We provide new expressions for the reflection amplitudes of a half space of randomly located identical spherical particles that can be regarded as an extension of Fresnel's formulas when scattering is prominent. We derive them rigorously from Maxwell's equations by solving an integral equation for the electric field within the effective-field approximation. The integral equation is given in terms of the nonlocal conductivity tensor of an isolated sphere. Approximate expressions for the reflection amplitudes are also proposed and their accuracy is analyzed, first for the case of a self-sustained suspension of silver particles, and then for the more realistic situation of silver particles in water. In this latter case the integral equation is modified by introducing the half-space Green's function dyadic instead of the one in free-space, but the method of solution is analogous in both. This extension of Fresnel's formulas, together with the numerical comparison of the different approximations proposed here, is necessary for an accurate interpretation of reflection-spectroscopy measurements in dilute colloidal suspensions of practical interest. The connection between the nonlocal conductivity tensor and the T-matrix operator of scattering theory is also made manifest.

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.

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.

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.

A challenging issue in photoacoustic biomedical imaging is to take into account the presence of dispersive acoustic media, since these are prone to induce amplitude attenuation and scattering of the photoacoustic frequency components. These perturbations are largely the cause for which the photoacoustic tomographic image reconstruction from projections lacks a plane-wave transport formalism. Attending this problem, we further develop an analytic formalism of the transport and its numerical implementation accounting for dispersive acoustic media. We differentiate three variations of an acoustically perturbing media. Our object of interest is a numerical description of the light absorption map of a coronal human breast image. Then, we analyze conditions for which the propagation of photoacoustic perturbations can obey the generalized Heaviside telegraph equation. In addition, we provide a study of the causality consistency of the wave propagation models. We observe transport implications due to the presence of dispersive acoustic media and derive model adjustments that include attenuation and diffusion approximations within the two-dimensional forward problem. Next, we restore the inverse problem description with the deduced perturbation components. Finally, we solve the nonlinear inverse problem with a numerical strategy for a filtered backprojection reconstruction. At a stage prior to the image reconstruction, we compensate for the effect of acoustic attenuation and diffusion to calculate the inversions of the wave perturbations located within the projections. In this way, we manage to significantly reduce reconstruction artifacts. In consequence, we prevent the use of some additional image processing of noise reduction. We demonstrate a feasible strategy on how to solve the stated nonlinear inverse problem of photoacoustic tomography accounting for dispersive acoustic media. In particular, we emphasize efforts to achieve an analytical description, and thus an algorithm is placed, for imaged sound perturbations to be cleaned from acoustic scattering in a simplified manner.