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Inhomogeneities of the electromagnetic field are observed at the edges of the electrodynamic delay systems which are designed based on the concept of periodic multiconductor line. The inhomogeneity manifests itself as a non-uniformity of the characteristic impedance and the effective permittivity of the multiconductor line consisting of a finite number of conductors. The influence of non-uniformity of impedance and effective permittivity of the multiconductor microstrip line on the frequency responses and characteristics of meander delay lines is studied in this paper. It is shown that matching characteristic impedance and effective permittivity of the multiconductor line the bandwidth of the delay line can be extended and delay time increased preserving its dimen

International audience; It is empirically shown by numerical modeling that a single metafilm formed by an array of cut wires on a silicon substrate behaves like a homogeneous layer for normal or oblique incidence.

In this work, two-dimensional simulations of the microwave dielectric properties of models with ellipses and realistic models of trabecular bone tissue are performed . In these simulations, finite difference time domain methodology has been applied to simulate two-phase structures containing inclusions. The results presented here show that the micro-structure is an important factor in the effective dielectric properties of trabecular bone. We consider the feasibility of using the dielectric behaviour of bone tissue to be an indicator of bone health. The frequency used was 950 MHz. It was found that the dielectric properties can be used as an estimate of the degree of anisotropy of the micro-structure of the trabecular tissue. Conductivity appears to be the most sensitive parameter in this respect. Models with ellipse shaped-inclusions are also tested to study their application to modelling bone tissue. Models with ellipses that had an aspect ratio of a / b = 1.5 showed relatively good agreement when compared with realistic models of bone tissue. According to the results presented here, the anisotropy of trabecular bone must be accounted for when measuring its dielectric properties using microwave imaging., Instituto de Física de Líquidos y Sistemas Biológicos, Grupo de Aplicaciones Matemáticas y Estadísticas de la Facultad de Ingeniería

Effects of two-body dipolar interactions on the effective permittivity/conductivity of a binary, symmetric, random dielectric composite are investigated in a self-consistent framework. By arbitrarily splitting the singularity of the Green tensor of the electric field, we introduce an additional degree of freedom into the problem, in the form of an unknown "inner" depolarization constant. Two coupled self-consistent equations determine the latter and the permittivity in terms of the dielectric contrast and the volume fractions. One of them generalizes the usual Coherent Potential condition to many-body interactions between single-phase clusters of polarizable matter elements, while the other one determines the effective medium in which clusters are embedded. The latter is in general different from the overall permittivity. The proposed approach allows for many-body corrections to the Bruggeman-Landauer (BL) scheme to be handled in a multiple-scattering framework. Four parameters are used to adjust the degree of self-consistency and to characterize clusters in a schematic geometrical way. Given these parameters, the resulting theory is "exact" to second order in the volume fractions. For suitable parameter values, reasonable to excellent agreement is found between theory and simulations of random-resistor networks and pixelwise-disordered arrays in two and tree dimensions, over the whole range of volume fractions. Comparisons with simulation data are made using an "effective" scalar depolarization constant that constitutes a very sensitive indicator of deviations from the BL theory., 14 pages, 7 figures

Transparent magnetic materials, among the others semiconductors, have recently come to the focus of interest in both basic and applied research because they have great potential in optical applications and they can be used in optical spectroscopy to investigate fundamental physical phenomena. The theoretical calculations introduce that these materials have some extraordinary properties like asymmetric reflectance when light impact the sample from the opposite angles. In this bachelor thesis, transfer matrix formalism is derived based on Maxwell equations, taking into account special form of effective permittivity. The reflection coefficient for one layer demonstrates, that the asymmetric reflectance appears for transversal- magnetic polarization of light and transversal magnetization in the studied material. The derived formulae are used to calculate the difference in reflectivities for the waves impacting the structure from opposite angles. Ga1−xMnxAs with different concentrations of manganese is assumed to be the essential transparent magnetic layer in the sample. 1

Carbon nanostructures such as carbon nanotubes and graphite nanoplatelets can be included in very low weight percentages in a polymer matrix to create new lightweight nanocomposites with improved performances. The development of simulation models for the prediction of the effective complex permittivity of such composites is very important for design and performance optimization purposes. In this study we propose a multiscale expression of Maxwell Garnett formula, with the aim of modeling the effective permittivity of multifiller composites, including multiwall carbon nanotubes or graphite nanoplatelets at the nanoscale, and nickel-coated short carbon fibers at the micro/macro-scale. A statistical model is also implemented in order to account for variations of the filler geometrical properties, which cannot be fully controlled at the synthesis level, in particular at the nanoscale.

