Designing optical filters with electrical models of photonic crystal defects

A systematic approach for designing photonic crystal based band-pass filters with different filter characteristics has been presented in this paper. The filter characteristics are manipulated by varying the location of the defects in a photonic crystal waveguide. The photonic crystal waveguide is modeled as a dispersive transmission line and the defects are modeled by equivalent electrical T-networks. A filter then is visualized as a cascade of the T-networks with suitable interconnecting sections of transmission line. S-parameters are used to find the transmission and reflection frequency response of the filter. An optimization approach is used to obtain the most optimal locations of the defects which give the desired frequency response. It is shown that more than one defect combinations are possible for getting the desired filter characteristics.