Theory of plasmon-enhanced Förster energy transfer in optically excited semiconductor and metal nanoparticles

We describe the process of F\"orster transfer between semiconductor nanoparticles in the presence of a metal subsystem (metal nanocrystals). In the presence of metal nanocrystals, the F\"orster process can become faster. The enhancement of F\"orster transfer occurs due to the effect of plasmon-assisted amplification of electric fields inside the nanoscale assembly. Simultaneously, metal nanocrystals lead to an increase of energy losses during the F\"orster transfer process. We derive convenient equations for the energy transfer rates, photoluminescence intensities, and energy dissipation rates in the please of plasmon resonances. Because of strong dissipation due to the metal, an experimental observation of plasmon-enhanced F\"orster transfer requires special conditions. As possible experimental methods, we consider cw- and time-resolved photoluminescence studies and describe the conditions to observe plasmon-enhanced transfer. In particular, we show that the photoluminescence spectra should be carefully analyzed since the plasmon-enhanced F\"orster effect can appear together with strong exciton energy dissipation. Our results can be applied to a variety of experimental nanoscale systems.