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

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90 CHAPTER 5. MODELLING AND ANALYSIS OF THE OPT. PROP.0.015R P||0.20R S┴R PR S0.150.0050.10a.200400600800 [nm]100012001400c.200400600800 [nm]1000120014008.3 nmpsps22 nme.30 nm0.15R S||0.010R p┴R SR P0.100.005b.200400600800 [nm]100012001400d.0.000200400600800 [nm]100012001400Figure 5.12: “Rectangular” sample. Left panels: p-polarized (a) and s-polarized (b) reflectivityspectra measured with the plane of incidence parallel (||) the LiF ridges. Rightpanels: s-polarized (c) and p-polarized (d) reflectivity spectra measured with the planeof incidence perpendicular (⊥) the LiF ridges. Red curves: excitation of transverse LSPmode (R ||S , R⊥ P ); black curves: excitation of longitudinal LSP mode (R⊥ S , R|| P). Thecontinuous lines represent the corresponding reflectivities calculated according the modeldescribed in §5.2.1. The dashed curves were computed with the same morphological parameterslike the previous ones but neglecting the dispersion of the depolarization factors.Panel e: schematic diagram representing the NPs arrangement and shape employed in theoptical calculations.p polarization the electric field is not purely parallel the surface, but has also a normalcomponent, which excites the LSP N mode.The “rectangular” sample (fig. 5.12) has instead a less pronounced optical anisotropy.The longitudinal LSP peak is found at λ S L = (561 ± 3) nm and λP L = (567 ± 3) nm,red shifted by only 15-20 nm with respect to the transverse LSP located at λ S T = λP T =(546±3) nm, and all the peaks exhibit roughly the same width of Γ ≈ 100 nm.As a general consideration, we point out that the main difference between the R S andR P spectra is the overall intensity, as expected due to the different optical coefficients,while the position and the width of the resonances is preserved; in particular, no clear
5.2. 2-DIMENSIONAL ARRAYS OF GOLD NANOPARTICLES 91evidence of N LSP modes was found in any R P curve, indicating that the polarizability forelectric fields normal the surface plane is much lower than along the in-plane directions.The corresponding reflectivities, computed according to the model for the goldnanoparticles, are plotted as continuous lines in the graphs of fig. 5.11 and fig. 5.12.The calculations were performed using the morphological parameters deduced from theAFM data, reported for reference in tab. 5.1; the schematic diagrams of the NPs geometryand arrangement employed for the calculations are also reported in panels (a) of the samefigures.Sample (a x ,a y ,a z ) Λ d y(nm) (nm) (nm)Square (11.5, 17, 8) 41 41Rectangular (8.3, 8.3, 5) 30 20Table 5.1: Morphological parameters deduced from AFM analysis for the square andrectangular samples, employed to calculate the reflectivity spectra reported in fig. 5.11and fig. 5.12. For each sample, the ellipsoid semi-axes (a x ,a y ,a z ) are listed, along withthe experimental values for Λ and d y .The distributions of depolarization factors L γ for the square and rectangular sampleswere deduced starting from the corresponding distributions of in-plane NPs semiaxes,extracted from the AFM images of fig. 5.9(b) and fig. 5.10(b). Due to the rather complexfunctional dependence of L from the ellipsoids semiaxes (cfr. eq. (1.43)), the originallognormal shape of the distribution is likely distorted, resulting in a complex distributionof L. For the sake of the present analysis, therefore, the L γ spread was assumed to obeya normal dispersion for all the ellipsoid axes. The standard deviations σ L were deducedby converting the spread σ a of the NPs axes by means of eq. (1.43), i.e. σ L = [L γ (a γ +σ a )−L γ (a γ −σ a )]/2. We found σ L ≈ 0.05 for the rectangular sample and σ L = 0.06 forthe square case.Although several strong assumptions have been made, the matching between the experimentaldata and the theoretical curves is quite good, as can be seen from fig. 5.11 andfig. 5.12, especially considering the non-trivial experimental geometry addressed (obliquereflectivity) and the achievement of a quantitative agreement between model calculationsand data.Thecomputedeffectivedielectricfunctionsε ξξeff , providedbythemodelinthetwocases,are shown in fig. 5.13. We can see that, in the proximity of the LSP resonances, ε eff isvery similar to the dielectric constant of a Lorentz oscillator (cfr. fig. 1.3): the imaginarypart of ε eff is peaked at the resonance, while the real part exhibits first a minimum andthen a maximum crossing the resonance at increasing wavelengths. All the three principalcomponents of the effective dielectric tensor follow the same trend as a function of thewavelength, with variations in the position, width and intensity of the resonances dueto the anisotropic NP shape or arrangement. In particular, we notice that the dielectricfunction ε zzeffcorresponding to the LSP N mode is considerably smaller than the other ones,in accordance with the fact that such mode is not observed in the R P reflectivity spectra.We can also qualitatively explain the different positions of the resonances when observedin reflection or transmission (cfr. fig. 4.9 and fig. 4.7(b)) in terms of the effective dielectricconstant: transmissivity is mostly determined by the absorption of light inside the NPslayer, thus it is mainly related to the imaginary part of ε eff ; in contrast, the reflected lightis generated by the EM radiation emitted from the induced dipoles, so it more relatedto the real part of ε eff , whose maximum is at a wavelength slightly longer than the peak
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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
Page 40 and 41: 40 CHAPTER 2. EXPERIMENTAL METHODSt
Page 44 and 45: 44 CHAPTER 2. EXPERIMENTAL METHODS2
Page 46 and 47: 46 CHAPTER 2. EXPERIMENTAL METHODSs
Page 50 and 51: [001][100]50 CHAPTER 3. SELF-ORGANI
Page 52 and 53: 52 CHAPTER 3. SELF-ORGANIZED NPS AR
Page 76 and 77: 76 CHAPTER 5. MODELLING AND ANALYSI
Page 98 and 99: 98 CHAPTER 6. COMPOSITE MEDIA BASED
Page 100 and 101: 100 CHAPTER 6. COMPOSITE MEDIA BASE
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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