Spatial-Dispersion Effects in One-Dimensional Photonic Crystals with Metallic Inclusions

The spectral properties of metal-dielectric and metal-semiconductor 1D photonic crystals (PCs) are theoretically investigated, considering spatial dispersion in the metal and in the semiconductor, respectively. In the case of 1D PCs, composed of alternating metallic and dielectric slabs, we apply the classical formalism of the Boltzmann´s kinetic equation for the distribution function of the conduction electrons in order to determine the nonlocal constitutive equation for the metallic slabs. Afterwards, we calculate the dispersion relation for the bulk modes in the 1D PC and compare it with that obtained within the Drude-Lorentz model, which is implicitly local. Another kind of nonlocal effects are studied by considering a metal-semiconductor 1D PC. In this case, the frequency-dependent dielectric function of the metallic component is described by the local Drude-Lorentz model, whereas for the semiconductor we use a Hopfield-Thomas dielectric function, which describes its nonlocal behavior near exciton resonance. The polariton dispersion curves for s-polarized modes in the metal- semiconductor photonic crystal are compared with those for a metal-dielectric PC. Because of the coupling of light with excitons, which undergo size quantization inside the thin semiconductor slabs, many photonic small bands appear. We study the changes in the photonic dispersion curves for the resonant 1D PC as the filling fraction of the metal is varied.