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.

We report on the numerical aspects of the `method of fictitious sources' which, for us, appears as a particular case of a more general method we have called `the synthesis method' in previous theoretical papers. As an illustration, the method is applied to different kinds of echelette, sinusoidal and wire gratings.

It is shown that the concept of localiton, introduced in the frame of localization of light by randomly rough surfaces, can be extended to other kinds of structures like impedance sheets or a set of random dielectric rods. Rigorous numerical calculations show the structure of these new localiton. Finally, the possibility of observing such a localized field from experimental measurements is suggested.

The diffraction by periodic structures using a representation of the field in some functional basis leads to a set of ordinary differential equations, which can be solved by numerical integration. When the basic functions are the exponential harmonics (Fourier decomposition) one arrives at the well-known classical differential method. In the case of simple lamellar profiles, the numerical integration can be substituted by eigenvalue-eigenvector technique, known in the field of diffraction by periodic systems under the name of rigorous coupled-wave analysis or method of Moharam and gaylord. When the basis functions are searched as the rigorous solutions of the diffraction problem inside the lamellar grooves, the theory is known under the name of modal method. A comparative analysis of the three methods is made to reveal the convergence rate for an arbitrary shaped grating using the staircase approximation. It is shown that in TM polarization this approximation leads to sharp peaks of the electric field near the edges. A higher number of fourir harmonics is then required to describe the field, compared with the case of a smooth profile, and a poor convergence is observed. The classical differential method, which does not use the staircase approximation does not suffer from this problem.

Dielectric periodic media can possess a complex photonic band structure with allowed bands displaying strong dispersion and anisotropy. We show that for some frequencies the form of iso-frequency contours mimics the form of the first Brillouin zone of the crystal. A wide angular range of flat dispersion exists for such frequencies. The regions of iso-frequency contours with near zero curvature cancel out diffraction of the light beam, leading to a self-guided (self-collimated) beam.

The emission of a dipole in a finite-thickness photonic band gap structure is investigated. The dipole is located at a large value of the local density of states and its wavelength is taken at the edge of a full band gap. The resulting emission is highly enhanced and is confined in a small angular region. This is confirmed numerically for two different structures designed from two different tree-dimensional crystal: the woodpile and the simple cubic photonic crystals.

In the recent years, many experimental and theoretical achievements have shown that meta-materials can simulate homogeneous materials with optical index less than unity or even negative. For example, a dielectric photonic crystal, used at the edge of a band gap, can generate phenomena of ultra-refraction (positive index less than unity) or negative refraction (negative index). Some applications of these phenomena will be shown, specially the design of directive antenna in the microwaves region. More recently, experimental and theoretical studies have been published on left-handed materials. These materials, which have a permittivity and a permeability equal to -1, have been the subject of controversies about their alleged property of making perfect lenses. It will be shown that such a perfect lens cannot exist. However, this kind of meta-material could be used for making better lenses than the best classical ones, a fact which could explain some experimental results. The vital influence of the size of the elementary cell on the performance of the lens will be pointed out. Finally, it will be shown that surprisingly, a left-handed material can be interpreted as a means to go through the mirror, as Alice in the novel of Lewis Carrol...

In this paper, we present a comparative study of the emission properties of line sources embedded in two-dimensional finite-size aperiodically-ordered "photonic-quasicrystal" slabs made of dielectric cylinders arranged according to representative categories of aperiodic tilings. Our study, based on a rigorous full-wave numerical method, indicates the possibility of achieving directive low-sidelobe emission at several frequencies. In this connection, parametric studies are presented, and similarities and differences with the periodic case are highlighted.

We report on our work about the electromagnetic theory of gratings made with anisotropic materials. We describe briefly and give the fields of application of both differential and integral methods. At the present time, a computer program based on the integral method works for an arbitrary uncoated dielectric anisotropic grating, the surface of which is given by y=f(x), provided that the principal axes of the permittivity matrix be the ones used to describe the geometry of the structure. The differential method, which is very flexible and easy to implement, allows us to deal with a great variety of problems. A computer program has been written which treats the problem of an anisotropic substrate covered with an anisotropic layer, and does not require any restrictive condition on the permittivity matrices. Unfortunately, the numerical difficulties which appear especially for deep and lossy gratings are not yet completely removed.

When both the integral and differential methods are applicable in the study of anisotropic gratings, we show that they lead to numerical results which are in good agreement. We think that it is a convincing proof of the reliability of our computer programs.