Design of optical building blocks for photonic integration - Chin, Mee Koy. (2008)
We present a transfer matrix analysis of a 2-D filter to study its frequency response functions. The (M xN) array consists of N independent columns of micro-ring resonators side-coupled to two channel bus waveguides, with equal spacing between columns and each column consisting of M coupled resonators. We show that the bandgap of the 2-D structure is a superposition of the non-overlapping bandgap of the two 1-D arrays. This non-overlapping property can be used to realize the "near-ideal" filter with flat and sharp passband, negligible sidelobes in the stop bands, and linear phase response over 80% of the passband. The existence of defect mode in linear and lossless ring resonator arrays is also demonstrated. The defect can be introduced by removing one ring or by making one ring bigger or smaller. Defect states within the photonic bandgaps behave like either donor or acceptor modes similar to other photonic crystals. The results based on transfer matrix model shows reasonable agreement with finite difference time domain (FDTD) simulations.