[EN] We present a theoretical and experimental study of the effective permittivity of a photonic crystal (PC) made of parallel dielectric rods in the long-wavelength limit. Using the plane-wave expansion method we derive an analytical expression for the imaginary part of the dielectric tensor. Angular dependence of the dissipative part of permittivity turns out to be more complicated than that for the real part. In particular, it exhibits stronger anisotropy for a PC with rectangular unit cell. Theoretical and numerical results are compared to the experimental measurements of microwave reflection and transmission through a PC fabricated from low-loss alumina rods. A good agreement between the theory and experiment was obtained in the limit where the effective medium approximation is valid. © 2011 Elsevier B.V., This work was supported by the Ministerio de Ciencia e Innovación of Spain under contracts TEC 2007-67239, TEC 2010-19751 and CONSOLIDER CSD2008-00066, by the US Department of Energy through the Grant No. DE-FG02-06ER46312, and by the Office of Naval Research through the Grant No. 000140910554. L.G. acknowledges the support by CONACyT (Mexico) and A.K. acknowledges the support by the Ministerio de Educación of Spain Contract No. SAB2009-00009. Authors thank F. Cervera for technical help.

University of Technology, Sydney. Faculty of Science. We develop an analytical electromagnetic model of a conducting film perforated by slits with subwavelength slit width and periodicity. We use a plane wave expansion methodology to calculate the reflected and transmitted fields diffracted by the conducting grating, with the exception that the sub-wavelength periodicity means that the diffracted field is composed of non-propogating surface waves rather than plane waves. We label the non-propogating surface waves evanescent diffracted waves EDWs. We show how the collection of all EDWs present can be treated as an effective medium described by an impedance and that the reflectance and transmittance of a plane wave incident on the grating can be calculated as if the plane wave where interacting with an effective medium. We find that depending on slit depth this effective medium allows for transmittances of 100% even when slit width is so narrow that it is negligable compared to slit periodicity. Thus our analytical model reproduces the extraordinary optical transmission reported in the literature. We show that the EDWs on either side of the grating also act like mirrors coupling to a standing wave in the grating with the result that slit depth determines whether transmission is high or low. We find that when the effective permittivity of the effective medium created by the EDWs is equal to the permittivity of the metal film then the EDWs collectively become a surface plasmon. We also find that except for films with no absorption the state in which EDWs are also a surface plasmon corresponds to low transmittance not high transmittance and thus surface plasmons appear to hinder rather than help transmittance for a grating composed of slits. We also develop an FDTD model of Maxwell's equations which reproduces the predictions of our analytical model. We further develop our analytical electromagnetic model of conducting gratings to also include the situation in which a planar conducting lens is placed under the grating. We demonstrate that such a lens can create a near-field focusing effect that enables sub-wavelength imaging so that incident light can produce a periodic intensity pattern in a substrate with periodic feature less than the wavelength of the incident light. We show that this sub-wavelength imaging is possible with or without surface plasmons being present.

