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Extra info for A course of mathematical analysis, Part I (International series of monographs on pure and applied mathematics;vol.44)
L. L. , Wavelength, concentration, and distance dependence of nonradiative energy transfer to a plane of gold nanoparticles. ACS Nano 6, 9283–9290 (2012) 9. L. A. M. Lupton, A. Meijerink, J. Feldmann, Energy transfer with semiconductor nanocrystals. J. Mater. Chem. 19, 1208–1221 (2009) 10. K. Lyo, Exciton energy transfer between asymmetric quantum wires: Effect of transfer to an array of wires. Phys. Rev. 1 Useful Formalae Förster-type Nonradiative Energy Transfer (FRET) Rate: 2 ctrans ¼ Im h Z dV !
D. Spataru, S. Ismail-beigi, X. G. Louie, Appl. Phys. A 78, 1129 (2004) Chapter 3 Nonradiative Energy Transfer in Assembly of Nanostructures This chapter is reprinted (adapted) with permission from Ref. . Copyright 2014 American Chemical Society. Here, we present the theoretical framework of generalized Förster-type nonradiative energy transfer (FRET) between one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) assemblies of nanostructures consisting of mixed dimensions in conﬁnement, namely, nanoparticles (NPs) and nanowires (NWs).
A is the angle between NW axis and the NP array axis (Fig. 1b). Note that the energy transfer rate distance dependency changes from c / d À6 to c / d À5 . Furthermore, the FRET rate Eq. 8) strongly depends on the angle when the donor is a QW or NW. 2 Energy Transfer Rates for Nanoparticle, Nanowire, or Quantum Well to 2D Nanoparticle Assembly We present simpliﬁed expressions for FRET rate in the long distance approximation when the donor is an NP, an NW, or a QW and the acceptor is a 2D NP assembly (plane) (Fig.