Search

We study an optical method to infer the size of nanoparticles in a thin film of a dilute nonabsorbing nanocolloid. It is based on determining the contribution of the nanoparticles to the complex effective refractive index of a suspension from reflectivity versus the angle of incidence curves in an internal reflection configuration. The method requires knowing only approximately the particles' refractive index and volume fraction. The error margin in the refractive index used to illustrate this technique was 2%. The method is applicable to sizing nanoparticles from a few tens of nanometers to about 200 nm in radius and requires a small volume of the sample, in the range of a few microliters. The method could be used to sense nanoparticle aggregation and is suitable to be integrated into microfluidic devices.

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.

We assess the validity and possible use of a simple formula for the complex effective refractive index of a colloidal suspension of very small particles obtained from the quasi-crystalline approximation. This approximation takes into account the so-called dependent scattering effects, which are strongest, in relative terms, in suspensions of non-absorbing nanometer-sized particles. We test experimentally the predictions of the model for the extinction of light in dispersions of sodium dodecyl sulfate micelles in tri-distilled water. We find that the theoretical model can be fitted to the experimental data and provide estimates of the micelles' size and the minimum distance between each other in suspension.

The main objective of this paper is to endorse a recently derived theoretical model for the coherent reflectance and transmittance from a surface supporting a disordered monolayer of large and tenuous particles by comparison with experimental measurements. The model is based on the so-called anomalous-diffraction approximation and is assumed to be valid for small and moderate angles of incidence. We prepared disordered monolayers of spherical polystyrene particles of 1.8 μm diameter and of human red blood cells on glass microscope slides. In both cases, particles were immersed in a liquid of refractive index close to that of the particle. We measured the relative reflectivity and transmissivity of the samples versus the wavelength of light at normal incidence and the reflectivity and transmissivity versus the angle of incidence at a fixed wavelength, and compared with predictions of the anomalous-diffraction approximation model. For the polystyrene particle samples, we also compare the results with another available theoretical model developed some years ago to deal with disordered monolayers of highly scattering particles. In the case of red blood cell monolayers, we also present measurements with a hemolyzed sample and a disordered multilayer film for comparison. We find that the anomalous diffraction model can be fitted very well to the experimental curves, in some cases, even for high angles of incidence.

We study the reflection of diffuse light from 1D randomly rough dielectric interfaces. Results for the reflectance under diffuse illumination are obtained by rigorous numerical simulations and then contrasted with those obtained for flat surfaces. We also explore the possibility of using perturbation theories and conclude that they are limited for this type of study. Numerical techniques based on Kirchhoff approximation and reduced Rayleigh equations yield better results. We find that, depending on the refractive index contrast and nature of the irregularities, the roughness can increase or decrease the diffuse reflectance of the surface.

We analyze a method recently proposed to retrieve the size, refractive index, and concentration of particles in nonabsorbing nanofluids from measurements of the complex effective refractive index of two dilutions of the nanofluid [Opt. Lett.39, 559 (2014)]. The method uses simple formulas to retrieve the particles' parameters. First, we discuss precautions needed with the new method when inferring the refractive index of the particles from measurements of the imaginary part of the effective refractive index of two dilutions of the original nanofluid. Then we analyze the use of this methodology to obtain some average radius in the size of polydisperse suspensions and in the case of suspensions of weakly absorbing particles. We also perform an error analysis considering fixed errors in measurements and calculating the errors in the retrieved size, refractive index, and concentration of particles. Finally, we characterize experimentally nanofluids of polymeric particles fabricated of poly(methyl-methacrylate) (PMMA) and polystyrene (PS) for which we achieved an uncertainty of 5×10(-3) and 1×10(-2) in the determination of the particle refractive index, respectively, and a precision better than 3% in the determination of their radii.

In photoacoustic imaging, the signal attenuation is a well-known source of artifacts over the image reconstruction. It is recognized that this is caused by optical absorption effects and by the ultrasound broadband scattering. However, the sound dispersion is generally neglected, although it appears notably in thick or heterogeneous tissues. In the present Letter, we give an experimental example in which both attenuation and sound dispersion are dealt with as relevant features to be taken into consideration. An analytic perspective of these perturbations leads us to a waveform transport-model extension that provides a linear description of the induced acoustic effects. We find a near match between the theoretical predictions and the experimental results in the frequency domain. These outcomes approximate projection data that represent forward solutions in photoacoustic image reconstruction.

We investigate experimentally the determination of the effective refractive index (RI) of a turbid particle suspension from the angle dependence of light scattered by the particles and then transmitted into a transparent prism of higher RI. We assembled a versatile experimental device that may be recognized as an Abbe-type refractometer in which the sample is illuminated from the prism side and use it to measure the intensity profile of diffuse light refracted into the prism around the critical angle. By fitting a recently proposed theoretical model we extract the complex RI of turbid suspensions of particles from the measured intensity profiles. We show that the real part of the effective RI is readily obtained with good precision regardless of how the sample is illuminated, whereas obtaining the imaginary part is done with less precision but nevertheless useful measurements can be obtained. The effective RI obtained with this method compares very well with the so-called van de Hulst effective RI and the one derived from Keller's model of the effective propagation constant.