Computational methods were used to characterize the dielectric properties of periodic heterostructures.We first report a systematic finite-difference time-domain study on the dielectric properties of two-dimensional two-phase heterostruc- tures. More specifically, we present extensive results of FDTD computations on the quasistatic effective permittivity of a single inclusion, with arbitrarily complex geometry (regular polygons and fractals), embedded in a plane. Next, a finite-element methodology has been applied to simulate two-dimensional (2D) two-phase heterostructures containing a dielectric inclusion with arbitrary shape. Finite-element (FE) simulations of the effective complex permittivity of perfo- rated two-dimensional (2D) lossy heterostructures are reported. Given the paucity of experimental and numerical data, we set out to systematically investigate the trends that shape and permittivity contrast between the inclusion and the host matrix have on the depolarization factor (DF). The effect of the first- versus second-order concentration virial coefficient on the value of the DF is considered for a variety of inclusion shapes and a large set of material properties. Our findings suggest that the DF for a 2D inclusion is highly tunable depending on the choice of these parameters.We also report finite- element (FE) calculations of the effective (relative) permittivity of composite materials consisting of particles and particle arrays with a core-shell structure embedded in a surrounding host. We carried out systematic FE simulations to evaluate the effect of particle shape, coating thickness, and constituent permittivity on the intrinsic electrostatic resonance (ER) of structures composed either of isolated particle, or square array of particles. While one may identify features of the ER which are common to core-shell structures characterized by permittivities with real parts of opposite signs, it appears that the predicted ER positions are sensitive to the shell thickness and can be tuned through varying this geometric parameter.; Ce travail porte sur la modélisation numérique des propriétés diélectriques de matériaux composites modèles à deux et trois phases comportant des inclusions de forme arbitraire. Deux approches numériques basées sur la méthode des éléments finis (FE) et celle des différences finies dans le domaine temporel (FDTD) sont implantées et validées. Dans un premier temps nous décrivons une méthode de simulation FDTD pour étudier l'influence de la géométrie de l'inclu- sion sur les propriétés diélectriques effectives d'une structure hétérogène non-dissipative bidimensionnelle à deux phases. Nous avons spécifiquement considéré une géométrie fractale de l'inclusion et examinons les conséquences de la symé- trie d'auto-similarité sur la permittivité du matériau composite. Dans un deuxième temps, nous utilisons une méthode de simulation FE permettant le calcul de la permittivité effective complexe de structures bidimensionnelles perforées. Ces calculs permettent d'apporter un éclairage innovant sur le rôle des différents paramètres (fraction surfacique et périmètre de l'inclusion, contraste de permittivité entre l'inclusion et la matrice hôte, pertes diélectriques, et forme des trous) in- fluençant la permittivité effective. Nous montrons également que le facteur de dépolarisation d'une inclusion dans une structure composite peut être finement ajusté selon la forme de l'inclusion, le contraste de permittivité entre l'inclusion et la matrice, ainsi que par la polarisation du champ électrique. L'originalité de la méthode est de mettre à profit le carac- tère dipolaire des interactions électrostatiques dans la limite diluée. Les propriétés diélectriques de matériaux artificiels (métamatériaux) sont également analysées afin d'en isoler des comportements spécifiques. Nous montrons que la forme de l'inclusion influe sur la position de la résonance électrostatique (RE). Selon la forme de l'inclusion, son arrangement dans le composite (isolée, ou structurée en réseau), ses paramètres intrinsèques, nous mettons en évidence une hiérarchie originale des positions de la RE. Enfin à l'aide de structures encapsulées, nous montrons qu'un contrôle précis des pro- priétés de RE de structures de type métamatériaux (permittivité dont la partie réelle est négative) peut être réalisé par la polarisation du champ excitateur et la topologie de l'inclusion. L'ensemble de ces résultats numériques permet d'apporter un éclairage innovant sur la réponse diélectrique de matériaux composites à la base d'un très grand nombre d'application technologiques.

