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Journal of Physics Condensed Matter

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

Published Oct 5, 1999• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0953-8984/11/42/301

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Resonant enhancement of two-photon transitions to the second excited 4f5dstate in Pr3+ : Y3 Al5 O12

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Resonantly enhanced, near-ultraviolet 4f3 → 4f25d two-photon transitions have been observed in trivalent neodymium-doped yttrium aluminum garnet (Nd3+:Y3Al5O12). The two-photon excitation spectra over the 40 400–46 730 cm−1 transition energy range are characterized by sharp resonance peaks on a slowly varying background caused by nonresonant transitions. The peak two-photon cross section involving the 2P1/2 resonant intermediate state is 9 × 10−51 cm4 s, and the integrated cross section is 2.2 × 10−38 cm4.

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4f2to 4f5d excited state absorption in Pr3+:YAlO3

S Nicolas, Mathieu Laroche, S Girard +5 more

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Journal of Physics Condensed Matter•Sep 24, 1999•35 citations
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 two-photon absorption cross section for transitions from the 3^{3}3H4{\mathit{H}}_{4}H4​ ground-state manifold to the second excited state of the 4f5d configuration of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in Y3{\mathrm{Y}}_{3}Y3​Al5{\mathrm{Al}}_{5}Al5​O12{\mathrm{O}}_{12}O12​ is observed to be enhanced by about two orders of magnitude when the excitation frequency happens to be resonant with the 3^{3}3PJ{\mathit{P}}_{\mathit{J}}PJ​ (J=0,1,2) and 1^{1}1I6{\mathit{I}}_{6}I6​ intermediate states of the 4f2{\mathit{f}}^{2}f2 configuration. The structure and line shape of the two-photon excitation spectrum spanning the 39 600--46 950 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ transition-energy range are entirely dominated by these resonantly enhanced transitions, while the contributions from nonresonant transitions appear as a slowly varying background beneath the strong resonance peaks. A two-photon absorption cross section as high as 4\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}50}$ cm4{\mathrm{cm}}^{4}cm4 s is measured at the peak of the resonantly enhanced transition at 44 246 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, which involves a level of the 3^{3}3P2{\mathit{P}}_{2}P2​ manifold as the intermediate state. The spectrally integrated cross section over that manifold is 3.3\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}38}$ cm4{\mathrm{cm}}^{4}cm4.
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.
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 optical-absorption transitions originating from the lowest 4f5d excited state of Pr3+{\mathrm{Pr}}^{3+}Pr3+ in Y3{\mathrm{Y}}_{3}Y3​Al5{\mathrm{Al}}_{5}Al5​O12{\mathrm{O}}_{12}O12​ have been studied. The experimental arrangement uses a 7-ns 266-nm light pulse to populate the lowest 4f5d state, and a spatially overlapped, time-sequenced pulse from a frequency-tunable dye laser to induce transitions from that excited state. The excited-state-absorption (ESA) spectrum covering the 900--300-nm probe wavelength range is characterized by two broad peaks centered at 700 and 350 nm on a slowly rising background. The peak ESA cross section at 355 nm is (1\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}17}$ cm2{\mathrm{cm}}^{2}cm2. The position, shape, and strength of the spectrum suggest that the terminal states of the ESA transitions are the second 4f5d state of Pr3+{\mathrm{Pr}}^{3+}Pr3+ and the conduction band of the host lattice. The ESA measurements have been extended to transitions from the 3^{3}3P0{\mathit{P}}_{0}P0​ and 1^{1}1D2{\mathit{D}}_{2}D2​ excited states of the 4f2{\mathit{f}}^{2}f2 configuration of Pr3+{\mathrm{Pr}}^{3+}Pr3+ as well. The ESA cross sections at a probe wavelength of 532 nm are (8\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}19}$ cm2{\mathrm{cm}}^{2}cm2 and (5.7\ifmmode\pm\else\textpm\fi{}0.6)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}19}$ cm2{\mathrm{cm}}^{2}cm2 for transitions from the 3^{3}3P0{\mathit{P}}_{0}P0​ and 1^{1}1D2{\mathit{D}}_{2}D2​ excited states, respectively. The terminal state of ESA transitions from these two levels is the lowest 4f5d state. The strong ESA completely inhibits the potential laser action based on emission from these states in this crystal.
Resonantly enhanced, near-ultraviolet 4f3 → 4f25d two-photon transitions have been observed in trivalent neodymium-doped yttrium aluminum garnet (Nd3+:Y3Al5O12). The two-photon excitation spectra over the 40 400–46 730 cm−1 transition energy range are characterized by sharp resonance peaks on a slowly varying background caused by nonresonant transitions. The peak two-photon cross section involving the 2P1/2 resonant intermediate state is 9 × 10−51 cm4 s, and the integrated cross section is 2.2 × 10−38 cm4.