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

5.2. 2-DIMENSIONAL ARRAYS OF GOLD NANOPARTICLES 91evidence of N LSP modes was found in any R P curve, indicating that the polarizability forelectric fields normal the surface plane is much lower than along the in-plane directions.The corresponding reflectivities, computed according to the model for the goldnanoparticles, are plotted as continuous lines in the graphs of fig. 5.11 and fig. 5.12.The calculations were performed using the morphological parameters deduced from theAFM data, reported for reference in tab. 5.1; the schematic diagrams of the NPs geometryand arrangement employed for the calculations are also reported in panels (a) of the samefigures.Sample (a x ,a y ,a z ) Λ d y(nm) (nm) (nm)Square (11.5, 17, 8) 41 41Rectangular (8.3, 8.3, 5) 30 20Table 5.1: Morphological parameters deduced from AFM analysis for the square andrectangular samples, employed to calculate the reflectivity spectra reported in fig. 5.11and fig. 5.12. For each sample, the ellipsoid semi-axes (a x ,a y ,a z ) are listed, along withthe experimental values for Λ and d y .The distributions of depolarization factors L γ for the square and rectangular sampleswere deduced starting from the corresponding distributions of in-plane NPs semiaxes,extracted from the AFM images of fig. 5.9(b) and fig. 5.10(b). Due to the rather complexfunctional dependence of L from the ellipsoids semiaxes (cfr. eq. (1.43)), the originallognormal shape of the distribution is likely distorted, resulting in a complex distributionof L. For the sake of the present analysis, therefore, the L γ spread was assumed to obeya normal dispersion for all the ellipsoid axes. The standard deviations σ L were deducedby converting the spread σ a of the NPs axes by means of eq. (1.43), i.e. σ L = [L γ (a γ +σ a )−L γ (a γ −σ a )]/2. We found σ L ≈ 0.05 for the rectangular sample and σ L = 0.06 forthe square case.Although several strong assumptions have been made, the matching between the experimentaldata and the theoretical curves is quite good, as can be seen from fig. 5.11 andfig. 5.12, especially considering the non-trivial experimental geometry addressed (obliquereflectivity) and the achievement of a quantitative agreement between model calculationsand data.Thecomputedeffectivedielectricfunctionsε ξξeff , providedbythemodelinthetwocases,are shown in fig. 5.13. We can see that, in the proximity of the LSP resonances, ε eff isvery similar to the dielectric constant of a Lorentz oscillator (cfr. fig. 1.3): the imaginarypart of ε eff is peaked at the resonance, while the real part exhibits first a minimum andthen a maximum crossing the resonance at increasing wavelengths. All the three principalcomponents of the effective dielectric tensor follow the same trend as a function of thewavelength, with variations in the position, width and intensity of the resonances dueto the anisotropic NP shape or arrangement. In particular, we notice that the dielectricfunction ε zzeffcorresponding to the LSP N mode is considerably smaller than the other ones,in accordance with the fact that such mode is not observed in the R P reflectivity spectra.We can also qualitatively explain the different positions of the resonances when observedin reflection or transmission (cfr. fig. 4.9 and fig. 4.7(b)) in terms of the effective dielectricconstant: transmissivity is mostly determined by the absorption of light inside the NPslayer, thus it is mainly related to the imaginary part of ε eff ; in contrast, the reflected lightis generated by the EM radiation emitted from the induced dipoles, so it more relatedto the real part of ε eff , whose maximum is at a wavelength slightly longer than the peak