Optical Fabry-Perot filter based on photonic band gap quasi-periodic one-dimensional multilayer according to the definite Rudin-Shapiro distribution

In this work, a new type of optical filter using photonic band gap materials has been suggested. Indeed, a combination of periodic H(LH)J and Rudin-Shapiro quasi-periodic one-dimensional photonic multilayer systems (RSM) were used. SiO2 (L) and TiO2 (H) were chosen as two elementary layers with refractive indexes nL = 1.45 and nH = 2.30 respectively. The study configuration is H(LH)J[RSM]PH(LH)J, which forms an effective Fabry-Perot filter (FPF), where J and P are respectively the repetition number of periodic and (RSM) stacks. We have numerically investigated by means of transfer-matrix approach the transmission properties in the visible spectral range of FPF system. We show that the number and position of resonator peaks are dependent on the (RSM) repetition number P and incidence angle of exciting light. The effect of these two parameters for producing an improved polychromatic filter with high finesse coefficient (F) and quality factor (Q) is studied in details.