Band gaps in photonic crystals with dispersion
Purpose - The paper presents the band gap computation in one- and two-dimensional photonic crystals built up from porous silicon. The frequency dispersion of the dielectric materials is taken into account. Design/methodology/approach - The behavior of the light in a photonic crystal can be well described by the Maxwell equations. The finite difference time domain (FDTD) method is applied to determine the band structure. The frequency dependence of the dielectric constant is taken into account by a sum of second-order Lorenz poles. The material parameters are determined applying a conjugate gradient-based minimization procedure. Passing a light pulse of Gaussian distribution through the photonic crystal and analyzing the transmitted wave can explore the photonic bands. Findings - The realized simulations and visualizations can lead to a much better understanding of the behavior of electromagnetic waves in dispersive photonic crystals, and can make possible to set up experimental conditions properly. The obtained results show again that silicon and porous silicon can be used for the fabrication of photonic crystals. Research limitations/implications - Due to the high computational requirements of the three-dimensional case we plan to work out a parallel version of the presented FDTD algorithm. Originality/value - This paper presents a simple way to take into account the frequency dispersion in the simulation of photonic crystals with the FDTD method.
silicon finite difference methods electromagnetic radiation