Abstract-Photonic Bandgap (PBG) materials have been investigated for their versatility in controlling the propagation of electromagnetic waves [1, 2]. In order to determine PBG structures responses, several analytical or numerical methods are used, such as:
- The plane wave method applied to solve Maxwell's equations .
- The transfer matrix method, based on the wire grating impedance developed by N. Marcuvitz .
- The Finite Element Method (FEM) exhibits, e.g., the frequency response of reflection and transmission coefficients of the PBG materials when they have infinite surfaces and are excited by plane wave. The FEM method can be also used in the case of finite structure fed by a dipole.
- solves the discretized Maxwell's equations in the time domain and evaluates the electromagnetic field components. These EM fields are then obtained in the frequency domain thanks to a Fourier Transform.
First of all, we present a parametrical study using a 3D Finite Element method software. This study allows to estimate the role of any parameters on the reflection and transmission coefficients and then to design a PBG structure in the X-band (8-12 GHz). Continuous and discontinuous structures are presented. Then, we present a numerical analysis of PBG structures, using the FDTD method in order to understand the propagation phenomena in these periodic materials.