Förster-type nonradiative energy transfer for assemblies of arrayed nanostructures: confinement dimension vs stacking dimension

Forster-type nonradiative energy transfer (NRET) provides us with the ability to transfer excitation energy between proximal nanostructures with high efficiency under certain conditions. Nevertheless, the well-known Forster theory was developed for the case of a single donor (e.g., a molecule, a dye) together with single acceptor. There is no complete understanding for the cases when the donors and the acceptors are assembled in nanostructure arrays, though there are special cases previously studied. Thus, a comprehensive theory that models Forster-type NRET for assembled nanostructure arrays is required. Here, we report a theoretical framework of generalized theory for the Forster-type NRET with mixed dimensionality in arrays. These include combinations of arrayed nanostructures made of nanoparticles (NPs) and nanowires (NWs) assemblies in one-dimension (1D), two-dimension (2D), and three-dimension (3D) completing the framework for the transfer rates in all possible combinations of different confinement geometries and assembly architectures, we obtain a unified picture of NRET in assembled nanostructures arrays. We find that the generic NRET distance dependence is modified by arraying the nanostructures. For an acceptor NP the rate distance dependence changes from gamma alpha d(-6) to gamma alpha d(-5) when they are arranged in a ID stack, and to gamma alpha d(-4) when in a 2D array, and to gamma alpha d(-3) when in a 3D array. Likewise, an acceptor NW changes its distance dependence from gamma alpha d(-5) to gamma alpha d(-4) when they are arranged in a 1D array and to gamma alpha d(-3) when in a 2D array. These finding shows that the numbers of dimensions across which nanostructures are stacked is equally critical as the confinement dimension of the nanostructure in determining the NRET kinetics.