Computational methods were used to characterize the dielectric properties of periodic heterostructures.We first report a systematic finite-difference time-domain study on the dielectric properties of two-dimensional two-phase heterostruc- tures. More specifically, we present extensive results of FDTD computations on the quasistatic effective permittivity of a single inclusion, with arbitrarily complex geometry (regular polygons and fractals), embedded in a plane. Next, a finite-element methodology has been applied to simulate two-dimensional (2D) two-phase heterostructures containing a dielectric inclusion with arbitrary shape. Finite-element (FE) simulations of the effective complex permittivity of perfo- rated two-dimensional (2D) lossy heterostructures are reported. Given the paucity of experimental and numerical data, we set out to systematically investigate the trends that shape and permittivity contrast between the inclusion and the host matrix have on the depolarization factor (DF). The effect of the first- versus second-order concentration virial coefficient on the value of the DF is considered for a variety of inclusion shapes and a large set of material properties. Our findings suggest that the DF for a 2D inclusion is highly tunable depending on the choice of these parameters.We also report finite- element (FE) calculations of the effective (relative) permittivity of composite materials consisting of particles and particle arrays with a core-shell structure embedded in a surrounding host. We carried out systematic FE simulations to evaluate the effect of particle shape, coating thickness, and constituent permittivity on the intrinsic electrostatic resonance (ER) of structures composed either of isolated particle, or square array of particles. While one may identify features of the ER which are common to core-shell structures characterized by permittivities with real parts of opposite signs, it appears that the predicted ER positions are sensitive to the shell thickness and can be tuned through varying this geometric parameter., Ce travail porte sur la modélisation numérique des propriétés diélectriques de matériaux composites modèles à deux et trois phases comportant des inclusions de forme arbitraire. Deux approches numériques basées sur la méthode des éléments finis (FE) et celle des différences finies dans le domaine temporel (FDTD) sont implantées et validées. Dans un premier temps nous décrivons une méthode de simulation FDTD pour étudier l'influence de la géométrie de l'inclu- sion sur les propriétés diélectriques effectives d'une structure hétérogène non-dissipative bidimensionnelle à deux phases. Nous avons spécifiquement considéré une géométrie fractale de l'inclusion et examinons les conséquences de la symé- trie d'auto-similarité sur la permittivité du matériau composite. Dans un deuxième temps, nous utilisons une méthode de simulation FE permettant le calcul de la permittivité effective complexe de structures bidimensionnelles perforées. Ces calculs permettent d'apporter un éclairage innovant sur le rôle des différents paramètres (fraction surfacique et périmètre de l'inclusion, contraste de permittivité entre l'inclusion et la matrice hôte, pertes diélectriques, et forme des trous) in- fluençant la permittivité effective. Nous montrons également que le facteur de dépolarisation d'une inclusion dans une structure composite peut être finement ajusté selon la forme de l'inclusion, le contraste de permittivité entre l'inclusion et la matrice, ainsi que par la polarisation du champ électrique. L'originalité de la méthode est de mettre à profit le carac- tère dipolaire des interactions électrostatiques dans la limite diluée. Les propriétés diélectriques de matériaux artificiels (métamatériaux) sont également analysées afin d'en isoler des comportements spécifiques. Nous montrons que la forme de l'inclusion influe sur la position de la résonance électrostatique (RE). Selon la forme de l'inclusion, son arrangement dans le composite (isolée, ou structurée en réseau), ses paramètres intrinsèques, nous mettons en évidence une hiérarchie originale des positions de la RE. Enfin à l'aide de structures encapsulées, nous montrons qu'un contrôle précis des pro- priétés de RE de structures de type métamatériaux (permittivité dont la partie réelle est négative) peut être réalisé par la polarisation du champ excitateur et la topologie de l'inclusion. L'ensemble de ces résultats numériques permet d'apporter un éclairage innovant sur la réponse diélectrique de matériaux composites à la base d'un très grand nombre d'application technologiques.

http://jap.aip.org/; International audience; The randomness in the structure of two-component dense composite materials influences the scalar effective dielectric constant, in the quasistatic limit. A numerical analysis of this property is developed in this paper. The computer-simulation models used are based on both the finite element method and the boundary integral equation method for two- and three-dimensional structures, respectively. Owing to possible anisotropy the orientation of spatially fixed inhomogeneities of permittivity epsilon(1), embedded in a matrix of permittivity epsilon(2), affects the effective permittivity of the composite material sample. The primary goal of this paper is to analyze this orientation dependence. Second, the effect of the components geometry on the dielectric properties of the medium is studied. Third the effect of inhomogeneities randomly distributed within a matrix is investigated. Changing these three parameters provides a diverse array of behaviors useful to understand the dielectric properties of random composite materials. Finally, the data obtained from this numerical simulation are compared to the results of previous analytical work.

