Resonant phenomena of hyper-Raman-scattering of optic phonons in aTiO2crystal

We report two-photon-resonant phenomena of hyper-Raman-scattering by optic phonons in ${\mathrm{TiO}}_2$. It is found that the scattering efficiency of the allowed mode in the 90°-scattering geometry increases remarkably as twice the incident photon energy, 2ħ${\mathrm{\omega }}_{\mathit{i}}$, approaches the direct forbidden energy gap from below. In addition, the configuration-forbidden LO mode in the backward-scattering geometry is found to show a sharp two-photon-resonant behavior at the band edge. The prominent polarization dependence of the phenomena is observed, reflecting the anisotropic nature of ${\mathrm{TiO}}_2$. Further, the absolute value of the scattering efficiency is estimated as a function of 2ħ${\mathrm{\omega }}_{\mathit{i}}$. It is shown that these results can be interpreted quantitatively with a model on the basis of the electronic band structure. In the course of the analysis, we have estimated the second-lowest-direct-gap energy as 3.10 eV. Finally, we emphasize that the resonant hyper-Raman spectroscopy would be useful as a method for studying the band structure in solids.