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

94 CHAPTER 5. MODELLING AND ANALYSIS OF THE OPT. PROP.respectively. The corresponding L/T splitting is about 40 nm, while the plasmonlinewidths are Γ 0 L = 148 nm and Γ0 L = 81 nm.1D Introducing the EM coupling between NPs belonging to the same chain leads to theappearance of an induced field E ind radiated by the neighbouring NPs (see fig. 5.16,top panels). When the electric field is transverse to the chain, E ind counteractsthe external field (red arrow in fig. 5.16(a)), thereby blue shifting the resonance; incontrast, for longitudinal excitation, the induced field adds up to the external field(fig. 5.16(b)), with a corresponding red shift of the LSP peak (cfr. §1.3.4) [58, 71–74, 76–78, 85, 86]. Moreover, due to the retardation effects of the interactions, theLSPmodesbecomealsobroader. Inourcase, theonsetofthedipolarcouplingwouldshift the L and T resonance peaks (blue curves in fig. 5.14(a, b)) to λ 1 L = 614 nm andλ 1 T = 524 nm, respectively, more than doubling the original 0D splitting (90 nm);correspondingly, the LSP widths become Γ 0 L = 187 nm and Γ0 L = 83 nm.2D In 2D, the local field acting on each particle acquires dipolar contributions E ∗ ind alsofrom NPs belonging to neighbouring chains, indicated in blue in fig. 5.16(c, d).For exciting fields both longitudinal and transverse to the ripples, E ∗ ind systematicallycounteracts the dipolar field E ind generated by NPs from the same chain (redarrows), thus reducing the LSP shifts observed in the 1D case. Accordingly, thecalculated L mode blue-shifts back to λ L = 600 nm while the T mode redshifts toλ T = 538 nm (black curves in fig. 5.14(a, b)), yielding a L/T splitting of 62 nm, inagreement with the experimental observations.For the “rectangular” sample (fig. 5.15) the situation is generally similar, but withsome extremely interesting changes.0D The in-plane spherical aspect of the NPs yields degenerate single-particle L and TLSPmodes, locatedatλ 0 L = λ0 T = 538nmandhavingalinewidthΓ0 L = Γ0 T = 77nm,i.e. no L/T splitting in the 0D case.1D The degeneracy is lifted in 1D, due to the presence of the dipolar field E ind ; here a30 nm splitting is observed, originating from the simultaneous redshift of L excitationsto λ 1 L = 561 nm and the blueshift of the T peak to λ1 T = 532 nm. The widthof the L resonances increases to Γ 1 L = 94 nm, Γ T remains unchanged.2D In 2D, the L mode slightly blue shift at λ T = 557 nm, while the T mode redshifts toλ L = 544 nm, finally yielding a L/T splitting of merely 18 nm, significantly lowerthan the one observed for the square samples. Correspondingly, the linewidths ofthe resonances increase up to Γ 2 T = 103 nm for the T mode and slightly decrease to= 92 nm for the L mode.Γ 2 LInterestingly, we notice that although the NPs lay on a square grid, the L and Tpeak positions (and their corresponding splitting) in the 2D case are not equivalent totheir 0D value. This happens because the anisotropic polarizability of the individual Auinclusions induces a correspondingly anisotropic radiated EM field [68, 72], that furtherreinforces the intrinsic system birefringence. This is schematically represented in panels(c) and (d) of fig. 5.16. When the external field is applied along the ripples, i.e. parallelto the major axis of the ellipsoids, the induced dipoles are weaker than for transversalexcitations. Correspondingly, the irradiated fields E ind and E ∗ inddepend on the directionof the external field, so, despite the square symmetry of the lattice, the collective L and