Spectroscopy and analysis of radiative and nonradiative processes in ${\mathrm{Ti}}^{3+}$:${\mathrm{Al}}_2$${\mathrm{O}}_3$ crystals

Experimental spectroscopic and time-resolved luminescence measurements of the ${\mathrm{Ti}}^{3+}$:${\mathrm{Al}}_2$ ${\mathrm{O}}_3$ crystalline system have been performed. The absorption and fluorescence spectra obtained have led to a reconsideration of prevailing theoretical models for the radiative relaxation process in Ti:sapphire crystals. A realistic, two-dimensional configuration-coordinate space model has been constructed to describe the Jahn-Teller distortion of the system. Consideration of the nonlinear contributions to the electron-lattice coupling potential was found to contribute little to the second luminescence emission maximum, thus indicating that the electron-phonon interaction is essentially linear in the ground state. The main effect of the nonlinearity was found to be in the value of the nonradiative activation energy. The spin-orbit coupling was also incorporated in the model and was shown to be responsible for the nonradiative transitions in ${\mathrm{Ti}}^{3+}$:${\mathrm{Al}}_2$ ${\mathrm{O}}_3$, while the phonon structure of the ground ${(}^2$ ${\mathit{T}}_2$) state of the system results from both spin-orbit and nonlinear coupling with the lattice.