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Physical Review

Cooperative Optical Absorption in Solids

David L. Dexter

Published Jun 15, 1962• 240 citations
Publisher

Abstract

A discussion is given of a mechanism for resonance energy transfer in the absorption of light by a pair of neighboring ions in a crystal, as recently demonstrated by Varsanyi and Dieke. An estimate of the probability for this process is given.
DOI
10.1103/physrev.126.1962

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tion of a single photon by a pair of rare-earth ions in a crystal, acting in cooperation. Neither ion by itself could possibly absorb the photon, since no single-ion state exists at the photon energies involved. Absorption of light occurs discretely at sums of energy-level separations in the two ions and is detected experimentally by the excitation spectrum of one of the emission lines. This is an extremely important new effect which will doubtless have important practical applications in the future as well as obvious scientific implications. It should be emphasized that this is not, in any significant degree, excitation of a molecular state. The basic reason this phenomenon is so unusual is related to the fact that the interaction of radiation with matter consists of a sum of one-electron operators, A Vi, where A is the vector potential. From this point of view, only one electron at a time could possibly be excited, hence only one ion. In this paper a procedure for computing the probability of this effect is outlined, and some of the implications of the associated phenomena are discussed. These views can be found expressed in greater detail in ref. 2.
The interactions of an atom with its neighbors in an idealized solid are taken into account explicitly in treating the absorption of light, as contrasted with the usual introduction of an "effective" field and mass. In the discussion of the magnitude of the absorption coefficient, two cases are treated: one, the absorption by an impurity atom, in which case we are led to an equation similar to Smakula's; and two, the absorption by one of the atoms of the perfect crystal. The computations are based on a simple idealized model whose validity is discussed for existing systems.
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.