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physica status solidi (b)

Two‐Photon Absorption of CaF2:Eu2+

Eberhard G. Bayer, Gerhard Schaack

Published Jan 1, 1970• 37 citations

Abstract

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.

DOI: 10.1002/pssb.19700410239

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Physical review. B, Condensed matter•Apr 15, 1985•10 citations

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.

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 Theoretical and experimental investigations are made of two‐photon absorption spectra of trivalent rare‐earth ions in crystals. Effective cross‐sections, selection rules, and relative intensities of the components are found. The most intensive two‐photon transitions are established. Two‐photon excitation spectra of luminescence of Er3+ and Ho3+ ions in CaF2 are obtained and effective excitation cross‐sections are measured using a tunable dye laser (715 to 850 nm). It is shown that the spectra have a peculiar structure which differs considerably from that of the one‐photon absorption spectra. The experimental results agree with theory. It is established that one of the levels in Ho3+ is the level 5G6 rather than 3K7 usually assumed.

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.

The energy levels of

{\mathrm{Gd}}^{3+}

in the

^{6}\mathrm{P}

,

^{6}\mathrm{I}

, and

^{6}\mathrm{D}

4

{f}^{7}

configuration in cubic, tetragonal, and cluster sites in

{\mathrm{CaF}}_{2}

have been excited by two-photon absorption. The relative two-photon intensities and polarization dependence show behavior which is similar to that previously observed for

{\mathrm{Gd}}^{3+}

:

{\mathrm{LaF}}_{3}

and

{\mathrm{Eu}}^{2+}

:

{\mathrm{CaF}}_{2}

and which requires higher-order perturbation theory in the virtual intermediate 4${f}^{6}$5d configuration.