Design criteria and 3D FEM modeling of air hole photonic crystal

This work presents a detailed numerical Finite Element Method FEM modeling for passive optical components such as photonic crystals (PhCs). The accurate modeling characterizes the PhCs structures by considering the field resonance and the radiation behavior of the periodic pattern. The frequency responses at each side of the photonic crystal are evaluated by considering the 3D periodic structure enclosed in a black box with six input/output ports. This scattering matrix approach (SMA) is useful in order to evaluate in plane and vertical PhCs the resonance of the photonic crystal. Through the analysis of all the frequency responses we characterize the passband regions and the stopband regions of the PhC slab.