Wave Propagation in a Three-Dimensional Photonic Crystal from Hollow Dielectric Cylinders

3D photonic crystals (PC) composed of equally oriented hollow dielectric cylinders of finite length with a rectangular and hexagonal lattice were investigated. The study investigated both the long wavelength range, when the wavelength is much longer than the crystal period, and the crystal itself is an artificial dielectric, and the short wavelength range, where bandgaps appear. Two crystal eigenmodes are shown to have different bandgaps. By varying the PC parameters, it is possible to achieve both coincidence (absolute photonic band gap) and difference of bandgaps, which can be used in various waveguide and polarization devices. All calculations are carried out by specially manufactured software that surpasses the stray packages of electrodynamic analysis in terms of calculation speed.