Reflecting filters based on one dimensional photonic crystal with large lattice constant

We change the optical thicknesses of different layers in one dimensional photonic crystals (1DPCs) by introducing sine and cosine functions into transfer matrix method and find that the changes of 1DPC's optical thicknesses from regular periodic structures to sine and cosine function structures, will make the reflection spectrums of 1DPCs appear multiple reflection peaks and these peak's widths and positions can be easily modulated by changing the fundamental parameters of sine and cosine functions. In this paper, we use this method to design two types of narrow band reflecting filters based on 1DPCs with large lattice constant.