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

101increased. Before the deposition (red curves in fig. 6.3), the longitudinal LSP mode isfound at λ L = 620 nm, with a width of Γ L = 170 nm; the transverse mode is insteadlocated at λ T = 570 nm and has a width of Γ T = 125 nm. Following the deposition (blackcurves in fig. 6.3), both modes redshift by few tens of nm, the L mode at λ ∗ L = 645 nmand the T mode at λ ∗ T = 585 nm, while the corresponding widths become Γ∗ L = 215 nmand Γ ∗ T = 145 nm, respectively.This trend is in accordance with the qualitative considerations in §1.3.3, where wediscussed the dependence of the dielectric environment on the LSP resonances. In particular,the simultaneous redshift of the resonances can be explained in terms of the Fröhlichcondition Re [ ε L,Tm (λ L,T ) ] = −2ε h (see eq. (1.45)), where ε m , ε L,Thand λ L,T are thedielectric constant of the individual Au NPs and of the host and the position of the resonances,respectively. ε m is shown in fig. 5.6(b), and its real part has a negative slopefor increasing wavelengths; in fig. 6.4 we report instead the dielectric constant of bulkmagnetite, extracted from ref. [220]. In analogy with the model of the previous chapter,in first approximation the dielectric constant ε h can be expressed as a linear combinationof the dielectric constants of the materials surrounding the Au NPs; therefore, followingthe deposition of the Fe 3 O 4 /OA NPs, ε h is expected to increase, because the real partof the dielectric constant of magnetite reads about ε 1 = 5 in correspondence of the goldnanoparticles LSP resonances. Then, according to the Fröhlich condition, if ε h increasesand ε m has a negative slope as a function of the wavelength, the LSP resonances of thegold NPs must red shift when embedded in the Fe 3 O 4 /OA layer.64.053.5Re []43.0Im []32.522.040060080010001200 [nm]Figure 6.4: Real (red line) and imaginary (black line) parts of the dielectric constant ofbulk magnetite in the visible and near-IR range, from ref. [220].In order to quantitatively evaluate the effects of the Fe 3 O 4 /OA NPs on the plasmonicresponse of the Au NPs array, we can apply the theoretical framework developed in theprevious chapter to the current system. In fig. 6.5(a) we report the computed R S spectrafor the “bare” Au/LiF nanostructures, compared to the corresponding experimentalvalues, for the L and T LSP modes, at an angle of incidence of θ = 50 ◦ . In analogywith before, the morphological parameters employed for the calculations were obtainedfrom the analysis of the AFM data: for the NPs spacings across and along the ripples weused d x = d y = 33 nm, while the values of the ellipsoids semiaxes were a x = 11.2 nm,a y = 14.0 nm and a z = 6.4 nm.The corresponding spectra in presence of the Fe 3 O 4 /OA NPs were computed keepingthe same input parameters, except two specific modifications. Considering a single