Influence of<i>d</i>orbitals on the nonlinear optical response of transparent transition-metal oxides

Abstract

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 ${\mathrm{\ensuremath{\chi}}}^{(1)}$ and lowest-order nonlinear polarizability ${\mathrm{\ensuremath{\chi}}}^{(2)}$, but not for ${\mathrm{\ensuremath{\chi}}}^{(3)}$. The d-orbital contributions to linear and nonlinear response are found to be negligible for bond lengths d\ensuremath{\gtrsim}2.3 \AA{}, but to increase rapidly as a function of decreasing bond length within each TM series to become dominant when d\ensuremath{\lesssim}2.0 \AA{}. Numerical evaluations of nonlinear refractive index ${\mathit{n}}_{2}$ are presented for each series of TM oxides.