Advanced optical effective medium modeling for a single layer of polydisperse ellipsoidal nanoparticles embedded in a homogeneous dielectric medium: Surface plasmon resonances

Abstract

We calculate, in the quasistatic coupled dipole approximation, the analytical expressions of the effective dielectric tensor of a single layer of polydisperse ellipsoidal nanoparticles with two of their principal axes in the layer's plane and embedded in a homogeneous dielectric medium. The organization (isotropic or anisotropic) and orientation (without or with a preferential in-plane orientation) of the nanoparticles is taken into account, together with their (possibly correlated) in-plane size, in-plane projected shape, and height distributions. In particular, we propose to describe the response of a layer of nanoparticles presenting a height distribution by using a vertically graded effective medium model. The expressions are tested in the case of finely characterized dielectric/silver/dielectric granular trilayers grown by means of vapor deposition in which the silver coalesced nanoparticles present correlated in-plane size and in-plane projected shape/height distributions and a moderate surface coverage of about 25%. A satisfactory quantitative agreement is obtained between the simulated and measured surface plasmon extinction bands of the metal nanoparticles. This agreement is permitted by the capability of the effective medium model of taking into account the ellipsoidal shape of the nanoparticles. The significant role of the size and shape distributions is also demonstrated.

Experimental and theoretical determination of the plasmonic responses and shape distribution of colloidal metallic nanoparticles

“…17,18 However, preparation routes unavoidably conduct to NPs showing a shape distribution which induces drastic changes in the optical properties of NP assembly. [19][20][21][22] Indeed, by combining Gibbs free energy calculation to discrete dipole approximation, Noguez et al [23][24][25] have shown that the morphology and so the optical properties of NPs depend on the temperature used to synthesize them. In addition, as reported by Sayah et al, 19 silver prolates grown in a mesoporous silica matrix exhibit a large length distribution which induces an inhomogeneous broadening of the L-SPR bands.…”

“…Toudert et al 21 have introduced the NP shape distribution in the Yamaguchi model. 26 However, this model can only be applied for two dimensional arrays of NPs.…”

Thin films composed of Ag nanoclusters dispersed in TiO2: Influence of composition and thermal annealing on the microstructure and physical responses

“…in the form of nanoparticles, have unique physical and chemical properties compared to their bulk form [1]. Among them, silver (Ag) and gold (Au) are the two most studied plasmonic materials since when they are embedded in a dielectric matrix they manifest localized surface plasmon resonances (LSPR) in the visible range [2] [3] [4].…”

“…The LSPR effect occurs when the metallic nanoparticles are well-separated and have dimensions significantly smaller than the wavelength of the incident electromagnetic field [3]. It is responsible for a broad and intense absorption of light in the vicinity of the resonance frequency and the enhancement of the local electromagnetic field [1]. The LSP resonance frequency, bandwidth and peak height depend markedly on the nanoparticles composition, their shape, size and size distribution and also on the host dielectric matrix [5].…”

Coupled dipole plasmonics of nanoantennas in discontinuous, complex dielectric environments

“…Spectrum-averaged refractive indices insufficiently describe nanoantennas supported by emergent materials like transition metal dichalcogenides [13]. Maxwell-Garnett and effective medium [14][15][16][17] analytic approaches describe mode energy shifts for random [17][18][19] and ordered [20][21][22] nanospheres using Mie theory and the coupled dipole approximation (CDA), respectively, but are limited to real-valued dielectric substrates with near-zero dispersion.…”