Transmission line model for extraction of transmission characteristics in photonic crystal waveguides with stubs: optical filter design

A simple and efficient transmission line model is proposed here to study how the transmission characteristics of photonic crystal waveguides are tailored by introduction of stubs patterned in the photonic crystal lattice. It is shown that band-pass and band-stop optical filters can be easily designed and optimized when stubs of appropriate length are brought in. Since the lengths of the designed stubs are not necessarily integer multiples of the photonic crystal lattice constant, a geometric shift in a portion of the photonic crystal structure is shown to be essential. The proposed model is verified by using a rigorous numerical method. An excellent agreement is observed between the numerical results and the transmission characteristics as extracted by the proposed model.