Fig. 1. (a) Supercell structure of Al2O3. (b) Four kinds of Ti3+−Ti3+ ion pair models. (c) 3Ti4+−VAl3− model. (d)–(f) Three kinds of Ti3+−3Ti4+−VAl3− models.

Fig. 2. Experimental absorption spectrum of Ti:sapphire sample with a doping concentration less than 0.16% (mass fraction) (on the left) and the simulated absorption spectrum of substitutional Ti-doped model with a theoretical doping concentration more than 3.6% (mass fraction) (on the right). There is a step at 860 nm on the experimental absorption spectrum, which is caused by the test system. The calculated PDOS distribution of Ti_3d is inserted into the simulated absorption spectrum.

Fig. 3. Band structure (on the left) and polarized absorption spectrum of line-contact Ti3+−Ti3+ ion pair model (on the right).

Fig. 4. The DOS of the supercell Ti2Al46O72, the LDOS of Al, O and Ti, and the PDOS of s, p, d electrons of line-contact Ti3+−Ti3+ ion pair model.

Fig. 5. Optimized charge distributions of HOMO, LUMO, and LUMO+i (i=1,2,3,4) of line-contact Ti3+−Ti3+ ion pair model. HOMO is the highest occupied molecule orbital. LUMO is the lowest unoccupied molecule orbital, while LUMO+1 means the first adjacent orbital above it, and so on for LUMO+i in a similar fashion. The blue-shaded area is the probability distribution of electrons in space, and the green spheres covered by it represent Ti ions.

Fig. 6. Band structure, Ti_3d_PDOS, and polarized absorption spectrum of 3Ti4+−VAl3− model.

Fig. 7. Band structure, Ti_3d_PDOS, and polarized absorption spectrum of face-contact Ti3+−Ti4+ ion pair model.

Fig. 8. Optimized charge distributions of HOMO, LUMO, and LUMO+j (j=1, 2, 3, 10) of face-contact Ti3+−Ti4+ ion pair model (see caption of Fig. 5 for details).