A comprehensive report and analysis of our observations of numerous parity-allowed direct two-photon transitions within the
4f7 configuration of the
Gd3+ 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
Gd3+:La
F3. In those cases ($^{8}S_{\frac{7}{2}}\ensuremath{\rightarrow}^{6}P_{\frac{5}{2}},^{6}D_{\frac{9}{2},\frac{3}{2},\frac{5}{2}}$) where a second-order theory of two-photon absorption adequately explains the integrated intensity, it also (with the exception of
6D29) explains the Stark-component intensities. The remaining transitions are anomalously strong, and in some cases violate the angular momentum selection rules $\ensuremath{\Delta}L,\ensuremath{\Delta}J\ensuremath{\le}2$ 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
4f65d 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 $^{8}S_{\frac{7}{2}}\ensuremath{\rightarrow}^{6}P_{\frac{3}{2}},^{6}I_{J},^{6}D_{\frac{1}{2}}$ in
Gd3+:La
F3 is explained quantitatively as a polarization-dependent interference between contributions to the intensity which are comparable in magnitude. Interference is destructive for $\stackrel{\ensuremath{\rightarrow}}{E}\ensuremath{\parallel}\stackrel{^}{z}$ and constructive for $\stackrel{\ensuremath{\rightarrow}}{E}\ensuremath{\perp}\stackrel{^}{z}$, creating an order-of-magnitude contrast in the line strength for the two polarizations. (3) A two-photon excitation spectrum of
Gd3+ in aqueous solution is reported. Linewidths comparable to those of room-temperature solids and Stark splittings which suggest a low-symmetry quasistatic environment are observed.
Eighteen selected two-photon absorption (TPA) transition line strengths with polarization angles θ = 0° and 45°, spanning several orders of magnitude, have been calculated for the Tb 3+ ion in the cubic host Cs 2 NaTbCl 6 . The results are in reasonable agreement with experimental results in the literature. The calculation utilized the crystal field (CF) wavefunctions for the initial and final states of the 4f 8 configuration, and utilized free ion or CF wavefunctions (with the corresponding energies) for 4f 7 core states of the whole intermediate 4f 7 5d configuration comprising 34 320 states. The intensities of certain transitions were found to be very sensitive to the inclusion of the CF interaction within the 4f 7 core. In contrast to previous fourth- or third-order calculations of the TPA transition line strength of the strong transition ( 7 F 6 )A 1g → ( 5 D 4 )A 1g using pure Russell–Saunders (RS) wavefunctions for the | 7 F 6 ⟩ initial and ⟨ 5 D 4 | final states, our second-order direct calculation shows that the admixed RS wavefunctions |[ 7 F 6 ]⟩ and ⟨[ 5 D 4 ]| must be used to account for its high intensity. The effects of CF interactions within the 4f 7 core, i.e. J -mixing and CF energy level splitting, upon the ( 7 F 6 )A 1g → ( 5 D 4 )E g TPA transition line strength have been separated, and the latter effect is shown to be more important for the transition investigated.
The authors report a detailed analysis of the intensity and polarisation dependence of the 8 S 7/2 to 6 P 7/2 two-photon transition Stark components of Gd 3+ in the concentrated magnetic insulator Gd(OH) 3 under an applied magnetic field (up to 3.5 T) at very low temperature (2 K). The experimental technique consisted of detecting the ultraviolet 6 P 7/2 to 8 S 7/2 one-photon fluorescent emission resulting from two-photon excitation in the 6 P 7/2 states, using a single pulsed dye-laser beam. The standard second-order theory of Axe is shown to fail in explaining the relative intensities of the Stark components. This is especially true in the case of the Delta M=0 transitions for which strong disagreements are observed. It is shown that the introduction of the third-order contribution involving the spin-orbit interaction within the 4f 6 5d states allows the experimental spectra to be reproduced in a correct way. Finally the effects of ion-ion interactions on the two-photon line profiles are discussed.
Two-photon absorption spectroscopy is used to investigate the 8 S 7/2 → 6 P J , 6 I 7/2 transitions of Gd 3+ ions in the cubic elpasolite Cs 2 NaGdCl 6 . The Gd 3+ ions occupy a centro-symmetric site (O h ); so the odd terms of the crystal field vanish and the pure electric dipole transitions should not be observed in one-photon experiments. As a consequence the electric dipole allowed two-photon transitions involving the 6 I 7/2 and 6 P 3/2 excited states are well observed in contrast with their weakness in the one-photon spectrum. Furthermore the magnetic dipole character of the transitions to the 6 P 5/2 and 6 P 7/2 levels is confirmed. The occurrence of the one-photon transition to 6 P 3/2 is tentatively explained by the J mixing involving the 6 P 7/2 excited state. A qualitative analysis of the relative intensities of the transitions to the 6 P J and 6 I 7/2 levels is presented.
Quantitative calculations show that numerous spin-forbidden linear optical transitions observed in trivalent rare earth ions acquire a major fraction of their intensity from hitherto neglected contributions involving spin–orbit linkages within excited configurations. Motivated by the importance of analogous linkages previously demonstrated in two-photon absorption, we derive a general expression applicable for all lN→lN transitions which can be incorporated into a revised Judd–Ofelt analysis of observed intensities. Presenting this revised analysis of observed linear absorption intensities for Gd3+ and Eu3+, we show that the new contribution is often comparable to standard contributions. With substantial modification of previously fitted phenomenological parameters, an improved fit to observed intensities is achieved, suggesting that reanalysis of linear intensity data for all trivalent rare earths is warranted.