Optical reflectivity of a disordered monolayer of highly scattering particles: coherent scattering model versus experiment

Abstract

Recently a multiple-scattering model for the reflectivity of a disordered monolayer of scattering particles on a flat surface was put forth [J. Opt. Soc. Am.29, 1161 (2012)]. The approximate theoretical model provides relatively simple formulas for the reflectivity, but it was developed for a monodisperse monolayer. Here we extend the model to the case of a polydisperse monolayer and derive the appropriate formulas to calculate the optical transmissivity of the monolayer supported by a flat interface. A second objective of this paper is to test the approximate theoretical model against experimental data with highly scattering particles. We prepared monolayers of three different surface coverage fractions of polydisperse alumina and titanium dioxide particles deposited randomly on a glass slide. We measured their optical reflectivity and transmissivity versus the angle of incidence using a laser with a wavelength of 670 nm. Using the nominal values for the particles' most probable radius and refractive index, we fitted the theoretical model to the experimental curves and found that it reproduces very well the experimental curves. Interestingly, a dip in the reflectivity curves at large angles of incidence is present for the alumina monolayers but not in the titanium dioxide monolayers. The dip corresponds to a maximum in the scattering efficiency by the alumina monolayers. The theoretical model reproduces very well this behavior.

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.…”

First-principles modeling of electromagnetic scattering by discrete and discretely heterogeneous random media

“…Note that we intentionally defined the three EOAs in terms of the linear operators Î and scâ ℑ acting on an optical observable rather than on the macroscopic field vectors (of course these definitions can be generalized to include types of optical observables other than the Poynting-Stokes tensor). Traditionally, however, EMAs have been introduced with the purpose of replicating the average macroscopic field vectors rather than specific optical observables [72][73][74][75][76][77][78][192][193][194][195][196][197][198][199]. In other words, a semi-stochastic EOA would normally be introduced as a recipe for replacing a stochastic morphologically complex scattering object by a fixed simple "effective" object such that in Eq.…”

“…Direct computer solutions of the MMEs for morphologically complex objects can be quite time-consuming and in many cases impracticable. As a consequence, there has been a widespread use of phenomenological so-called effective-medium rules intended to drastically simplify the computation (see [72][73][74][75][76][77][78][192][193][194][195][196][197][198][199] and references therein). Implicitly, the main idea of an effective-object approximation (EOA) (more commonly known as an effective-medium approximation, or EMA) is to replace a morphologically complex object, either fixed or randomly varying in time, by a much simpler "effective" object possessing essentially the same scattering properties.…”

Direct detection of aggregates in highly turbid colloidal suspensions of polystyrene nanoparticles

“…However, in the case of a highly turbid medium there is detectable loss in TIR intensity owing to scattering even for these small penetration depths, which had not been carefully accounted for until our work in Refs. [17,19,20], and recent elegant work by others [26][27][28]. Our model calculates the scattering-induced loss in TIR intensity by introducing the concept of an angle-dependent n i , i.e., n i θ i n i κθ i .…”