Nearest-Neighbor Dominance in Cooperative Luminescence

Cooperative luminescence is the microscopic reverse of simultaneous pair excitation, and in Yb + involves the emission of a green photon following NIR Fy/2 Fj/2 excitation by the simultaneous relaxation of two excited ions to the ground state. In general, cooperative upconversion systems can be treated by the same rate equations as those given in Eq. (10), where now E = G, k2b = Ik -, and the cooperative luminescence rate constant is k oop = 2a Under low-power conditions, where G ki and N2 Ni, the steady-state cooperative luminescence rates in the limit of a purely radiative system are described by Eqs. (29) and (30)  

This general conclusion is beautifully illustrated by the example of 10% Yb + RbY2Bry. In this host lattice, Yb + may occupy one of two crystallographi- 

AA and B B — BB. The integrated intensity pattern averaged over both excitation wavelengths is approximately 1 17 1. 

The relative cooperative luminescence intensities observed in Fig. 11c are directly attributable to the importance of R in determining the magnitude of kcoop (see Eqs. 30 and 31). As shown by the repeating structural unit in Fig. 11a (inset), there exist two types of nearest-neighbor pairs, both of which are AB pairs. R for the two shortest AB pairs (1 = 4.05 A and 2 R b = 4.53 A) are 

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