Third- and fourth-order analysis of the intensities and polarization dependence of two-photon absorption lines ofGd3+in LaF3and aqueous solution

A comprehensive report and analysis of our observations of numerous parity-allowed direct two-photon transitions within the $4f^7$ configuration of the ${\mathrm{Gd}}^{3+}$ ion is presented. The experimental technique is ultraviolet fluorescence detection following optical excitation with a dye-laser beam. Previous results and analyses are extended in three ways. (1) The intensities and polarization dependence of individual Stark components, in addition to integrated multiplet intensities, are reported and analyzed for ${\mathrm{Gd}}^{3+}$:La${\mathrm{F}}_3$. In those cases (${}_{}{}^8{}_{}{}^{}S_{\frac{7}{2}}^{}{}_{}{}^{}\to {}_{}{}^6{}_{}{}^{}P_{\frac{5}{2}}^{}{}_{}{}^{},{}_{}{}^6{}_{}{}^{}D_{\frac{9}{2},\frac{3}{2},\frac{5}{2}}^{}{}_{}{}^{}$) where a second-order theory of two-photon absorption adequately explains the integrated intensity, it also (with the exception of ${}_{}{}^6{}_{}{}^{}D_{\frac{9}{2}}^{}{}_{}{}^{}$) explains the Stark-component intensities. The remaining transitions are anomalously strong, and in some cases violate the angular momentum selection rules $\Delta L,\Delta J\le 2$ and exhibit strong anisotropies, in contradiction to the second-order theory. It is shown that introduction of third- and fourth-order contributions involving spin-orbit and/or crystal-field interactions among levels of the $4f^{6}5d$ configuration, which serve as intermediate states, can account for both the integrated and Stark-component intensities of these transitions. (2) The strong anisotropy observed for the transitions ${}_{}{}^8{}_{}{}^{}S_{\frac{7}{2}}^{}{}_{}{}^{}\to {}_{}{}^6{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{},{}_{}{}^6{}_{}{}^{}I_J^{}{}_{}{}^{},{}_{}{}^6{}_{}{}^{}D_{\frac{1}{2}}^{}{}_{}{}^{}$ in ${\mathrm{Gd}}^{3+}$:La${\mathrm{F}}_3$ is explained quantitatively as a polarization-dependent interference between contributions to the intensity which are comparable in magnitude. Interference is destructive for $\overrightarrow{E}\parallel \hat{z}$ and constructive for $\overrightarrow{E}\perp \hat{z}$, creating an order-of-magnitude contrast in the line strength for the two polarizations. (3) A two-photon excitation spectrum of