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

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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
5.2. 2-DIMENSIONAL ARRAYS OF GOLD NANOPARTICLES 950.18LSP L mode LSP T modeR Sa.R S0.140.104000.200.150.10500600 [nm]7000D1D2D0D1D2D800LSPR width [nm] L/T gap [nm] LSPR position [nm]6005755505257550250150100LTTLb.400500600 [nm]700800c.0D 1D 2DFigure 5.15: Panels a, b: R S reflectivity spectra computed as a function of the systemdimensionality for the “rectangular” sample, in parallel (a) and perpendicular (b) opticalconfigurations. Panel c: wavelength position and linewidth of longitudinal (solid markers)andtransverse(openmarkers)LSPresonancesandtheirsplitting(diamonds)asafunctionof the system dimensionality, deduced from the R S spectra in panels (a), (b).T LSP modes are not degenerate. Thus, the collective optical anisotropy of the squaresamples arises from a superposition of single-NP effects (i.e. the splitting in 0D) andof anisotropic EM collective coupling, the latter having the net effect of enhancing theoriginal L/T splitting.In the rectangular case, in contrast, the circular in-plane aspect of the NPs yieldsan isotropic polarizability of the inclusions, hence no intrinsic 0D L/T splitting and nosubsequent anisotropy in the EM radiation. The only source of anisotropic plasmonicresponse is therefore the rectangular symmetry of the array, which induces the appearanceof different dipolar fields E ind and E ∗ indfor longitudinal or transverse excitations, due tothe not equivalent NPs spacings within the array; these effects are however somewhatsmaller as compared to the square sample.We can therefore conclude that the tuning of the plasmon response of self-organized2D arrays appears to be more flexibly and successfully performed when starting fromanisotropic elementary building blocks, for which intrinsic and collective properties effectivelyreinforce each other in determining the overall LSP characteristics. Ellipsoidalnanoparticles with different aspect ratios provide the most efficient way to tune the po-
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Università degli studi di GenovaFa
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4 CONTENTS5.2.2 Optical anisotropy
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6 Introductionconfining the EM ener
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8 Introduction
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10 CHAPTER 1. THEORYEλBkFigure 1.1
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12 CHAPTER 1. THEORYfrom which, sep
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14 CHAPTER 1. THEORY≈ ω 0 like
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16 CHAPTER 1. THEORYε 1 (λ) = N 2
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18 CHAPTER 1. THEORYThe correspondi
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20 CHAPTER 1. THEORYso the induced
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22 CHAPTER 1. THEORYε MG −ε aε
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24 CHAPTER 1. THEORYUV range, this
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26 CHAPTER 1. THEORYwhich is called
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28 CHAPTER 1. THEORYwhere Γ 0 = v
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30 CHAPTER 1. THEORYpoints of the c
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32 CHAPTER 1. THEORYand then monoto
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34 CHAPTER 1. THEORYposition, has t
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36 CHAPTER 1. THEORYfieldorequivale
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38 CHAPTER 1. THEORY
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40 CHAPTER 2. EXPERIMENTAL METHODSt
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42 CHAPTER 2. EXPERIMENTAL METHODSt
Page 44 and 45: 44 CHAPTER 2. EXPERIMENTAL METHODS2
Page 46 and 47: 46 CHAPTER 2. EXPERIMENTAL METHODSs
Page 48 and 49: 48 CHAPTER 2. EXPERIMENTAL METHODSt
Page 50 and 51: [001][100]50 CHAPTER 3. SELF-ORGANI
Page 52 and 53: 52 CHAPTER 3. SELF-ORGANIZED NPS AR
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Page 98 and 99: 98 CHAPTER 6. COMPOSITE MEDIA BASED
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Page 102 and 103: 102 CHAPTER 6. COMPOSITE MEDIA BASE
Page 104 and 105: 104 Conclusionsparticular cases of
Page 106 and 107: 106 Acknowledgements
Page 108 and 109: 108 BIBLIOGRAPHY[14] Shouheng Sun,
Page 110 and 111: 110 BIBLIOGRAPHY[44] Q A Pankhurst,
Page 112 and 113: 112 BIBLIOGRAPHY[74] Prashant K. Ja
Page 114 and 115: 114 BIBLIOGRAPHY[103] Tobias Kraus,
Page 116 and 117: 116 BIBLIOGRAPHY[137] F. Brouers, J
Page 118 and 119: 118 BIBLIOGRAPHY[169] Christy L. Ha
Page 120 and 121: 120 BIBLIOGRAPHY[201] G. Baldacchin
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