Journal of Luminescence 96 (2002) 149–154 One-phonon assisted energy transfer in periodic arrays of optically active ions I. Avgin a , D.L. Huber b, * a DepartmentofElectricalandElectronicsEngineering,EgeUniversity,Bornova35100,Izmir,Turkey b DepartmentofPhysics,UniversityofWisconsin-Madison,1150UniversityAvenue,Madison,WI53706,USA Received 18 December 2000; received in revised form 17 May 2001; accepted 17 May 2001 Abstract Energy transfer in periodic arrays of optically active ions is investigated. It is assumed that the transfer of excitation between ions takes place incoherently via a one-phonon process where the wavelength of the phonon is large in comparison with the inter-ion spacing. It is pointed out that the energy transfer can only occur where there is a mismatch in energy between the excited states of the two ions. The energy diffusion constant is calculated in an effective medium approximation assuming a Gaussian lineshape with no correlation between the excited state energies of neighboring ions. The temperature dependence of the diffusion constant is established for cubic lattices with nearest- neighbor transfer. Energy transfer in one-dimensional arrays with nearest-neighbor transfer is studied using an extension of the coherent exchange approximation developed for random ferromagnets. The coherent exchange approximation reproduces the asymptotic non-diffusive behavior found in numerical studies of fluorescence line narrowing in one-dimensional systems. r 2002 Elsevier Science B.V. All rights reserved. PACS: 78.47.+p; 78.20.Bh; 78.55.m Keywords: Energy transfer; One-phonon process; Energy diffusion constant; Fluorescence line narrowing 1. Introduction The transfer of optical excitation between ions (or, more generally, chromophores) and its effect on the fluorescence dynamics, is a process of wide ranging importance underlying, for example, the development of improved phosphors for fluores- cent lights and the dynamics of photosynthesis in living systems. Broadly speaking, the transfer process can be subdivided into two categories: coherent transfer, as it happens in systems whose excited states are Frenkel excitons, and incoherent transfer, where the transfer process can be characterized in terms of a Master Equation for the occupation probabilities of the excited state. In this paper, our interest is in the latter for situations where the transfer process involves the emission or absorption of a single phonon. One-phonon transfer in dilute systems has recently been explored in both experimental [1,2] and theoretical [3] studies. All the three of these investigations pertained to systems where there was a random distribution of optically active ions. Here we focus on the complementary situation where there is a *Corresponding author. Tel.: +1-608-265-4035; fax: +1- 608-265-2334. E-mailaddress: huber@src.wisc.edu (D.L. Huber). 0022-2313/02/$-see front matter r 2002 Elsevier Science B.V. All rights reserved. PII:S0022-2313(01)00217-4