Resonant add-drop filter based on a photonic quasicrystal

We present a numerical study of optical properties of an octagonal quasi-periodic lattice of dielectric rods. We report on a complete photonic bandgap in TM polarization up to extremely low dielectric constants of rods. The first photonic bandgap remains open down to dielectric constant as small as e = 1.6 (p = 1.26). The properties of an optical microcavity and waveguides are examined for the system of rods with dielectric constant e = 5.0 (p = 2.24) in order to design an add-drop filer. Proposed add-drop filer is numerically characterized and further optimized for efficient operation. The two-dimensional finite difference time domain method was exploited for numerical calculations. We provide a numerical evidence of effective add-drop filter based on low index material, thus opening further opportunities for application of low refractive index materials in photonic bandgap optics.