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We present a theoretical investigation of a semiconductor quantum dot interacting with a strongly localized optical field as encountered in high-resolution near-field optical microscopy. The strong gradients of these localized fields suggest that higher-order multipolar interactions will affect the standard electric dipole transition rates and selection rules. For a semiconductor quantum dot in the strong confinement limit we calculated the interband electric quadrupole absorption rate and the associated selection rules. We found that the electric quadrupole absorption rate is comparable with the absorption rate calculated in the electric dipole approximation. This implies that near-field optical techniques can extend the range of spectroscopic measurements beyond the standard dipole approximation. However, we also show that spatial resolution cannot be improved by the selective excitation of electric quadrupole transitions.

We calculate the damping of a classical oscillator induced by the electromagnetic field generated by thermally fluctuating currents in the environment. The fluctuation-dissipation theorem is applied to derive the linear-velocity damping coefficient γ. It turns out that γ is the result of fourth-order correlation functions. The theory is applied to a particle oscillating parallel to a flat substrate and numerical values for γ are evaluated for particle and substrate materials made of silver and glass. We find that losses are much higher for dielectric materials than for metals because of the higher resistivity. We predict that measurements performed on metal films are strongly affected by the underlying dielectric substrate and we show that our theory reproduces existing theoretical results in the non-retarded limit. The theory provides an explanation for the observed distance-dependent damping in shear-force microscopy and it gives guidance for future experiments. Also, the theory should be of importance for the design of nanoscale mechanical systems and for understanding the trade-offs of miniaturization.

The central motivation of this theoretical revisitation comes from the fact that some experimental works about Förster energy transfer report improvement of the Förster efficiency when the donor-acceptor molecular pair is in the vicinity of a metallic particle, while others found efficiency deterioration. In the presence of a nanoscale metallic sphere, we calculate contour plots of the Förster energy transfer rate KF and the Förster efficiency η as a function of the acceptor position rA for a fixed donor position. These contour plots clearly highlight the influence of the sphere on KF and η as the donor position, the orientations of donor and acceptor dipoles, and the particle size are varied; also the impact on KF(rA) and η due to the excitation of surface plasmons is easily noticeable from these contour plots. Moreover, we obtain the enhancement factor KF/KF0 (KF0 refers to the case without sphere) against the donor-surface separation for particular donor-acceptor spatial distributions, several particle sizes, and distinct molecular dipole orientations. Therefore, our calculations provide a systematic analysis of the Förster energy transfer in the presence of a metallic nanosphere. Based on these results, we formulate hypotheses for explaining the aforementioned contradictory experimental results about η. To complement our study, we examine the impact of the local density of states ρ on KF. KF is practically unperturbed by sphere when the intermolecular separation R is ≲ 3 nm, since the direct donor-acceptor electromagnetic interaction is dominant. On the contrary, when R ≳ 3 nm, the nanosphere perturbs KF and this perturbation is stronger if plasmonic resonances are excited. KF/KF0 can greatly be enhanced in certain regions, but these regions coincide with low-efficiency regions, compromising applications involving the Förster process. In the presence of the nanosphere, the high Förster efficiency region (η ≥ 0.5) has the same shape as that for the case without sphere, but its extension (Förster radius Ro) is reduced; this effect is a consequence of the large increase of the donor direct decay rate and Ro depends strongly on donor position. Consequently, the sphere controls Ro that is associated with the efficiency pattern that corresponds to the unbounded medium; this effect can be exploited in the measuring technique of nanoscale displacements of proteins that is based on the fluorescence resonant energy transfer. The functional form of KF(ρ) is determined by the intermolecular separation R, the spatial configuration and the dipole orientations of the molecular pair, and the donor proximity to the nanoparticle.

We derive the magnetic dipole selection rules and the magnetic dipole absorption rate for a spherical semiconductor quantum dot. We find that electric dipole and magnetic dipole transitions are exclusive and therefore can be spectrally distinguished. The magnitudes of electric and magnetic absorption rates are compared for excitation with a strongly focused azimuthally polarized beam. It turns out that spatial optical resolution can be increased by detection of the ratio of magnetic and electric absorption rates. Resolution is limited only by the purity of the laser mode used for excitation.