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arXiv:physics/9811033

Two-Photon Laser Spectroscopy of Transition Ions in Crystals: Inter- Configurational Transitions

Mohammed Daoud A, M. Kibler

Published Nov 18, 1998• 0 citations
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Abstract

Symmetry adaptation techniques are applied to the determination of the intensity of two-photon absorption transitions, between Stark levels of configurations with opposite parities, for transition ions in finite symmetry environments. The equivalence between third-order mechanisms and second- plus first-order mechanisms is clearly established. A compact formula is derived for the intensity of a two-photon transition between two levels with well-defined symmetries. A set of (selection) rules which controls the number of intensity parameters for inter-configurational transitions is given. The formalism is illustrated with the case of an ion with 4f configuration in tetragonal symmetry.

DOI
10.48550/arxiv.physics/9811033

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Symmetry adaptation techniques are applied to the determination of the intensity of two-photon absorption transitions, between Stark levels of configurations with opposite parities, for transition ions in finite symmetry environments. The equivalence between third-order mechanisms and second- plus first-order mechanisms is clearly established. A compact formula is derived for the intensity of a two-photon transition between two levels with well-defined symmetries. A set of (selection) rules which controls the number of intensity parameters for inter-configurational transitions is given. The formalism is illustrated with the case of an ion with 4f configuration in tetragonal symmetry.
Abstract The technique of two‐photon‐absorption spectroscopy with polarized laser‐light is applied to localized excitations of 4f‐electrons in crystals. The relevant selection rules are discussed. A method is outlined for the unique determination of the relative magnitude of partial transition‐probabilities with different types of symmetry using linear and circular polarization of the incident light. The anisotropy of the two‐photon absorption has been measured in single crystals of cubic CaF2:Eu2+ at five different wavenumbers. The relative intensities of transitions belonging to the three different types of symmetry active in two‐photon absorption are constant in the range of the e‐band (26,000 to 29,000 cm−1) but differ from these values at 37,700 cm−1 in the range between the e‐ and the t‐band. This result is discussed in the frame of existing interpretations of the 4f65d‐configuration of Eu2+ in CaF2.
The two-photon transitions between the Stark levels of the 7F0^{7}\mathrm{F}_{0}7F0​ and 5D2^{5}\mathrm{D}_{2}5D2​ multiplets of the Sm2+{\mathrm{Sm}}^{2+}Sm2+ ion in BaClF are investigated both from an experimental and theoretical viewpoint. Direct two-photon excitation spectra of the 5D2^{5}\mathrm{D}_{2}5D2​ fluorescence resulting from an optical excitation with an infrared laser beam are presented and the polarization dependence of the observed transitions is analyzed. These new data are interpreted along the lines of a simple model which originates in the second-order theory developed by Axe [Phys. Rev. 136, A42 (1964)] for two-photon processes in complex atoms. The extension of this theory to the case of rare-earth ions embedded in crystalline fields is carried out by use of symmetry-adaptation techniques based on the use of an SU(2)\ensuremath{\supset}G∗{\mathrm{G}}^{\mathrm{*}}G∗ chain of groups. It is shown that the resulting model (limited up to second-order terms) describes correctly the relative intensities of the two-photon transitions between the Stark levels of the 7F0^{7}\mathrm{F}_{0}7F0​ and 5D2^{5}\mathrm{D}_{2}5D2​ multiplets of Sm2+{\mathrm{Sm}}^{2+}Sm2+ in BaClF.
The theory of one- and two-photon transitions between a given pair of impurity levels of the same parity is developed. As is well known, lattice vibrations assist the otherwise forbidden one-photon transition, increasing its intensity with temperature. The two-photon transition rate is shown to have a complementary decrease with increasing temperature. A measurement of both temperature dependences determines the effective frequency and coupling constant for the interaction. The formalism is applied to predicting the two-photon transition rate for the $4{d}^{10}\ensuremath{-}4{d}^{9}5s$ transition of the silver ion in NaCl:Ag. For an experiment using a ruby laser and an ultraviolet beam the maximum absorption coefficient predicted for the ultraviolet beam is $3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}48}\mathrm{FN}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ at low temperatures, where FFF is the flux (photons/cm2{\mathrm{cm}}^{2}cm2 sec) of the laser and NNN is the Ag+{\mathrm{Ag}}^{+}Ag+ concentration. This should be within reach of present experimental techniques.
Recent observations of two-photon absorption within the configuration 4f 7 of Gd 3+ in LaF 3 have indicated an anomalously high line strength for the transition 8 S 7/2 to 6 P 7/2 compared with 8 S 7/2 to 6 P 5/2 and 8 S 7/2 to 6 P 3/2 . It is shown that the standard expression for the two-photon intensity is unusually small for all three transitions and that a higher-order correction, involving matrix elements of the spin-orbit interaction within the intermediate configuration 4f 6 5d, predominates. The principal term is scalar, implying (in the absence of J mixing by the crystal field) isotropic contributions to the various components of the Delta J=0 transition. The line strengths that have been observed can be accounted for reasonably well without having to invoke variations in the radial integral (4f mod r mod 5d) or inadequacies in the closure approximation. Expressions for the transition matrix elements are given for the general configuration l N .
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.