International audience; We present computer simulation data for the effective permittivity (in the quasistatic limit) of a system composed of discrete inhomogeneities of permittivity epsilon(1), embedded in a three-dimensional homogeneous matrix of permittivity epsilon(2). The primary purpose of this paper is to study the related issue of the effect of the geometric shape of the components on the dielectric properties of the medium. The secondary purpose is to analyse how the spatial arrangement in these two-phase materials affects the effective permittivity. The structures considered are periodic lattices of inhomogeneties. The numerical method proceeds by an algorithm based upon the resolution of boundary integral equations. Finally, we compare the prediction of our numerical simulation with the effective medium approach and with results of previous analytical works and numerical experiments.

Compact closed-form mathematical expressions are presented for the effective permittivity, characteristic impedance and attenuation constant of coplanar waveguides with thick electrodes and high-frequency dispersion. Excellent agreements, for a wide range of frequencies, up to 100 GHz and for conductor thicknesses up to 40 m are found with full-wave finite-element results from commercial software (HFSS) in a margin of geometric parameter values and frequencies of interest for the design and optimisation of high-speed electro-optical modulators. The formulae are simple and specially tailored to the narrow gap widths and thick electrodes typical of electro-optical modulator applications. Other approaches to closed-form formulae for CPW parameters are also compared and analysed.

Interesting electromagnetic properties of ferromagnetic micro- and nanowires suggest that, by using them as inclusions in composite materials, artificial materials with novel and controllable properties can be realized. In this paper, we present a homogenization procedure to estimate the effective permittivity of dense (with respect to the wavelength) arrays of ferromagnetic wires. This general model can be applied to the design of systems based on ferromagnetic micro- and nanowires in the microwave and millimeter wave frequency ranges. The derived effective permittivity shows a complex frequency dispersion originated from the interplay between the geometry effects and the magnetic response of the ferromagnetic wires. Distinct phenomenology is observed as a function of the wire radius, which is studied in detail. Theoretical results are validated with numerical simulations.

Thin film of silver nanoparticle (Ag)-PMMA composite was synthesized and characterized. The angle of minimum reflectivity (SPR angle) for the composite film was figured out using the Kretschmann two prism set up. The shift in the SPR angle of the composite film from that of the pure silver film was analyzed. Using Bruggemann effective medium theory, the effective permittivity of the composite film was determined.

Cet article traite les effets des métallisations réelles dans les lignes GaAs pour circuits intégrés microondes. Une approche théorique originale, qui est en fait une extension de la Méthode Spectrale classique, est présentée dans cette communication. Cette approche est appliquée à une ligne Metal-Isolant-Semiconducteur (MIS) sur GaAs. On montre l'effet de l'épaisseur des rubans sur les caractéristiques de propagation : permittivité effective, pertes de propagation et impédance caractéristique.

Material characterization by ring-resonator based measurements is well established since the early 20th century. Since then, the demand on spectral complex permittivity characterizations of RF materials and dielectric covers at higher microwave frequencies rises. Nowadays, both free space applications, e.g. 77 GHz automotive radar systems, and dielectrics for microchip packages require accurate knowledge of the relative permittivity in order to optimize RF circuit designs. With increasing frequencies, the conductor shape of photochemically etched ring-resonators gets more influence on the effective ring radius, and therefore the measured resonance frequencies, which results in an error for the relative permittivity determination. This paper provides correction factors for the ring radii up to 110 GHz, compensating the altered field distribution due to trapezoidal edges.

This article describes the modeling of biological tissues at microwave frequency using equivalent lumped elements. A microwave biosensor based on microstrip ring resonator (MRR), that has been utilized previously for meat quality evaluation is used for this purpose. For the first time, the ring-resonator loaded with the lossy and high permittivity dielectric material, such as; biological tissue, in a partial overlay configuration is analyzed. The equivalent circuit modeling of the structure is then performed to identify the effect of overlay thickness on the resonance frequency. Finally, the relationship of an overlay thickness with the corresponding RC values of the meat equivalent circuit is established. Simulated, calculated and measured results are then compared for validation. Results are well agreed while the observed discrepancy is in acceptable limit.

International audience; We present a numerical method based upon the resolution of boundary integral equations for the calculation of the effective permittivity of a lossless composite structure consisting of a two component mixture, each with its own dielectric anti shape characteristics. The topological arrangements considered are periodic lattices inhomogeneities. Our numerical simulations are compared to the effective medium approach and with results of previous works.