Influence ofdorbitals on the nonlinear optical response of transparent transition-metal oxides

The bond-orbital theory of linear and nonlinear electronic response in optically transparent materials, developed earlier for pretransition-metal halides and chalcogenides, is expanded to embrace the transition-metal (TM) oxides. The extension requires an explicit recognition of the influence of cationic empty d orbitals on electronic polarizability. Two competing mechanisms, involving, respectively, virtual electronic excitations to the d orbitals and to the conduction-band ‘‘sp orbitals,’’ are shown to be essentially additive for linear polarizability ${\mathrm{\chi }}^{\mathrm{}\left(1\right)\mathrm{}}$ and lowest-order nonlinear polarizability ${\mathrm{\chi }}^{\mathrm{}\left(2\right)\mathrm{}}$, but not for ${\mathrm{\chi }}^{\mathrm{}\left(3\right)\mathrm{}}$. The d-orbital contributions to linear and nonlinear response are found to be negligible for bond lengths d≳2.3 Å, but to increase rapidly as a function of decreasing bond length within each TM series to become dominant when d≲2.0 Å. Numerical evaluations of nonlinear refractive index ${\mathit{n}}_2$ are presented for each series of TM oxides.