The Behavior of Electromagnetic Wave Propagation in Photonic Crystals with or without a Defect

Abstract

In this study, the electromagnetic wave propagation behavior of two-dimensional photonic crystal plates with a defect is investigated. For this purpose, the partial differential equation for the electromagnetic wave propagation in various photonic crystal plates containing a defect or not is obtained by using Maxwell’s equations. The defect is also defined in the electromagnetic wave propagation equation appropriately. In order to solve the electromagnetic wave propagation equation, the finite differences method is used. The material property parameters of the photonic crystal plates are determined with respect to the defects. Accordingly, the effects of material property parameters on electromagnetic wave propagation frequencies, phase velocities, and group velocities are examined. The effects of the size and position of the defects on the electromagnetic wave propagation frequencies are also discussed. The highest electromagnetic wave propagation fundamental frequency value obtained from the analyses performed is 1.198 Hz. This fundamental frequency value is obtained for the electromagnetic wave propagation in the t-shaped photonic crystal plate. Electromagnetic field distribution maps for the fundamental frequencies of the photonic crystal plates whose electromagnetic wave propagation behaviors are examined are obtained with the ANSYS package program based on the finite differences time-domain (FDTD) method.