Analytical modeling of optical reflectivity of random plasmonic nano-monolayers

Abstract

In this paper, we compare three different models that have been used to interpret reflectivity measurements of supported monolayers of nanoparticles. Two of them: (i) isotropic Maxwell Garnett and (ii) anisotropic two-dimensional-dipolar model are based on an effective-medium approach, while the third one (iii) coherent-scattering model, lies within the framework of multiple-scattering theory. First, we briefly review, on physical grounds, the foundations of each model and write down the corresponding formulas for the calculation of the reflectivity. In the two-dimensional-dipolar model, the dilute limit of the pair-correlation function (also called hole-correlation function) is always used in the calculation of the effective optical response. Then we use these formulas to plot and analyze graphs of the reflectivity of a monolayer of gold nanoparticles on a glass substrate, as a function of several relevant parameters, for two different commonly used experimental configurations. Finally, we discuss the importance of our results and how they can be used to infer the limits of validity of each model.

Enhancement of Light Absorption by Leaky Modes in a Random Plasmonic Metasurface

“…The DM is well-suited to study metasurfaces with particles much smaller than the incident wavelength since it considers only the electric dipole moment induced within each particle. The second approach is a more sophisticated analytical model developed a few years ago, called the coherent scattering model (CSM), − which represents an approximate solution to Maxwell’s equations that takes into account multiple-scattering effects. It aims to study the optical response of a two-dimensional random array of spherical particles forming a monolayer.…”

“…Here k 0 is the wavenumber in vacuum, θ i is the angle between k⃗ 1 and ê z , and γ is the anisotropy factor defined as γ = ε ∥ eff /ε ⊥ eff . Further details of the DM model can be found in refs and .…”

“…Regarding the CSM model, the reflection amplitude coefficient for a random monolayer of spherical particles supported on a flat substrate in a TIR configuration can be written as where θ t = arcsin­(( n s / n m )­sin θ i ), β = 2 k 0 an m cos θ t , r 13 corresponds to the standard Fresnel amplitude coefficient of reflectance between the substrate and the matrix, and with α = 2Θ/( x m 2 cos θ i ), where Θ is the surface coverage, x m = k 0 an m is the size parameter, and S (0) and S s,p (π – 2θ i ) denote the amplitude scattering coefficients for a single spherical particle at the scattering angles 0 and π – 2θ i , respectively. The s and p subindices in S s,p stand for s or p polarization of the incident light.…”

“…The scattering amplitude coefficients can be calculated using the standard Mie solution . A detailed derivation of the CSM for a monodisperse monolayer on a flat substrate can be found in refs − , , and . Likewise, in ref an extended version of the CSM model for the case of a polydisperse monolayer on a substrate is derived.…”

Extinction Coefficient Modulation of MoO3 Films Doped with Plasmonic Nanoparticles: From an Effective Medium Theory Description

“…This latter configuration has generated significant interest due to the ability to modulate the absorbance in the visible range, a feature of great importance in photocatalytic applications, biological sensing, smart windows, and photovoltaic cells [ 22 ]. This property is attributed to a phenomenon called superficial plasmon resonance (SPR) [ 23 , 24 ]. In the study of photovoltaic cells, there are many phenomena that are studied with the aim of enhancing the plasmonic harvesting of sunlight in solar cells.…”