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Physical review. B, Condensed matter

Static and dynamic contributions to the lowest 4f→5dtwo-photon transition in CaF2 : Ce3+

R C Leavitt

Published Jun 15, 1987• 23 citations
Publisher

Abstract

A theoretical analysis of the lowest zero-phonon 4f\ensuremath{\rightarrow}5d two-photon absorption cross section in ${\mathrm{CaF}}_{2}$:${\mathrm{Ce}}^{3+}$ is presented. The transition is parity allowed because of an interaction of the rare-earth ion with the odd-parity components of the crystal field. This interaction takes two forms. The static contribution serves to mix the 4f and 5d orbitals, while a dynamic term couples the rare-earth orbitals to the nearby ligand states. A comparison of the predicted polarization anisotropy to the experimentally measured value allows an estimate of the relative strengths of the static and dynamic terms. The theoretical estimates of both the polarization anisotropy and the absolute magnitude of the cross section compare well with the experimental results.

DOI
10.1103/physrevb.35.9271

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Two-photon excitation (TPE) spectra of the 4f 1 -?5d 1 transitions of Ce 3 + in LuP0 4 and YP0 4 have been investigated.For Ce3+ in LuP04, transitions to four out of the five 5d 1 levels are observed as zero-phonon lines.The symmetry properties of the levels were obtained from the polarization dependence of the TPE signals.Measurements on Ce 3 + inYP0 4 support the given assignments.Although a crystal-field fit yields a satisfactory RMS energy deviation, an unrealistic value of the spin-orbit coupling parameter, ( 5 d1, is obtained.The • vibronic coupling appears to be smaller than for the single-photon absorption spectra, and the vibronic bands show a rich structure.There are striking differences between the energies and the relative intensities of the vibronic lines and the associated zero-phonon lines.The vibronic coupling is also found to be strongly dependent on the Ce 3 + concentration.78.50.Ec,42.65.-k

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The density matrix resonant two-photon absorption (TPA) theory applicable to laser crystals doped with rare earth ions is described. Using this theory, resonant TPA cross sections for transitions from the ground state to the second excited state of the 4f5d configuration in Pr3+:Y3Al5O12 are calculated. The peak value of TPA cross section calculated is 2.75 × 10-50 cm4 s which is very close to the previous experimental value 4 × 10-50 cm4 s. The good agreement of calculated data with measured values demonstrates that the density matrix resonant TPA theory can predict resonant TPA intensity much better than the standard second-order perturbation TPA theory.

Journal of Physics Condensed Matter•Oct 5, 1999•0 citations
A theoretical analysis of the lowest zero-phonon 4f\ensuremath{\rightarrow}5d two-photon absorption cross section in CaF2{\mathrm{CaF}}_{2}CaF2​:Ce3+{\mathrm{Ce}}^{3+}Ce3+ is presented. The transition is parity allowed because of an interaction of the rare-earth ion with the odd-parity components of the crystal field. This interaction takes two forms. The static contribution serves to mix the 4f and 5d orbitals, while a dynamic term couples the rare-earth orbitals to the nearby ligand states. A comparison of the predicted polarization anisotropy to the experimentally measured value allows an estimate of the relative strengths of the static and dynamic terms. The theoretical estimates of both the polarization anisotropy and the absolute magnitude of the cross section compare well with the experimental results.
A theoretical estimate of the two-photon absorption (TPA) cross section for the lowest 4f\ensuremath{\rightarrow}5d zero-phonon transition in Ce3+{\mathrm{Ce}}^{3+}Ce3+:CaF2{\mathrm{CaF}}_{2}CaF2​ is presented. A point-charge crystal-field model is used to calculate the odd component of the C4v{C}_{4v}C4v​ crystal field which mixes states of opposite parity into the initial and final states participating in the transition. The sum over intermediate states is evaluated by assuming a constant energy denominator and using a closure approximation. The calculated magnitude and polarization anisotropy of the TPA cross section are compared with the experimentally measured values and methods to improve the calculation are discussed.
The theory of two-photon f-d transitions developed by Sztucki and Strek has been adopted to the particular case of the Ce3+ ion in LuPO4. The intensities of two-photon transitions from the ground state [MATH] to the five crystal-field components of the 5d1 state has been calculated and compared with the experimental data. It has been shown that the crystal-field mechanism is not able to reproduce the experimental results properly. Taking into account the contribution produced by light induced polarization of ligands (so called dynamic mechanism) led to the fairly good agreement between theory and experiment. It has been demonstrated how the analysis of the relative intensities of TP transitions can serve as an experimental test of the theoretical ratio between the static and dynamic contributions.
Two-photon excitation (TPE) spectra of the 4f 1 -?5d 1 transitions of Ce 3 + in LuP0 4 and YP0 4 have been investigated.For Ce3+ in LuP04, transitions to four out of the five 5d 1 levels are observed as zero-phonon lines.The symmetry properties of the levels were obtained from the polarization dependence of the TPE signals.Measurements on Ce 3 + inYP0 4 support the given assignments.Although a crystal-field fit yields a satisfactory RMS energy deviation, an unrealistic value of the spin-orbit coupling parameter, ( 5 d1, is obtained.The • vibronic coupling appears to be smaller than for the single-photon absorption spectra, and the vibronic bands show a rich structure.There are striking differences between the energies and the relative intensities of the vibronic lines and the associated zero-phonon lines.The vibronic coupling is also found to be strongly dependent on the Ce 3 + concentration.78.50.Ec,42.65.-k
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 density matrix resonant two-photon absorption (TPA) theory applicable to laser crystals doped with rare earth ions is described. Using this theory, resonant TPA cross sections for transitions from the ground state to the second excited state of the 4f5d configuration in Pr3+:Y3Al5O12 are calculated. The peak value of TPA cross section calculated is 2.75 × 10-50 cm4 s which is very close to the previous experimental value 4 × 10-50 cm4 s. The good agreement of calculated data with measured values demonstrates that the density matrix resonant TPA theory can predict resonant TPA intensity much better than the standard second-order perturbation TPA theory.