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.
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.
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.
In this work, we show that photonic crystals with geometries of lower symmetry, such as the rectangular geometry, are uniquely suited for applications involving the superprism effect. The extra degree of freedom provided by the anisotropy of the unit cell allows more freedom in searching for suitable iso-frequency curves. Also, the appearance of multiple orders of diffraction allows more than one incident plane wave to couple to the same Bloch mode. This extra degree of freedom is decisive when trying to optimize the transmission. We illustrate this on a particular rectangular configuration which ensures a strong angular superprism effect, a well collimated transmitted beam, and power transmissions of up to 80%. We also study the effect of the incident beam width on the super-prism effect, and propose a possible solution to the problem of beam diffraction at the exit surface.