Sensitivity analysis of narrowband photonic crystal filters and waveguides to structure variations and inaccuracy

Photonic crystal microcavities, formed by local defects within an otherwise perfectly periodic structure, can be used as narrowband optical resonators and filters. The coupled-cavity waveguide (CCW) is a linear array of equally spaced identical microcavities. Tunneling of light between microcavities forms a guiding effect, with a central frequency and bandwidth controlled by the local defects' parameters and spacing, respectively. We employ cavity perturbation theory to investigate the sensitivity of microcavities and CCWs to random structure inaccuracies. For the microcavity, we predict a frequency shift that is due to random changes in the lattice structure and show an approximate linear dependence between the standard deviation of the structure inaccuracy and that of the resonant frequency. The effect of structural inaccuracy on the CCW devices, however, is different; it has practically no effect on the CCW performance if it is below a certain threshold but may destroy the CCW if this threshold is exceeded.