Augusto García-Valenzuela

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.

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.

Sensitivity of optical sensors based on laser-excited surface-plasmon waves

We investigate the effect of the divergence of a Gaussian laser beam on the resonance curve and the sensitivity of optical sensors based on surface-plasmon resonance (SPR). For He-Ne laser beams it is found that, for beams with a waist radius of less than 300 microm, the SPR-curve characteristics differ appreciably from the case in which a plane wave is considered. Simple expressions for the sensitivity of (bio)chemical sensors are given. A simple Lorentzian model is used to estimate the maximum possible sensitivity when a multilayer system is used to enhance the resonance peak. It was found that the sensitivity can reach its highest value when the width of the SPR curve is equal to the laser-beam divergence. The results could be particularly important when a SPR curve is used to measure the absolute value of the refractive index of a sample or the dielectric constant and the thickness of a metal layer.

Rough-surface capacitor: approximations of the capacitance with elementary functions

We consider the electrical capacitance of a parallel-plate capacitor with one rough electrode. The roughness is characterized by its amplitude and its wavenumber scale; the capacitance depends on both of these variables as well as the form of the roughness. We calculate the capacitance in the four limit cases of the two variables mentioned above. On the basis of these limit cases, we approximate the capacitance with elementary functions for the case of any surface roughness. We compare the capacitances calculated in this approach with precise numerical solutions for different forms of roughness.

Rigorous theoretical framework for particle sizing in turbid colloids using light refraction

Using a non-local effective-medium approach, we analyze the refraction of light in a colloidal medium. We discuss the theoretical grounds and all the necessary precautions to design and perform experiments to measure the effective refractive index in dilute colloids. As an application, we show that it is possible to retrieve the size of small dielectric particles in a colloid by measuring the complex effective refractive index and the volume fraction occupied by the particles.

Noise in optical measurements of cantilever deflections

The optical beam deflection method using the knife edge detection technique is one of the simplest optical sensing methods. We investigate theoretically the limit to the resolution when sensing the displacements of a mechanical cantilever using the knife edge detection technique implemented with a quasimonochromatic thermal-like optical source. Simple formulas for the minimum detectable displacement of the cantilever’s front end are derived assuming all nonoptical noises negligible. It is shown that superluminiscent diodes can yield a minimum detectable displacement of the cantilever about 5 dBs above the shot noise for 1 mW of optical power. It is also shown that in many cases of practical interest the source induced noise is smaller than the thermal-vibration noise of the cantilever. Thus, in many cases, using an inexpensive thermal-like source with the knife edge detection technique can be as effective as using a high-coherence shot-noise limited source.

Optical model enabling the use of Abbe-type refractometers on turbid suspensions

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.

Principles and Methodology for the Simultaneous Determination of Thickness and Dielectric Constant of Coatings With Capacitance Measurements

We propose a new methodology to measure both the dielectric constant and thickness of dielectric coatings on a flat conducting substrate from two capacitance measurements. We discuss the principles of the method and demonstrate its feasibility using 2-D numerical simulations. We present a proof of principles experiment confirming the viability of the method in practice. Finally, we propose and analyze a multisphere electrode geometry

Detection limits of an internal-reflection sensor for the optical beam deflection method

The theoretical detection limit on angle deflection measurement when the quasi-critical internal-reflection method is used is calculated and compared with the more common method of using a bicell position-sensitive detector. Simple formulas for the sensitivity and resolution when the system is shot noise limited are given. It is shown that, even though the bicell detector is potentially much more sensitive for wide and well collimated beams, under typical laboratory restrictions, the internal reflection method may be more sensitive and have better resolution. It is argued that the internal-reflection method may be a tool in developing compact sensors based on the optical beam deflection method.