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 epsilon = 1.6 (n = 1.26). The properties of an optical microcavity and waveguides are examined for the system of rods with dielectric constant epsilon = 5.0 (n = 2.24) in order to design an add-drop filter. Proposed add-drop filter 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.