Abstract
We consider two-dimensional three-component photonic crystals wherein one component is modeled as a drude-dispersive metal. It is found that the dispersion relation of light in this environment depends critically on the configuration of the metallic and dielectric components. In particular, 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, as would be expected for a purely dielectric photonic crystal. 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.
Highlights
Metamaterial environments have the potential to enhance or supress the emission of light as well as to slow light propagation and even achieve a negative index of refraction
Metamaterials composed of coupled metal and dielectric components with feature sizes comparable to or less than the wavelength of light display rich optical behavior such as negative index of refraction and slow pulse propagation
finite-difference time-domain (FDTD) [7, 8], variations of the plane wave expansion technique [13, 14, 15, 16, 17], and other techniques [18, 19] have proven useful for calculating the photonic band structures of systems with metallic components arranged in a periodic array
Summary
Metamaterial environments have the potential to enhance or supress the emission of light as well as to slow light propagation and even achieve a negative index of refraction. FDTD [7, 8], variations of the plane wave expansion technique [13, 14, 15, 16, 17], and other techniques [18, 19] have proven useful for calculating the photonic band structures of systems with metallic components arranged in a periodic array. We extend the theoretical framework of the plane wave technique [11, 12, 13, 14] for the calculation of photonic band structures to three-component photonic crystals containing one metallic component. The theoretical framework utilized in this report is based on a plane wave expansion This approach converges nicely for E-polarization but encounters numerical convergence problems for H-polarization.
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