A scaling analysis of the extraordinary transmission by subwavelength holes is provided. The structure under study is a lamellar grating. The grating can be described by homogeneous permittivity and permeability tensors. The permeability is dispersive and the peaks of transmission result from a Bragg condition.
The low-frequency behavior of a set of wires with a very high conductivity is studied. The effective non-local
constitutive relation is derived for wires with a finite height. Some numerical examples are described.
The effective electromagnetic properties of a metamaterial made of nanorods are investigated. It is found that near inner
resonances there is a effective magnetic behavior. The domain of validity of the effective permeability model is
determined with respect to the wavelength and the filling ratio by means of rigorous numerical computations. It is
concluded that the relative dielectric constant should be higher than 32 and the filling ratio lower than 1/2.
The homogeneous and transport properties of a set of metallic fibers was studied. The existence of a plasma
frequency was shown and a precise formula was derived. A homogenized system for finite length ohmic wires
was derived. Some numerical simulations were made to study the influence of disorder.
Wave propagation in thin nanostructured films in the low frequency regime were studied. By means of a two-scale analysis, the medium can be homogenized, i.e. described by effective electromagnetic parameters. The effective permeability and permittivity were obtained from a set of partial differential equations. A numerical approach based on the Fourier Modal Method was devised in order to solve these equations.
Wave propagation in thin nanostructured films in the low frequency regime is studied. By means of a two-scale
analysis, it is shown that the medium can be homogenized, i.e. described by effective electromagnetic parameters.
The effective permeability and permittivity are obtained by solving a set of partial differential equations. A
numerical aproach based on the Fourier Modal Method is proposed in order to solve these equations.
A new homogenization theory has been proposed by Bouchitte and Felbacq1 for a bounded obstacle made of
periodically disposed parallel high conducting metallic fibers of finite length and very thin section. Although the
resulting constitutive law is non local, a cut-off frequency effect can be evidenced when fibers become infinitely
long. In this paper we present a very surprising byproduct of this model: by reproducing periodically the same
kind of obstacle at small scale and after undergoing a reiterated homogenization procedure, we obtain a local
effective law described by a permittivity tensor that we explicit as a function of the frequency. An important
issue is that the eigenvalues of this tensor have real part changing of sign and possibly very large within some
range of frequencies.
Wave propagation and diffraction in a membrane photonic crystal with finite height were studied in the case where the free-space wavelength is large with respect to the period of the structure. The photonic crystals studied are made of materials with anisotropic permittivity and permeability. Use of the concept of two-scale convergence allowed the photonic crystals to be homogenized.
We homogenize a 2D dielectric photonic crystal by means of a multiple scale approach. We show that if the rods constituting the crystal have Mie resonances at large enough wavelengths, the crystal presents an effective permeability exhibiting anomalous dispersion. When embedding in a negative permittivity medium, this leads to a negative index material.
We first outline an approximate method to study the diffraction by monoperiodic and biperiodic absorbing structures whose thickness is small compared with the incident wavelength. Then the numerical implementation is discussed.