Related papers: From Whitney Forms to Metamaterials: a Rigorous Ho…
The homogenization of a composite material comprising three isotropic dielectric materials was investigated. The component materials were randomly distributed as spherical particles, with the particles of two of the component materials…
We develop a general formalism to describe the propagation of a near-resonant electromagnetic field in a medium composed of magnetodielectric resonators. As the size and the spatial separation of nanofabricated resonators in a metamaterial…
We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to L\^e and Teissier, which reformulates Whitney regularity in terms of conormal…
Metamaterial homogenization is often based on implicit assumptions inspired to natural material models. Retrieved effective permittivity and permeability, however, are often non-physical, especially near the array resonances, of most…
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 asymptotic theory is developed to generate equations that model the global behaviour of electromagnetic waves in periodic photonic structures when the wavelength is not necessarily long relative to the periodic cell dimensions;…
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 present a formulation for high-order generalized periodicity conditions in the context of a high-order electromechanical theory including flexoelectricity, strain gradient elasticity and gradient dielectricity, with the goal of studying…
We show that artificial magnetism of periodic dielectric or metal/dielectric structures has limitations and is subject to at least two "uncertainty principles". First, the stronger the magnetic response (the deviation of the effective…
Effective medium theory replaces a given fine-scale heterostructure with a homogeneous one in such a way that the physically measurable quantities, e.g. reaction fields and losses, remain approximately the same. This Letter shows that 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…
We study the time harmonic Maxwell equations in a meta-material consisting of perfect conductors and void space. The meta-material is assumed to be periodic with period $\eta > 0$; we study the behaviour of solutions $(E^{\eta}, H^{\eta})$…
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…
Based on our previous work, we propose a homogenized model of acoustic waves propagating through periodically perforated elastic plates with metamaterial properties due to embedded arrays of soft elastic inclusions serving for resonators.…
Unique and highly tunable optical properties of PT-symmetric systems and metamaterials enable a plenty of entirely new linear and nonlinear optical phenomena with numerous applications, e.g., for designing subdiffraction lenses,…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
A periodic assembly of acoustically-rigid blocks (termed 'grating'), situated between two half spaces occupied by fluid-like media, lends itself to a rigorous theoretical analysis of its response to an acoustic homogeneous plane wave. This…
In this study, we illustrate the effective medium theories in the designs of three-dimensional composite metametails of both negative permittivity and permeability. The proposed metamaterials consist of coated spheres embedded in a…
The homogenization of one-dimensional acoustic or elastic structures of finite extent is considered. A new homogenization method based on transfer matrices is derived. The new homogenization method may account for variable cross sectional…
Deep-subwavelength all-dielectric composite materials are believed to tightly obey the Maxwell Garnett effective medium theory. Here, we demonstrate that the Maxwell Garnett theory could break down due to evanescent fields in…