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physica status solidi (b)

Coherent four‐photon spectroscopy of two‐photon eesonances of trivalent rare‐earth ions

L. A. Yuguryan, A. G. Makhanek

Published May 1, 1986• 1 citation
Publisher

Abstract

Abstract Using wave functions which are transformed in irreducible representations of corresponding point groups of symmetry, an analysis is carried out of the tensor structure of resonance cubic susceptibility. Polarization characteristics are found of a four‐photon parametric process in the conditions of two‐photon resonance between the components of fine structure of trivalent rare‐earth ions in crystals. The number of independent and nonzero tensor components of resonance cubic susceptibility is determined and their number is shown to be much smaller than it follows from the general features of the crystal symmetry. The signs of resonance cubic susceptibility are calculated for concrete two‐photon transitions.

DOI
10.1002/pssb.2221350135

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•Apr 1, 2005•0 citations
Abstract Using wave functions which are transformed in irreducible representations of corresponding point groups of symmetry, an analysis is carried out of the tensor structure of resonance cubic susceptibility. Polarization characteristics are found of a four‐photon parametric process in the conditions of two‐photon resonance between the components of fine structure of trivalent rare‐earth ions in crystals. The number of independent and nonzero tensor components of resonance cubic susceptibility is determined and their number is shown to be much smaller than it follows from the general features of the crystal symmetry. The signs of resonance cubic susceptibility are calculated for concrete two‐photon transitions.
To study the role of stepwise and relaxation processes under effective excitation of anti-Stokes luminescence of rare-earth (RE) ions in crystals the time-shifted pulse method is used. It is shown that direct comparison of measured single- and two-photon luminescence excitation spectra often enables one to make immediate conclusions on the position and classification of electron levels of RE ions. The Tb3+ and Eu3− level structures (crystal CaF2) in the near ultraviolet are considered as an example. The peculiarities connected with the polarization characteristics of the two-photon absorption of radiation by the trivalent RE ions in a crystal matrix are discussed. To obtain the two-photon spectra a frequency-tunable organic dye solution laser (ODSL) is used.
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.
It is shown that in order to obtain a correct interpretation of experiments on four-photon nonlinear spectroscopy within the absorption line, it is necessary to allow not only for a coherent four-photon process due to a resonant electronic nonlinearity but also for a similar process involving generation of optically induced diffraction gratings followed by the diffraction of one of the probe beams from these gratings. It is also necessary to allow for the contribution of highly excited molecular states to the resonant electronic nonlinearity. General expressions are derived and investigated for the cubic susceptibility in an isotropic medium. It is found that all nonzero components of this tensor may be expressed in terms of a single scalar function of the interacting wave frequencies. The explicit form of this function is determined in the lowest order of perturbation theory.
The off-diagonal matrix elements of the polarizability operator when operating within an lN{l}^{N}lN configuration of a complex atom can be approximately written in simple tensor-operator form. The resulting expressions are discussed in terms of two-photon absorption and the recently observed electronic Raman scattering in the trivalent rare-earth ions.
Three-wave mixing experiments demonstrate resonance enhancement of the third-order susceptibility due to electronic transitions in rare-earth ions. The position, width, and strength of eight resonances in the 2100–2500-cm−1 range in terbium aluminum garnet (TbAlG) are determined. These resonances are due to 7F5→7F6 intermanifold transitions of terbium. In addition, the nonresonant susceptibility has been measured for TbAlG : xNRxxxx = (12.4±2.5)×10−14 m3/J and xNRxyyx = (3.8±0.8)×10−14 m3/J.