The homogeneous and transport properties of a set of metallic fibers were studied. The existence of a plasma frequency was deduced and a precise formula for it was derived. A homogenized system for finite length ohmic wires was derived. Some numerical simulations were made to study the influence of disorder. The persistence of a low-frequency band gap was demonstrated numerically even in the case of a strong disorder. The existence of localized modes was explained in terms of the statistical properties of the medium.

On montre l'existence de résonances électrostatiques dans le comportement basse fréquence de réseaux bidimensionnels métalliques.

we compute the excitonic states and wave functions for various anisotropies and applicate this to AlN

It has been noted that the usual approaches for homogenization (e.g. Bruggeman) could lead to singularities when considering composites comprising materials with positive and negative permittivities. This situation is specifically encountered in the field of metamaterials, in particular in the visible range. The question then arises to unerstand if these resonances are just artifacts or possess, on the contrary, a clear physical meaning. In this work, we study the homogeneous properties of a bidimensional structure that is made of a periodic set of metallic wires embedded in a dielectric host medium. The structure is considered in a region of wavelengths that are much larger than the period of the structure. The work comprises a theoretical part where we develop a two-scale approach to the homogenization of the structure. As it is the case for the common physical approach, it leads to an effective permittivity with strong (electrostatic) resonances as well. The theoretical results, and the presence of resonances, are confirmed by numerical computations based on a rigorous modal approach. In the numerical results we consider specifically the case of silver and gold nanowires, described by a dispersive negative permittivity. We show that the main parameters for the onset of resonances is the optical filling ratio of the structure. Keeping in mind the possibility of performing experiments, it is far easier to keep the geometrical filling ratio constant and to consider strongly dispersive materials in the range of wavelengths considered. Here, besides the crucial fact that they are widely used in nanotechnology, silver and gold nanowires comply with our needs in the visible region of the spectrum.

The recent interest in the imaging possibilities of photonic crystals (superlensing, superprism, optical mirages, etc.) call for a detailed analysis of beam propagation inside a finite periodic structure. An answer to the following question was sought: “Where does the beam emerge?’ We found that, contrary to common knowledge, it is not always true that the shift of a beam is given by the normal to the dispersion curve. This phenomenon can be explained in terms of evanescent waves and a renormalized diagram yields the correct direction.

In this paper we propose an efficient technique for micromachining lithium niobate that is used in Ti-diffused waveguides. The use of Focused Ion Beam (FIB) etching allows obtaining homogeneous periodic microstructures. Bragg gratings with a period of 1.05 m and an aspect ratio of 6:1 (depth-to-half period ratio) have been achieved. A reflectivity greater than 95% associated with a bandwidth at half maximum of about 100 nm within a window centered at 1550 nm, is demonstrated for a Bragg grating of period m and a length of 144 m, in good agreement with theoretical predictions.

The parametric formulation of the combined boundary conditions method (CBCM) with spatial adaptive resolution is extended to multilayered structures of strip gratings. Furthermore, it is shown that it is not necessary to solve the eigenvalue problem in all the layers of these structures; leading to drastic reduction of the computational load.