Overview of an effective‐medium approach to the reflection and refraction of light at a turbid colloidal half‐space

Abstract

It has been recently shown that the effective electromagnetic bulk response of a dilute colloidal system, composed by a large collection of identical big spheres, located at random, is spatially dispersive (non-local). Here, we extend this effectivemedium approach to the calculation of the reflection and transmission amplitudes of the same system but with a flat interface. We use an integral-equation approach for the calculation of the average electric field. The integral equation is solved within the effective-field approximation, by proposing a plane-wave solution with effective parameters that are calculated by solving a set of consistency equations. We obtain explicit expressions for the transmission and reflection amplitudes as a function of the filling fraction, the radius of the inclusions and the angle of incidence. We show and discuss numerical results for a system of silver particles.

Refractive index measurement of turbid media by transmission of backscattered light near the critical angle

“…The coherent component corresponds to the average of the electromagnetic fields over all the permitted microscopic configurations of the system, whereas the diffuse component relates to the fluctuations of the electromagnetic fields around its average [1,5,[14][15][16]19,20,25]. When scattering is strong the coherent component decays rapidly within the bulk of the material and all is converted to diffuse light or absorbed.…”

“…When absorption by the material is small, most of the energy flux is carried by the diffuse component. The effective RI assigned to the coherent component of light has been investigated in recent years [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], and its nonlocal nature has been established [19,25]. However, as already said the effective RI seen by diffuse light has been barely investigated, and the only reference reporting efforts in the past that helps address this question is that of Meeten and North [6].…”

“…The concept and measurement of the effective RI has been associated only with the so-called coherent component of light [11,[14][15][16][17]19,25]. Therefore its measurement in turbid media has been pursued primarily using the propagation or reflection of the coherent component of light.…”

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

“…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.…”

“…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.…”