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The Journal of Chemical Physics

Ionic transitions hypersensitive to environment

B. R. Judd

Published Jun 1, 1979• 177 citations
Publisher

Abstract

It is shown that the so-called dynamic-coupling mechanism of Mason, Peacock and Stewart, which was introduced to account for the peculiar hypersensitivity of the optical transitions of rare-earth ions with respect to their environment, is formally identical to an earlier proposed mechanism based on an inhomogeneous dielectric. Errors in the derivation of the dynamic-coupling mechanism are corrected, and examples of the rare-earth trihalides are considered.

DOI
10.1063/1.437372

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•Apr 26, 1987•0 citations
It is shown that the so-called dynamic-coupling mechanism of Mason, Peacock and Stewart, which was introduced to account for the peculiar hypersensitivity of the optical transitions of rare-earth ions with respect to their environment, is formally identical to an earlier proposed mechanism based on an inhomogeneous dielectric. Errors in the derivation of the dynamic-coupling mechanism are corrected, and examples of the rare-earth trihalides are considered.
The change of intensities of optical transitions of atoms, molecules, and their ions in the near field of nanoobjects is of interest for researchers from both basic and applied points of view. The concept of a near field was used as early as the 1960s to study the mechanisms of hypersensitive transitions of rare-earth (RE) ions. In this work, it is once more emphasized that, precisely for these transitions, changes in characteristics under the action of local properties of the medium are especially strong and, correspondingly, these transitions are especially promising for use. The Judd method for the calculation of the intensities of hypersensitive transitions of RE ions taking into account the inhomogeneous ligand field is extended to RE ions in the near field of nanoobjects. A simple analytical expression for the Judd-Ofelt intensity parameter Ω 2 for RE ions in the field of spherical nanoparticles of a subwavelength size is derived.
A new scheme to realize an abnormal dielectric response at optical wavelength is developed on the basis of two-level electronic transition of rare-earth ion doped crystals. Based on the semi-classical theory and the Judd—Ofelt theory, the electric dipole transition under a weak field is analyzed, and a general expression for the frequency-dependent dielectric constant is obtained. As an example, the permittivity of (Er x Y 1−x ) 3 Al 5 O 12 is calculated numerically in consideration of the transition between 4 I 15/2 and 4 F 9/2 . An optimized dielectric property with a negative real part and low absorption is achieved. This proposes a new mechanism for building extraordinary electromagnetic media at optical frequencies by using a quantum process.
The absorption of a single photon by the simultaneous excitation of two rare-earth ions was first reported by Varsanyi and Dieke in 1961.1 D. L. Dexter explained this unusual observation by including the electron-electron interactions (that also give rise to energy transfer) between the rare earth ions with perturbation theory.2 In the 70's Dexter became interested in electronic-vibrational coupling. A theory of two-center optical transitions was developed for a rare-earth ion weakly coupled to a high energy, internal vibrational mode of a near-lying ion.3 Using theoretical techniques that had been developed for rare-earth ion pairs, intensities and selection rules could be determined.
The absorption of single photons by coupled pairs of ions in rare-earth solids was first observed by Varsanyi and Dieke.1 They noticed that weak absorption of light occurred in PrCl3 at frequencies close to the sum of transition frequencies of individual Pr ions, giving rise to rare-earth fluorescence. This effect was explained by the perturbation theory of Dexter.2 He showed that weak multipole or exchange interactions between rare-earth ions permitted the simultaneous promotion of two ions to excited states by the action of one absorbed photon in an electric dipole allowed transition. Similarly, two ions initially in excited states could emit one sum frequency photon in a cooperative manner.