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

36 CHAPTER 1. THEORYfieldorequivalentlyreinforcingtherestoringforces(fig.1.19(d)); therefore, inthiscasetheresonance frequency is increased, and the LPS mode blue-shifts (fig. 1.19(c)). Moreover,duetotheretardationeffectsoftheinteractions,theradiationdampingofcoupledparticlesis larger than of isolated ones, so the LSP modes become broader.The splitting and broadening of the single-particle resonances are determined by thestrength of the interactions between adjacent particles, and they can be tuned by varyingthe separation (fig. 1.20(a)) or the number (fig. 1.20(b)) of the particles forming the chain[58, 60, 153, 162, 170].In particular, the splitting of the single-particle LSP modes has been demonstrated[86, 171] to play a key role for the coherent transport of EM energy. Exploiting the abilityof metallic nanostructures to localize and strongly enhance the EM radiation, uniaxialchains of nanoparticles can be employed as waveguides at nanoscale, allowing the propagationof EM signals with lateral confinement beyond the the diffraction limit [171]. Allthe main characteristics of the waveguide (group velocity, bandwidth, attenuation of thepropagating waves) are dependent on the energy separation between the longitudinal andthe transverse LSP modes, excited by electric fields along and normal the waveguide.For example, in fig. 1.20(c) we report the dispersion relation ω(k) for the longitudinal L(blue line) and transverse T (red line) modes, computed for an infinite chain of sphericalnanoparticles assuming dipolar interactions between nearest-neighbours [86, 171]; thegroup velocity v g for energy transport corresponds to the slope of the curves. For both Land T modes, v g is null and the frequency splitting ∆ω is maximum for uniform excitations,i.e. k = 0 along the chain. Increasing the wave number k of the exciting field, v gincreases while ∆ω decreases. For k = π/d the splitting of the L and T modes collapsesto zero and their energy reduces to the single-particle LSP; correspondingly, the groupvelocity reaches the maximum values and v L g = 2v T g , due to the stronger EM coupling forL waves than for T waves. Maximum values of v g up to 0.1c and transmission efficienciesup to 64% were predicted [86].Tω Tω 0ωω LLa. b. c.0πdπ2d0kπ2dπdFigure1.20: Panela: dependenceoftheplasmonpeakpositionontheinterparticlespacingd for both the longitudinal (L) and transverse (T) excitation of the collective mode in2D arrays of gold nanoparticles chains (from ref. [60]); the dotted line shows the 1/d 3dependencepredictedbyapointdipoleinteractionmodel[86]. Panelb: collectiveplasmonresonance energies for both L and T excitations for Au nanoparticle chains of differentlengths (from ref. [58]). Panel c: computed dispersion relation ω(k) for L and T LSPmodes in a infinite chain of metallic nanoparticles, according to a point dipole interactionmodel [86, 171].In summary, the basic theory of the interaction between light and heterogeneous mediahas been review, with particular emphasis on the optical response of metallic inclusions