Radiative plasmon model, excited-state

Figure 19.1 (A) 2D projection of the calculated local field intensity distribution around a pair of 15 nm diameter silver nanoparticles excited with Xi = 400 nm light polarized along the interpaiticle axis. The edge-to-edge particle separation is 2 nm and the free space incident light intensity Ej,x P taken to be unity. The local field intensity near the pair is shown in false color. The calculation was done using dipole-dipole approximation (DDA) method with each dipole unit being a square with sides of 0.2 nm. (B) Model of the photophysics of a molecule represented by a three level system and how the excitation and decay dynamics are affected by plasmon enhancement of radiative rates and the introducticm of a rate for quenching Icq of the excited state due to proximity to the metal surface. E (X ) and E (X2) are the field enhancements at the position of the molecule for the excitation and emission wavelengths respectively, kn and kMR represent the radiative and non-radiative decay rates of the molecule in the absence of plasmon enhancement.

Understanding the field enhancement of radiative rates is insufficient to predict how molecular photophysical properties such as enhancement of fluorescence quantum yield will be affected by interactions of the molecule with plasmons. A more detailed model of the photophysics that accounts for non-radiative rates is necessary to deduce effects on photoluminescence (PL) yields. Such a model must include decay pathways present in the absence of metal nanoparticles as well as additional pathtvays such as charge transfer quenching that are associated with the introduction of the metal particles. Schematically, we depict the simplest conceivable model in Figure 19. IB. Note that both the contributions of radiative rate enhancement and the excited state quenching by proximity to the metal surface will depend on distance of the chromophore from the metal assembly. In most circumstances, one expects the optimal distance of the chromophores from the surface to be dictated by the competition between quenching when it is too close and reduction of enhancement when it is too far. The amount of PL will be increased both due to absorption enhancement and emissive rate enhancement. Hence, it is possible to increase PL substantially even for molecules with 100 % fluorescence yield in the absence of metal nanoparticles. 

Earlier observations by Cesario et al. [60] of a decay in fluorescence for arrays of Au nanoparticles spaced above a Ag film by a Si02 layer of increasing thickness, were interpreted as due to the finite vertical extent of the evanescent fields associated with a surface plasmon. In this model the coupling results in an enhanced interaction between individual localized plasmons at individual nanostructures [61] and thus an enhancement in the radiative efficiency increasing the spacer layer thickness moves the nanowires out of the evanescent field of the surface plasmon. A possible physical mechanism for the experimentally observed decay involves nonradiative decay of the excited states. The aluminum oxide deposited in these experiments was likely to be nonstoichio-metric, and defects in the oxide could act as recombination centers. Thicker oxides would result in higher areal densities of defects, and decay in fluorescence. A definitive assignment of the mechanism for the observed fall off of fluorescence would require determination of the complex dielectric function of our oxides (as deposited onto an Ag film), and inclusion in the field-square calculations. Finally it should be noted that at very small thicknesses quenching of the fluorescence is expected [38,62] consistent with observations of an optimum nanowire-substrate spacer thickness. 

The decay of the nanoparticle plasmons can be either radiative, ie by emission of a photon, or non-radiative (Figure 7.5). Within the Drude-Sommerfeld model the plasmon is a superposition of many independent electron oscillations. The non-radiative decay is thus due to a dephasing of the oscillation of individual electrons. In terms of the Drude-Sommerfeld model this is described by scattering events with phonons, lattice ions, other conduction or core electrons, the metal surface, impurities, etc. As a result of the Pauli exclusion principle, the electrons can be excited into empty states only in the CB, which in turn results in electron-hole pair generation. These excitations can be divided into inter- and intraband excitations by the origin of the electron either in the d-band or the CB (Figure 7.5) [15]. 

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