DISPERSION RELATION AND BAND GAPS OF 3D PHOTONIC CRYSTALS MADE OF SPHERES

In this paper, we introduce a dispersion equation for 3D photonic crystals made of parallel layers of non-overlapping spheres, valid when both wavelength and separation between layers are much larger than the distance between neighbouring spheres. This equation is based on the Korringa-Kohn-Rostoker (KKR) wave calculation method developed by Stefanou et al. and can be used to predict the spectral positions of bandgaps in structures made of dispersive spheres. Perfect agreement between the spectral positions of bandgaps predicted with our simplifled equation and those obtained with the numerical code MULTEM2 was observed. We flnd that this simplifled relation allows us to identify two types of bandgaps: those related to the constitutive parameters of the spheres and those related to the three dimensional periodicity (distance between layers). Bandgaps of the flrst type are independent of the frequency and the distance between layers, while those of the second type depend only on these two quantities. We then analyze the in∞uence of the constitutive parameters of the spheres on the spectral position of bandgaps for spheres immersed in dielectric or magnetic homogeneous media. The number and positions of the bandgaps are afiected by the permitivity (permeability) of the host medium if the spheres have dispersive permitivity (permeability).