70 CHAPTER 4. SELF-ORGANIZED NPS ARRAYS: OPTICAL PROP.absorption at λ = 600 nm, while the minimum in T ⊥ blue shifts from λ ≈ 650 nm toλ ≈ 560 nm <strong>and</strong> gets narrower. We notice that the positions <strong>of</strong> the resonances whenobserved in transmission or in reflection are slightly different, the peaks <strong>of</strong> R being systematicallyred shifted with respect to the minima <strong>of</strong> T; we will discuss these effects in§5.2.2.We can interpret the variations in the optical <strong>properties</strong> induced by the annealing procedureusing the same arguments <strong>of</strong> the previous sections. We saw in §3.2 that, followingthe annealing, the layer <strong>of</strong> gold reorganizes in ordered <strong>arrays</strong> <strong>of</strong> nanoparticles; however,due to the convolution <strong>of</strong> the AFM tip, we could not determine from the AFM data wheneverthe particles were disconnected or not. In this respect, reflectivity <strong>and</strong> transmissivityprovide complementary tools to characterize the NP <strong>arrays</strong>. In the previous section weassociated the presence <strong>of</strong> a sharp LSP resonance, in the direction perpendicular the ripples,to the formation <strong>of</strong> disconnected wires <strong>of</strong> gold. In the same way, we can explain thesharp resonance, observed when the electric field is applied along the ripples, as the result<strong>of</strong> the formation <strong>of</strong> isolated metallic nanostructures within each groove: comparing theseconsiderations with the AFM data, we can then confirm that the nanoparticles <strong>of</strong> goldare disconnected both along <strong>and</strong> perpendicular to the ripples.4.2.3 Gold nanoparticlesWe now focus on the analysis <strong>of</strong> the optical <strong>properties</strong> <strong>of</strong> the 2D <strong>arrays</strong> <strong>of</strong> nanoparticles.In particular, we separately consider the dependence <strong>of</strong> the <strong>plasmonic</strong> resonances on theripples periodicity <strong>and</strong> on the gold coverage. For simplicity, we identify 3 distinct plasmonmodes, related tothe geometry <strong>of</strong> the system (fig. 4.10): alongitudinal (L) mode is excitedwhen the electric field oscillates along the ripples; a transverse (T) mode is excited whenthe electric field is applied across the ripples in the plane <strong>of</strong> the sample; a normal (N)mode is excited when the electric field has a component normal the sample surface. Wewilldiscussinthenextchapterthevalidity<strong>of</strong>thisassumption. Consideringthereflectivitygeometries introduced in the previous sections, we can deduce that R ||S <strong>and</strong> R⊥ S geometriesallow to excite the T <strong>and</strong> L modes only, respectively, while in R || P / R⊥ P geometries theN mode is activated beside the L/T mode. However, as we will see in the next sections,the intensity <strong>of</strong> the N mode is typically much weaker than the L <strong>and</strong> T ones, thereforethe corresponding contribution to the reflectivity or absorption peaks remains always“hidden” by the other optical features, <strong>and</strong> only the L <strong>and</strong> T modes are clearly observedin reflection or transmission.TNLFigure 4.10: Schematic representation <strong>of</strong> the three different LSP modes for the goldnanoparticles. Longitudinal mode (L): EM excitation along the ripples. Transverse mode(T): excitation transverse to the LiF ridges. Normal mode (N): excitation normal theplane <strong>of</strong> the sample.Following the same notation <strong>of</strong> the <strong>plasmonic</strong> modes, we define the length, the width
4.2. OPTICAL PROPERTIES OF AU NANOPARTICLES ARRAYS 71<strong>and</strong> the height <strong>of</strong> the particles as the dimensions along <strong>and</strong> across the ripples <strong>and</strong> normalto the surface, respectively.Dependence <strong>of</strong> LSP modes on ripple periodicityWe first investigate the influence <strong>of</strong> the ripples periodicity on the position <strong>of</strong> the <strong>plasmonic</strong>resonances. In fig. 4.11 we report sets <strong>of</strong> reflectivities measured on several <strong>arrays</strong> <strong>of</strong> inplanespherical particles at 50 ◦ <strong>of</strong> incidence. In all cases ≈5 nm <strong>of</strong> gold were deposited,<strong>and</strong> the samples have different periodicities <strong>of</strong> the underlying ripple structure: Λ ≈ 30 nmfor black lines (sample in fig. 3.8(a)), Λ ≈ 35 nm for blue lines, <strong>and</strong> Λ ≈ 40 nm for redlines (sample in fig. 3.8(b)).psps = 30 nm = 35 nm = 40 nm0.04R P||L modeER S┴0.30R P0.020.20RS0.100.004006008001000a. [nm] [nm] b.40060080010000.30R S||T modeR p┴0.03R S0.20E0.02RP0.100.014006008001000c. [nm] [nm]d.Figure 4.11: Sets <strong>of</strong> reflectivities at θ = 50 ◦ incidence, for s- <strong>and</strong> p-polarized incidentlight, measured on nanopatterned LiF(110) samples with different periodicities Λ, afterthe deposition <strong>of</strong> t Au = 5 nm Au at T ≈ 100 ◦ C <strong>and</strong> annealing at T = 400 ◦ C. Plane <strong>of</strong>incidence parallel (left panels) <strong>and</strong> perpendicular (right panels) the ripples. Excitation <strong>of</strong>LSP L mode (panels a, b) <strong>and</strong> T mode (panels c, d).For decreasing Λ, we observe two main variations <strong>of</strong> the resonances: both the L <strong>and</strong>T modes shift towards longer wavelengths, the L mode shifting from λ ≈ 580 nm for4006008001000