Photonic bands of metallic systems. I. Principle of calculation and accuracy

The dispersion relation, the field distribution. and the lifetime of the radiational eigenmodes in two-dimensional photonic crystals composed of metallic cylinders were calculated for the E polarization by means of the numerical simulation of the dipole radiation based on the finite-difference time-domain (FDTD) method. The convergence and the central processing unit time were compared with the plane-wave expansion method. The opaque frequency ranges in the transmission spectra calculated by the method of Pendry and MacKinnon corresponded quite well to the band gaps and the antisymmetric modes found in the photonic band diagram. The dispersion relation and the symmetry of the eigenmodes obtained by the numerical calculation were consistent with the prediction of the group theory and the analytical expression by the long-wavelength approximation.