Feasibility of manipulating the lifetime and speed of light in a matrix of metallodielectric cylinders

We consider two-dimensional three-component photonic crystals wherein one component is modeled as an electron gas. The problem is treated within the plane wave formalism. For the case of an incident electromagnetic wave with electric field vector parallel to the axis of the cylinders it is shown that the presence of dielectric shells covering the metallic cylinders leads to a closing of the structural band gap with increased filling factor of the metallic component. For the same polarization, the photonic band structure of an array of metallic shell cylinders with dielectric cores do not show the closing of the structural band gap with increased filling factor of the metallic component. In this geometry, the photonic band structure contains bands with very small values of group velocity with some bands having a maximum of group velocity as small as .05c. It is shown that by considering dielectric shells and cores with positive and negative values of imaginary part of permittivity one can control the lifetime of electromagnetic modes; adding a small negative imaginary part to the constant permittivity of the dielectric cores or shells results in a band structure where the amplitudes of all bands except the lowest-lying grow in time. For the case of magnetic field vector parallel to the axis of the cylinder convergence problems for bands below the plasma frequency are observed. They have much in common with the convergence problems which affect the plane wave method of calculating photonic band structures of simpler two-component non-dispersive systems when permittivities are allowed to take negative values. Qualitative aspects of the photonic band structures for this polarization reveal much of the physics and do not depend on convergence. The presence of a dielectric core or shell does not significantly affect band structures for this polarization. It is found that the lifetime of H -polarized states associated with near-linear dispersion of low-lying bands near the Γ point of the Brillouin zone are the longest, and the imaginary part of these states can be made positive by adding a negative imaginary part to the constant permittivity of the dielectric.