First-principles Fourier approach for the calculation of the effective dielectric constant of periodic composites

Conductivity of periodic composites made of matrix and polydispersed aggregates

We present closed-form expressions of the effective conductivity of composites made of matrix and impenetrable polydispersed particles. The approach developed in a recent work has been generalized to treat periodic multiphase composite materials. Particular cases including orthorhombic arrangements of spherical or spheroidal inclusions and random distributions of spheres are considered where simple closed-form expressions are obtained. The case of random distributions allows us to recover Mori-Tanaka estimation after introducing partial structure factors as a statistical information on the microstructure.

Finite element modeling of the radiative properties of Morpho butterfly wing scales

With the aim of furthering the explanation of iridescence in Morpho butterflies, we developed an optical model based on the finite-element (FE) method, taking more accurately into account the exact morphology of the wing, origin of iridescence. We modeled the photonic structure of a basal scale of the Morpho rhetenor wing as a three-dimensional object, infinite in one direction, with a shape copied from a TEM image, and made out of a slightly absorbing dielectric material. Periodic boundary conditions were used in the FE method to model the wing periodic structure and perfectly matched layers permitted the free-space scattering computation. Our results are twofold: first, we verified on a simpler structure, that our model yields the same result as the rigorous coupled wave analysis (RCWA), and second, we demonstrated that it is necessary to assume an absorption gradient in the true structure, to account for experimental reflectivity measured on a real wing.

Electrostatic resonances of heterostructures with negative permittivity: homogenization formalisms versus finite-element modeling

We investigate the effective permittivity epsilon of two-phase two-dimensional heterostructures, consisting of an inclusion (or cross section of infinite parallel, infinitely long, identical, cylinders, where the properties and characteristics are invariant along the perpendicular cross sectional plane), of permittivity epsilon_(2)=epsilon_(2);(')+epsilon_(2);('')i with epsilon_(2);(') being positive or negative, in a matrix of permittivity epsilon_(1) (hereafter, assumed to be real valued and positive). Our method for computing epsilon=epsilon;(')+epsilon;('')i is based on formulating the conservation of electric displacement flux through the interface separating the two media on systems with periodic boundary conditions in one direction. We identify two distinct behaviors in the surface fraction varphi_(2) dependence of the effective permittivity according the value of mid R:epsilon_(2);(')mid R:/epsilon_(1) relative to 1, which is a consequence of the duality symmetry. The incorporation of negative values of epsilon_(2);(') into our calculations leads to a peak in epsilon;('')(varphi_(20) whereas epsilon;(')(varphi_{2}) decreases to zero, which are both results of an electrostatic resonance (ER) phenomenon. We demonstrate that one can generate heterostructures characterized by an upward shift in the ER position as epsilon_(2);('') is increased. This suggests that, in principle, this property can be used to provide a wide range of innovative structures from specially designed composite materials, e.g., reconfigurable composite device. The comparison of our data with Maxwell Garnett (MG) and Bruggeman (SBG) homogenization formalisms permits a quantitative assessment of the ability of the two methods to capture the effects of surface fraction on epsilon . These methods have severe inadequacies, which arise physically from an incorrect treatment of the higher multipoles than dipole moments. We argue that the inappropriateness of SBG formula can originate from its prerogative that phase 1 and phase 2 are treated symmetrically. Our calculations show that MG formula may provide reasonable estimates for epsilon , even close to the ER position, of homogenized two-phase heterostructures with the real part of the complex-valued permittivities of phases having opposite signs and provided that mid R:epsilon_(2);(')mid R:< or =epsilon_(2);('') .

Finite-element method for calculation of the effective permittivity of random inhomogeneous media

The challenge of designing new solid-state materials from calculations performed with the help of computers applied to models of spatial randomness has attracted an increasing amount of interest in recent years. In particular, dispersions of particles in a host matrix are scientifically and technologically important for a variety of reasons. Herein, we report our development of an efficient computer code to calculate the effective (bulk) permittivity of two-phase disordered composite media consisting of hard circular disks made of a lossless dielectric (permittivity epsilon2) randomly placed in a plane made of a lossless homogeneous dielectric (permittivity epsilon1) at different surface fractions. Specifically, the method is based on (i) a finite-element description of composites in which both the host and the randomly distributed inclusions are isotropic phases, and (ii) an ordinary Monte Carlo sampling. Periodic boundary conditions are employed throughout the simulation and various numbers of disks have been considered in the calculations. From this systematic study, we show how the number of Monte Carlo steps needed to achieve equilibrated distributions of disks increases monotonically with the surface fraction. Furthermore, a detailed study is made of the dependence of the results on a minimum separation distance between disks. Numerical examples are presented to connect the macroscopic property such as the effective permittivity to microstructural characteristics such as the mean coordination number and radial distribution function. In addition, several approximate effective medium theories, exact bounds, exact results for two-dimensional regular arrays, and the exact dilute limit are used to test and validate the finite-element algorithm. Numerical results indicate that the fourth-order bounds provide an excellent estimate of the effective permittivity for a wide range of surface fractions, in accordance with the fact that the bounds become progressively narrower as more microstructural information is incorporated. Future directions of the active field of computational studies of the structure-property relations for composite systems are briefly discussed.