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Physical review. B, Condensed matter

Analysis of the lowest4f→5dtwo-photon transition in Ce3+ : CaF2

Swapan Kumar Gayen, D. S. Hamilton, Ralph H. Bartram

Published Dec 1, 1986• 27 citations
Publisher

Abstract

A theoretical estimate of the two-photon absorption (TPA) cross section for the lowest 4f\ensuremath{\rightarrow}5d zero-phonon transition in ${\mathrm{Ce}}^{3+}$:${\mathrm{CaF}}_{2}$ is presented. A point-charge crystal-field model is used to calculate the odd component of the ${C}_{4v}$ 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.

DOI
10.1103/physrevb.34.7517

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

R C Leavitt

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.

Physical review. B, Condensed matter•Jun 15, 1987•23 citations

Two-Photon Excitations of Higher 5d States in Ce3+:CaF2

Swapan Kumar Gayen, Gerald J. Pogatshnik, D. S. Hamilton

The 4f-->5d near-ultraviolet transitions in Ce3+:CaF2 are dipole allowed in one-photon absorption (OPA) and first-order parity-forbidden for two-photon absorption (TPA). A relaxation of the parity selection rule due to odd crystal-field components has previously been observed1 in the TPA from the 4f ground state to the lowest 5d state. In this paper the TPA measurements are extended to include transitions to the higher 5d states.

International Conference on Luminescence - 1984•Jan 1, 1984•2 citations

Theoretical analysis of the two-photon absorption spectrum of Tb3 in Cs2NaTbCl6

Dianyuan Wang, Lixin Ning, Shangda Xia +1 more

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.

Journal of Physics Condensed Matter•Apr 22, 2003•8 citations

Calculations of cross sections of resonant two-photon transitions to the second excited 4f5d state in Pr3+:Y3Al5O12using density matrix theory

Zhenwen Dai, Jing‐yao Liu, Siyuan Zhang

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

Two-photon excitation of the [MATH] transitions of Ce3+ in LuPO4 : a comparison between theoretical and experimental intensities

Jarosław Sztucki, Joost Sytsma

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.

Journal de Physique IV (Proceedings)•Apr 1, 1994•0 citations

Theoretical and experimental study of the 6S-8S two-photon absorption cross-section in cesium atoms

Michael Caracas Núñez, Miguel A. Gonzalez, Mayerlin Núñez Portela

The probability of a two-photon absorption (TPA) process is quantified by means of the TPA cross-section. In this work the TPA cross-section for the 6 S 1/2 → 8 S 1/2 transition in cesium (Cs) atoms is obtained from a theoretical and experimental approach. It is calculated using second order perturbation theory including hyperfine structure and Doppler broadening for a thermal atomic vapor. The theoretical values for the TPA cross-sections of the two allowed hyperfine transitions are σ ~ 3,3 =3.10×10 −24 cm 4 /W and σ ~ 4,4 =3.65×10 −24 cm 4 /W. An experiment is set up to measure these cross-sections based on the quadratic dependence between the TPA transition rate and the intensity of the laser light. Values of σ ~ 3,3 =(3.6±1.1)×10 −24 cm 4 /W and σ ~ 4,4 =(4.6±1.1)×10 −24 cm 4 /W are obtained from the measurements. The results show an agreement between theory and experiment. To the best of our knowledge, this is the first time that these cross-sections are reported.

Optics Express•Aug 14, 2023•4 citations
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.
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.
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.
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.
The probability of a two-photon absorption (TPA) process is quantified by means of the TPA cross-section. In this work the TPA cross-section for the 6 S 1/2 → 8 S 1/2 transition in cesium (Cs) atoms is obtained from a theoretical and experimental approach. It is calculated using second order perturbation theory including hyperfine structure and Doppler broadening for a thermal atomic vapor. The theoretical values for the TPA cross-sections of the two allowed hyperfine transitions are σ ~ 3,3 =3.10×10 −24 cm 4 /W and σ ~ 4,4 =3.65×10 −24 cm 4 /W. An experiment is set up to measure these cross-sections based on the quadratic dependence between the TPA transition rate and the intensity of the laser light. Values of σ ~ 3,3 =(3.6±1.1)×10 −24 cm 4 /W and σ ~ 4,4 =(4.6±1.1)×10 −24 cm 4 /W are obtained from the measurements. The results show an agreement between theory and experiment. To the best of our knowledge, this is the first time that these cross-sections are reported.