Fabio Mangini

Spectral domain method for the electromagnetic scattering by a buried sphere

A rigorous method to analyze the electromagnetic scattering of an elliptically polarized plane wave by a sphere buried in a dielectric half-space, is presented. The electric field components of the incident and the scattered monochromatic plane waves are expanded in series of vectorial spherical harmonics, with unknown expansion coefficients. The scattered-reflected and scattered-transmitted fields are computed by exploiting the plane-wave spectrum of the scattered field, considering the reflection and transmission of each elementary plane wave by the interface. The boundary-condition imposition leads to a linear system that returns the unknown coefficients of the scattered field. To achieve a numerical solution, a code has been implemented, and a truncation criterion for the involved series has been proposed. Comparisons with the literature and simulations performed with a commercial software are presented. A generalization of the method to the case of a short pulse scattered by a buried sphere is presented, taking into account the dispersive properties of the involved media.

Homogenization of a multilayer sphere as a radial uniaxial sphere: Features and limits

We consider a multilayer sphere with a fixed external radius and with an arbitrary number of layers as a possible realization of a radial uniaxial (RU) sphere. We start from the well-known quasi-static model for the polarizability of the multilayer sphere and, after a validation with a dynamic code previously presented, we try to understand the limits in which the multilayer sphere can be considered a RU sphere. We employ different techniques for layering the spheres and we find which of them is convenient in terms of convergence speed. Moreover, we deal with the case of plasmonic layers and we find some rules for the realization of the multilayer sphere in order to obtain the desired homogenized parameters. Finally, we present a study on the behavior of plasmon resonances of the multilayer sphere when the number of layers is increased.

Electromagnetic interaction with two eccentric spheres

In this paper, we consider the interaction of an electromagnetic field with two eccentric spheres. We propose a quasi-static approach in order to calculate the scattered field and the polarizability and the effective permittivity of the eccentric spheres. We analyze the behavior of the scattering parameters as a function of the dimension and position of the spherical inclusions. Moreover, we consider the case of plasmonic spheres and study the behavior of the plasmon resonances for different reciprocal positions of the two spheres.

Electromagnetic scattering by a buried sphere in a lossy medium of an inhomogeneous plane wave at arbitrary incidence: Spectral-domain method

A rigorous theoretical treatment to analyze the electromagnetic scattering of an inhomogeneous elliptically polarized plane wave by a sphere buried in a lossy half-space is presented. To consider the losses in the media an inhomogeneous plane wave is considered. The incident and the scattered electric field components are expanded in series of vectorial spherical harmonics using the Legendre functions generalized via hypergeometrical and gamma functions, with unknown expansion coefficients. The spectral-domain method to represent the scattered electric field is used in order to compute the scattered-reflected and scattered-transmitted fields, considering the reflection and transmission of each elementary plane wave by the interface. Finally, the unknown coefficients of the scattered field are computed by imposing the boundary condition on the spherical surface. In order to validate the model, a homemade code has been implemented. Comparisons with the simulations performed with a commercial software and the results in the literature are presented.

Vectorial spherical-harmonics representation of an inhomogeneous elliptically polarized plane wave.

In this paper, a generalization of the vectorial spherical-harmonics expansion of an inhomogeneous elliptically polarized plane wave is presented. The solution has been achieved using the Legendre functions generalized via hypergeometric and gamma functions, shifting the difficulty to the determination of only expansion coefficients. In order to validate the presented method, a Matlab code has been implemented. To compare the results a Mie scattering by a sphere is considered, then a truncation criterion for the numerical evaluation of the series is proposed, and the Mie scattering coefficients by perfectly conducting and dielectric spheres excited by an inhomogeneous elliptically polarized plane wave are shown.

In silico validation procedure for cell volume fraction estimation through dielectric spectroscopy

Dielectric spectroscopy has proved to be a good tool for analyzing the passive electrical properties of biological tissues as well as those of inhomogeneous materials. This technique promises to be a valid alternative to the classical ones based on metabolites to monitor the growth and cell volume fraction of cell cultures in a simple and minimally invasive way. In order to obtain an accurate estimation of the cell volume fraction as a function of the permittivity of the suspension, a simple in silico procedure is proposed. The procedure is designed to perform homogenization from the micro-scale to the macro-scale using simple analytical models and simulation setups hypothesizing the properties of diluted suspension (cell volume fraction less than 0.2). Results obtained show the possibility to overcome some trouble involving the analytical treatment of the cellular shape by considering a sphere with the same permittivity in the quantitative analysis of the cell volume fraction. The entire study is based on computer simulations performed in order to verify the correctness of the procedure. Obtained data are used in a cell volume fraction estimation scenario to show the effectiveness of the procedure.

Electromagnetic scattering of an inhomogeneous elliptically polarized plane wave by a multilayered sphere

In this paper, a rigorous method in order to analyze the electromagnetic scattering by a multilayered sphere of an inhomogeneous elliptically polarized plane wave, is presented. One has to do with inhomogeneous plane waves when the scatterer is immersed in a medium generally dispersive and dissipative. The expression of the vectorial spherical harmonics expansion of an inhomogeneous elliptically polarized plane wave has been derived using the Legendre functions generalized via hypergeometric and gamma functions. The problem of the stratified sphere has been solved using the transfer-matrix approach, applied to each spherical surface, obtaining the coefficients of the scattered field and the internal field to the sphere system. In order to validate the presented method, a Matlab code and a numerical model based on the finite element method has been implemented. The comparison between the two methods is shown.

Introduction to electromagnetic scattering: tutorial

In this paper, an introduction to electromagnetic scattering is presented. We introduce the basic concepts needed to face a scattering problem, including the scattering, absorption, and extinction cross sections. We define the vector harmonics and we present some of their properties. Finally, we tackle the two canonical problems of the scattering by an infinitely long circular cylinder, and by a sphere, showing that the introduction of the vector wave function makes the imposition and solution of the boundary conditions particularly simple.

Analysis of the polarizability of an array of spherical metallic inclusions in a dielectric host sphere

The polarizability of an array of metallic spheres embedded in a dielectric host sphere is obtained by means of a quasi-static analysis of the electromagnetic interaction. The proposed model is validated through comparisons with the results obtained with software based on the finite element method. A parametric study of the polarizability as a function of the number of inclusions, their radii, and their positions is presented. An analysis of the plasmon resonances of the particle as a function of the same parameters is performed.

Numerical analysis of electromagnetic interactions by a cell during the mitosis phases: Numerical Analysis of Electromagnetic Interactions by Cell Mitosis

In this work, a numerical study of the interaction of an electromagnetic field with a biological cell in the different phases of mitosis is presented. In particular, the validity of the single-shell model during mitosis from a geometrical viewpoint has been considered. We consider the Jurkat cell for our analysis and model the content of the cell, composed by the nucleus and different organelles immersed in cytoplasm and delimited by the cell membrane, as a single material with appropriate electromagnetic properties derived by making use of effective medium approximation methods, i.e., we used a quasistatic approach to deal with the cell. To validate the model, a comparison between the original and 2 approximated geometry models is made and the results are in very good accordance. Subsequently, an analysis of the scattered field indicates that the most sensitive component to the mitosis phase is the one parallel to the segment joining the centers of the cells.