The effects of periodic and quasi-periodic orders on the photonic bandgap structures of microring coupled-resonator optical waveguides

Abstract

We present a coupling matrix formalism to investigate the effects of periodic and quasi-periodic orders on the photonic bandgap (PBG) structures of coupled-resonator optical waveguides (CROWs) based on microring resonators. For the periodic order case, size-tuned defects are introduced at periodic locations among the regular rings, which are size-untuned, to form a periodic ordered CROW system. The periodic coupled defects result in multiple localization states that lead to the formation of mini-defect bands and mini-PBGs within the PBG of a defect-free CROW. The position and number of such mini-defect bands depend on the size tuning of the defects. For the quasi-periodic order case, the arrangement of the defects and the regular rings in the ring cascade is an intermediate between periodic order and randomness, thus forming a quasi-periodic ordered CROW system. The effects of quasi-periodicity on the PBG structures are illustrated using the Fibonacci sequences, which result in a single high-Q localized state to appear that gradually transits to a mini-band within a wide photonic stop band as the number of lattice cells increases.