Photoelastic effect in Ti3+-doped sapphire.

We have used photothermal-beam-deflection spectroscopy to measure the change in the index of refraction of ${\mathrm{Ti}}^{3+}$-doped sapphire after pulsed excitation at 532 nm with a neodymium-doped yttrium aluminum garnet laser. The beam-deflection signal arises from both thermal and nonthermal sources. The nonthermal part of the signal decays with the fluorescence lifetime of ${\mathrm{Ti}}^{3+}$ in sapphire. The shape of the nonthermal part depends on whether the probe beam is polarized perpendicular (\ensuremath{\sigma}) or parallel (\ensuremath{\pi}) to the c axis of the crystal. This behavior can be explained by a photoelastic law based upon the anisotropic volume expansion caused by a strong Jahn-Teller effect of the ${\mathrm{TiO}}_{6}$ complex in the excited state. The experimental values of the change in the index of refraction for each ion per unit volume are \ensuremath{\Delta}n/N=3.3 A${\mathrm{\r{}}}^{3}$ and \ensuremath{\Delta}n/N=1.2 A${\mathrm{\r{}}}^{3}$ for \ensuremath{\sigma} and \ensuremath{\pi} polarization, respectively, compared with the calculated values of \ensuremath{\Delta}n/N=3.73 A${\mathrm{\r{}}}^{3}$ (for \ensuremath{\sigma}) and \ensuremath{\Delta}n/N=1.50 A${\mathrm{\r{}}}^{3}$ (for \ensuremath{\pi}) for a model that includes the photoelastic law. The bulk expansion per ${\mathrm{TiO}}_{6}$ complex, derived from the beam-deflection signal, is \ensuremath{\approxeq}11.8 A${\mathrm{\r{}}}^{3}$, while the calculated value based on the configuration-coordinate model is \ensuremath{\approxeq}9.9 A${\mathrm{\r{}}}^{3}$.