twice the incident photon energy, 2ħ${\mathrm{\omega }}_{\mathit{i}}$, approaches ${\mathit{E}}_{\mathit{g}}$ from below. The result can be reasonably interpreted in terms of a two-photon ingoing resonance with ${\mathit{E}}_{\mathit{g}}$. Further, the forbidden LO mode in the backward-scattering geometry was also found to show a sharp two-photon resonant behavior at the band edge. The origin may be attributed to resonance with the excitons due to the q-dependent Fröhlich interaction.