Related papers: Homogenizing metamaterials, three times
In this work, we develop a new systematic and self-consistent approach to homogenize arbitrary non-magnetic periodic metamaterials. The proposed method does not rely on the solution of an eigenvalue problem and can fully characterize the…
In this chapter we describe a selection of mathematical techniques and results that suggest interesting links between the theory of gratings and the theory of homogenization, including a brief introduction to the latter. By no means do we…
An analytical model for homogenization of Metamaterials (MM) with interacting Metaatoms (MA) is developed based on multipole approach for bulk media. The interaction is assumed to be near field type. i.e. no retardation in lateral direction…
When used in bulk applications, mechanical metamaterials set forth a multiscale problem with many orders of magnitude in scale separation between the micro and macro scales. However, mechanical metamaterials fall outside conventional…
This paper presents a homogenization framework for elastomeric metamaterials exhibiting long-range correlated fluctuation fields. Based on full-scale numerical simulations on a class of such materials, an ansatz is proposed that allows to…
Metamaterials are artificial composite structures designed for controlling waves or fields, and exhibit interaction phenomena that are unexpected on the basis of their chemical constituents. These phenomena are encoded in effective material…
The paper extends and enhances in several ways the recently proposed homogenization theory of metamaterials [J. Opt. Soc. Am. B 28, 577 (2011)]. The theory is based on a direct analysis of fields in the lattice cells rather than on an…
There is a growing mechanics literature concerning the macroscopic properties of mechanism-based mechanical metamaterials. This amounts mathematically to a homogenization problem involving nonlinear elasticity. A key goal is to identify the…
Homogenization of metamaterials is a crucial issue as it allows to describe their optical response in terms of effective wave parameters as e.g. propagation constants. In this paper we consider the possible homogenization of chiral…
Anisotropic homogeneous metamaterials that are neither wholly dissipative nor wholly active at a specific frequency are permitted by classical electromagnetic theory. Well-established homogenization formalisms indicate that such a…
We propose an extensive discussion on the homogenization and scattering analysis of second-order nonlinear metasurfaces. Our developments are based on the generalized sheet transition conditions (GSTCs) which are used to model the…
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…
A unified homogenization procedure for split ring metamaterials taking into account time and spatial dispersion is introduced. The procedure is based on two coupled systems of equations. The first one comes from an approximation of the…
A micromorphic computational homogenization framework has recently been developed to deal with materials showing long-range correlated interactions, i.e. displaying patterning modes. Typical examples of such materials are elastomeric…
We investigate the ab-initio homogenization of separable metamaterials with factorized dielectric permittivity profile which can be achieved through suitable grey-scale permittivity design techniques. Separability allows such metamaterials…
A general process is proposed to experimentally design anisotropic inhomogeneous metamaterials obtained through a change of coordinate in the Helmholtz equation. The method is applied to the case of a cylindrical transformation that allows…
Here homogenization theory is used to establish a connection between the symmetries of a periodic elastic structure associated with the microscopic properties of an elastic material and the material symmetries of the effective, macroscopic…
This note gives a brief and `crash' introduction to the method of Homogenization with the use of wave equation and diffusion equation with periodic in space coefficients as instructive examples. We expose the method with the use of an…
The theory of inhomogeneous analytic materials is developed. These are materials where the coefficients entering the equations involve analytic functions. Three types of analytic materials are identified. The first two types involve an…
In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the convergence of the iteration scheme of this algorithm and the…