Morphology and plasmonic properties of self-organized arrays of ...

32 CHAPTER 1. THEORYand then monotonically increases. These trends are mainly due to surface damping andretardation effects. For small particles, the former is dominant, so the LSP positionis slightly affected by the size, while the linewidth has a a contribution Γ(a) ∝ a −1(see equation (1.54)). At higher size, dynamic depolarization and radiation damping,respectively proportional to a 2 and a 3 , rapidly grow, inducing a strong red shift andbroadening of the peaks, and reducing their intensity.Q ext2015105Spheres h = 1.4, a [nm]:515253545556575 max[nm]700650600550 maxFWHM20015010050FWHM [nm]0500 600 700 800 900a. [nm]b.020 40 60radius [nm]80Figure 1.16: Left panel: computed extinction efficiencies Q ext for non-interacting goldspherical particles, having different radii, dispersed in a homogeneous dielectric host (ε h =1.4); the dielectric function of gold is plotted in the inset of fig. 1.14. Right panel: position(λ max , red line) and full width at half maximum (FWHM, black curve) of the LSP peaksin panel (a) as a function of the particle radius.Lastly, in fig. 1.17 the absorption and scattering contributions to the total extinctionefficiency are shown separately for two different particles with radius a = 5 nm and 50 nm,respectively. As already predicted before, in the former case Q ext is entirely determined byabsorption (Q abs ∝ a), the scattering efficiency being more than three orders of magnitudesmaller. Increasing the volume, Q sca grows much more rapidly than Q abs (Q sca ∝ a 4 ), fora = 50 nm is comparable with Q abs and eventually it becomes dominant at higher radii.1.3.4 Effects of EM interactionsUp to this point we always considered ensembles of isolated nanoparticles, where the particlesspacing was so high that the direct interactions could be neglected. When severalparticles are brought close to one another, electromagnetic coupling effects set in, andthe LSP resonances are determined by the collective behaviour of the system, so that theoverall optical response can be significantly modified with respect to the isolated case.Usually, two different interactions regimes are distinguished, depending on the interparticledistance d: for closely spaced particles, d ≪ λ, near-field interactions proportional tod −3 dominate and the particles can be described as an array of interacting point dipoles;due to the rapid scaling of the interaction strength with distance, this regime holds forparticle separations below ≈ 150 nm. For larger separations, the near field can be neglectedand the dipolar coupling is mainly through far field of the scattered light, whichscales as d −1 . In this work we will not consider the latter case, but only concentrate onthe so-called near-field. In particular, in order to gain qualitative insight on the effectsof interactions, we will analyse two different configurations, namely an isolated particlesupported on a dielectric substrate and a pair of close particles.