Rubén G. Barrera

Vector spherical harmonics and their application to magnetostatics

An alternative and somewhat systematic definition of the vector spherical harmonics, in analogy with the commonly used scalar spherical harmonics, is presented. The new set of vector spherical harmonics satisfies the properties of orthogonality and completeness, and is compared with other existing definitions of vector spherical harmonics. Some applications to problems in magnetostatics are illustrated.

Plasmonic nanobilliards: controlling nanoparticle movement using forces induced by swift electrons.

Manipulation of nanoscale objects to build useful structures requires a detailed understanding and control of forces that guide nanoscale motion. We report here observation of electromagnetic forces in groups of nanoscale metal particles, derived from the plasmonic response to the passage of a swift electron beam. At moderate impact parameters, the forces are attractive, toward the electron beam, in agreement with simple image charge arguments. For smaller impact parameters, however, the forces are repulsive, driving the nanoparticle away from the passing electron. Particle pairs are most often pulled together by coupled plasmon modes having bonding symmetry. However, placement of the electron beam between a particle pair pushes the two particles apart by exciting antibonding plasmonic modes. We suggest how the repulsive force could be used to create a nanometer-sized trap for moving and orienting molecular-sized objects.

Surface correlation effects on gloss

A general expression for gloss within the scalar Kirchhoff s theory is de- rived in terms of the detector collecting angle, and two statistical parameters that characterize the surface roughness. Analytical expressions for gloss are derived for an exponential and a Gaussian correlation function, and numerical results for these and other quasi-exponential correlation functions are presented. It is shown that the inco- herent contribution to gloss is significant in common polymeric surfaces. The latter implies that surface height correlations cannot be neglected in the evaluation of gloss. It is also shown that for a correlation function with a single characteristic length, gloss scales with the correlation length Lc in the same way as with the detector collecting angle. This fact can be used to determine Lc with a glossmeter, and an experimental method to achieve this is proposed. q 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 1321-1334, 1998

Coherent reflectance in a system of random Mie scatterers and its relation to the effective-medium approach

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.

Scattering efficiency of clusters composed by aggregated spheres

We present a detailed study of the variation of the average scattering cross section of various aggregates of titanium dioxide crystallites as a function of their sizes and shapes. To perform the analysis, we use a recursive T-matrix algorithm that we developed. We show how the aggregation phenomenon can tremendously decrease the local scattering properties of a white paint film and consequently affects its hiding power. We also compare the results with the equivalent spherical volume approximation which is used in particle size analysis using static or dynamic light-scattering methods. We show how the equivalent volume approximation used in those methods should be handled with care.

Point charge in a three‐dielectric medium with planar interfaces

A simple method of obtaining integral representations of the electrostatic potential, the induced surface charge density, and the image potential for a point charge in a three‐dielectric medium with infinite planar interfaces is presented. The total induced charge at the interfaces is readily evaluated. Numerical results for the image potential in several illustrative cases are also shown. The case of a point charge between two grounded conducting plates becomes a special limiting case of the present problem.

Coherent reflection of light from a turbid suspension of particles in an internal-reflection configuration: Theory versus experiment.

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.

Measurement of the effective refractive index of a turbid colloidal suspension using light refraction

We propose and analyse a simple method to measure simultaneously the real and imaginary parts of the effective refractive index of a turbid suspension of particles. The method is based on measurements of the angle of refraction and transmittance of a laser beam that traverses a hollow glass prism filled with a colloidal suspension. We provide a comprehensive assessment of the method. It can offer high sensitivity while still being simple to interpret. We present results of experiments using an optically turbid suspension of polystyrene particles and compare them with theoretical predictions. We also report experimental evidence showing that the refractive behaviour of the diffuse component of light coming from a suspension depends on the volume fraction of the colloidal particles.

Optical reflectance anisotropy of Ag and Au (110) single crystals

We have developed a theoretical model for describing the electromagnetic response of noble metal surfaces. The model takes into account the d to s-p interband transitions as well the actual crystalline geometry. The surface response is incorporated in a calculation of the optical reflectance, and it yields corrections to Fresnels formulae which depend on the angle between the polarization vector and the surface principal directions. The anisotropy effect has been confirmed by surface reflectance anisotropy spectroscopy experiments performed on (110) Ag and Au surfaces. We show that the main contribution to the anisotropy is the screened surface local-field effect on resonant dipolar oscillations localized near the surface.

Visible spectral dependence of the scattering and absorption coefficients of pigmented coatings from inversion of diffuse reflectance spectra

A spectral-projected gradient method and an extension of the Kubelka-Munk theory are applied to obtain the relevant parameters of the theory from measured diffuse reflectance spectra of pigmented samples illuminated with visible diffuse radiation. The initial estimate of the spectral dependence of the parameters, required by a recursive spectral-projected gradient method, was obtained by use of direct measurements and up-to-date theoretical estimates. We then tested the consistency of the Kubelka-Munk theory by repeating the procedure with samples of different thicknesses.