Inhomogeneous broadening in the optical spectra of impurity chromophores in crystals and glasses is a manifestation of a static distribution of impurity environments, which gives rise to a distribution of the absolute energies for a given impurity electronic state. The inhomogeneous line shape for a transition from state a to state /3 is obtained from a convolution of the probability distribution for the energy of state a, P a (E), and iPa (E 'I E), the conditional probability that a chromophore has energy E ' in state /3 given that it had energy E in state a. Experiments that involve a transition between two states followed by radiative or nonradiative relaxation to a third state, such as fluorescence line narrowing (FLN) or hole burning (HB), provide additional interesting information about these absolute distributions and conditional probabilities. In a 1985 paper,1 Lee, Walsh, and Fayer (LWF) proposed a phenomenological model of inhomogeneous broadening, which they used to explain a series of FLN and HB experiments. They assumed that the energy distributions of the individual states are Gaussian in form, and that the conditional probabilitiesiPa (E 'IE) are simply equal to Pp (E'). Thus all the pairs of absolute energies are completely uncorrelated. The model ofL WF has recently been generalized by Suter et al. 2 In an alternative viewpoint, which has been discussed by Selzer,3 one assumes that there is a one-to-one correspondence between the energy in one state, and the energy in some other state, so that the conditional probabilities would all be delta functions. Inhomogeneous broadening arises in this model because the absolute energy distributions for the two levels have different widths. In a recent paper,4 we have developed a molecular theory that describes the response of the inhomogeneous line shape after a persistent hole has been burned, to external changes in pressure. This effort was motivated by experiments performed by Sesselmann et a[.5 We came to realize that, using a modified version of our formalism, it is possible to develop a theory within which the energy distributions and conditional probabilities discussed phenomenologically by L WF and Selzer can be calculated from the microscopic parameters of a system. In what follows, we will briefly outline this theory and comment on how the L WF and Selzer assumptions are recovered in certain limits. We consider a system consisting of a dilute concentration of impurities embedded in a glass or crystal. In some zeroth-order scheme, the impurities are characterized by a set of levels {a} with energies E~. We then suppose that each impurity interacts with a large number of static defects (which for a crystal would include dislocations, interstitials, etc., and for a glass would be the solvent molecules themselves4), each of which produces a perturbation Va (R) on the ath impurity level, where R is the set of relevant defect coordinates, including its position relative to the impurity. The (normalized) distribution of state a energies is then given by
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Oct 1, 1996
A V Kharitonov + 1
Open Access