We compare light reflectivity measurements as a function of the angle of incidence for an interface between an optical glass and a turbid suspension of small particles, with theoretical predictions for the coherent reflectance calculated with different available theoretical models. The comparisons are made only in a small range of angles of incidence around the critical angle of the interface between the glass and the matrix of the colloidal suspensions. The experimental setup and its calibration procedure are discussed. We considered two Fresnel-based approximations and another two based on a multiple-scattering approach, and we present results for monodisperse latex colloidal suspensions of polymeric spherical particles in water with particle diameters of 120 and 520 nm, polydisperse titanium dioxide (rutile) particles suspensions in water with a most probable diameter of 404 nm, and suspensions of copper particles in water with diameters of 500 nm. The comparisons between experiment and theory are made without fitting any parameters.

We calculated the real and imaginary parts of the effective refractive index n eff of blood as functions of wavelength from 400 to 800 nm; we employed van de Hulst's theory, together with the anomalous diffraction approximation, for the calculation. We modelled blood as a mixture of plasma and erythrocytes. Our results indicate that erythrocyte orientation has a strong effect on n eff , making blood an optically anisotropic medium except when the erythrocytes are randomly oriented. In the case in which their symmetry axis is perpendicular to the wave vector, n eff equals the refractive index of plasma at certain wavelengths. Furthermore, the erythrocytes' shape affects their contribution to n eff in an important way, implying that studies on the effective refractive index of blood should avoid approximating them as spheres or spheroids. Finally, the effective refractive index of blood predicted by van de Hulst's theory is different from what would be obtained by averaging the refractive indices of its constituents weighted by volume; such a volume-weighted average is appropriate only for haemolysed blood. We then measured the real part of the refractive index of various blood solutions using two different experimental setups. One of the most important results of our expriment is that n eff is measurable to a good degree of precision even for undiluted blood, although not all measuring apparatuses are appropriate. The experimental data is self-consistent and in reasonable agreement with our theoretical calculations.

This paper addresses a long-standing concern of whether one can measure the refractive index of a turbid colloid as if it were an equivalent homogeneous medium using standard techniques. We analyze the accuracy of determining the effective refractive index of turbid colloids when measuring the critical angle by reflection of light in an internal reflection configuration and then using Snell’s law. It is assumed that the critical angle is taken as the inflection point of the reflectance curve and that the effective refractive index of the turbid colloid is well approximated by the van de Hulst approximation. Experimental measurements are used to show the viability of measuring the inflection point of an angular-reflectance curve with highly turbid colloids. The refractive index of aqueous suspensions of and latex particles (sizes in the range of 100–500 nm) were determined with an accuracy of  ±0.0025. Then, a multiple-scattering model for the coherent reflection of light from turbid colloids is used to produce 2D maps of the estimated error in determining the effective refractive index of turbid colloids by the critical angle method as a function of the size and volume-filling fraction of the colloidal particles.

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.

The growing interest in functional transition metal oxides for efficient energy consumption or in the bio-sensing process; indicates that is necessary to develop a new theoretical method that describes experiments. This article presents a new theoretical methodology to characterize molybdenum trioxide (MoO 3) thin films doped with resonant gold-nanoparticles (Au-NPs) and non-resonant titaniumnanoparticles (Ti-NPs). The modulation of surface plasmon resonance (SPR) and the implications in the MoO 3 transmittance spectrum is described by applying an effective medium theory. The transmittance modulation was modified by variating three parameters, the radius of the NPs, the concentration of the NPs as well as the variation of the MoO 3 thin films thickness. It was found that the nanoparticles concentration is the most important parameter in the transmittance modulation. Additionally, the orthorhombic and monoclinic structure of MoO 3 was studied, from which it was obtained that the monoclinic structure of the MoO 3 doped with Au-NPs favors the reduction in the transmittance values in the visible region which is associated with the increase of the SPR signal. Similar analyses are performed for non-resonant nanoparticles such as Ti, where it was found that optical modulation is not as marked as the case of gold nanoparticles. Optical properties of different kind of systems has attracted attention for many researchers around the world 1-5. Developing new devices with interesting optical properties has been a technological and experimental challenge 6,7. In order to describe optical properties from a theoretical point of view, it have been developed sophisticated multiphysics modeling finite element commercial software, such as Comsol Multiphysics, Lumerical FDTD or BEM which allow you to calculate, reflection or transmission frequency-dependent or scattering parameters and near or far electromagnetic field projections. However, many of them are difficult to access since they are expensive or they are not very intuitive software's. So, implementing new theoretical formalisms to characterized and analyzed thin films with new, interesting and unexpected effects could be useful for developing new devices with different kinds of optical properties. There are some different approaches to characterize thin films 8-10 , particularly for thin films doped with different materials, using an effective medium theory to describe the radiation interaction with the doped thin films could be an alternative. In effective medium models, one of the most important approximation is the large size limit. The most studied formalisms that consider effective medium theories (EMTs) are Maxwell Garnett or Bruggeman, these models are applied to described materials with granular topology 11 and materials with intermixed components 12 , respectively. These EMTs are based on small spheres approximation, which means that the size of the particles is small compared with the incident radiation wavelength 13. An alternative formalism to study effective me...