We study theoretically the extinction of collimated light in random systems of highly scattering particles embedded in nonabsorbing media. We aim to provide rough guidelines on the behavior of the extinction coefficient in the so-called dependent-scattering regime. We base our analysis on Keller's second order perturbative approximation to the effective propagation constant. To gain physical insight, we also analyze a simple model based on the physical notion that particles in a dense system scatter light in an effective medium.

We derive a simple model for the angular-intensity profiles of diffuse light transmitted from a turbid colloid into a transparent medium of higher refractive index (RI) near the critical angle. Adjusting this model to experimental profiles obtained with an Abbe-type refractometer offers a sensitive and robust way of measuring the complex effective RI of highly scattering media.

Using a multiple-scattering formalism, we derive closed-form expressions for the coherent reflection and transmission coefficients of monochromatic electromagnetic plane waves incident upon a two-dimensional array of randomly located spherical particles. The calculation is performed within the quasi-crystalline approximation, and the statistical correlation among the particles is assumed to be given simply by a correlation hole. In the resulting model, the size of the spheres and the angle of incidence are both unrestricted. The final formulas are relatively simple, making the model suitable for a straightforward interpretation of optical-sensing measurements.

The transmission of an optical beam through the compound cell of a differential refractometer with an absorbing sample is analyzed. Formulas for the lateral shift and the deflection angle of the transmitted optical beam for a complex refractive-index difference are obtained.

We develop a coherent-scattering model for the reflection of light from a monolayer of large particles and low surface coverage. The model takes into account multiple scattering between particles of the monolayer and with the substrate, and it can be used around the critical angle in an internal reflection configuration. We compare the results of the model with our own reflectivity data taken with latex particles adsorbed on a glass-water interface and with a simpler effective-medium model.

We compare a recently developed coherent-scattering model for the reflectance of light from a turbid colloidal suspension of particles with experimental measurements. The experimental data were obtained in an internal reflection configuration around the critical angle using a glass prism in contact with a monodisperse colloidal suspension of latex particles, and a polydisperse suspension of TiO2 particles. First, we review the coherent scattering model and extend it to the case of polydisperse suspensions in an internal reflection configuration. The experimental data is then compared with results of the coherent scattering model and results obtained assuming that the colloidal system can be treated as a homogeneous medium with an effective index of refraction. We find that the experimental results are not compatible with the effective medium model. On the other hand, good fits to the experimental curves can be obtained with the coherent scattering model.

We investigate the use of laser reflectometry near the critical angle to monitor particle adsorption onto a flat glass surface. Experimental results show that positive particles are adsorbed onto the glass surface and that their adsorption kinetics depend strongly on the volume fraction occupied by the particles in suspension but not appreciably on the particle size. The reflectance near the critical angle is dominated by the particles on the surface, with the contribution of the particles in suspension being very low. We compare the reflectance change near the critical angle with the change in reflectance near the Brewster angle when particles are adsorbed onto the glass surface. We find that reflectometry near the critical angle is 3000 times more sensitive than it is near the Brewster angle. Some optical images are presented to validate our results.

We consider the coherent reflection and transmission of electromagnetic waves from a slab of a dilute system of randomly located, polarizable, spherical particles. We focus our attention on the case where the size of the spheres is comparable to the wavelength of the incident radiation. First, using wave-scattering and Mie theories, we derive expressions for the coherent fields that are transmitted and reflected by a very thin slab. Then we find the effective-current distribution that would act as a source of these fields. We conclude that if the effective currents were induced in an effective medium, this medium must possess, besides an effective electric permittivity, also an effective magnetic permeability. We find that both of these optical coefficients become functions of the angle of incidence and the polarization of the incident wave. Then we calculate the reflection coefficient of a half-space by considering a semi-infinite pile of thin slabs and compare the result with Fresnel relations. Numerical results are presented for the optical coefficients as well as for the half-space reflectance as a function of several parameters. The reflectance is compared with that obtained without considering the magnetic response. Finally, we discuss the relevance and the physics behind our results and indicate as well the measurements that could be performed to obtain an experimental verification of our theory.

One can use the angle-modulated reflectance of a gaussian beam near the critical angle to sense with high resolution the index of refraction of the external medium. We analyze in detail the reflectivity of a gaussian beam near the critical angle and its dependence on the optical absorption of the external medium. The given formulation is relatively simple and is useful in discerning the effects of the various parameters involved on the reflectivity and its differentials with respect to the angle of incidence. The results presented can be readily used for the quantitative design of novel sensors based on modulated reflectance near the critical angle. We provide a simple algebraic expression for the loss of sensitivity of modulated reflectance near the critical angle as the sample's absorption coefficient increases. We find that, in a typical case, the sensitivity has decreased to approximately half its value for transparent samples when the absorption coefficient has increased to 25 cm(-1). We conclude that modulated reflectance near the critical angle remains a competitive technique for monitoring the index of refraction of an external medium with an absorption coefficient of as much as 120 cm(-1). We compared experimentally obtained curves of the first differential of the reflectivity with respect to the angle of incidence with theory and found good agreement.