Resonance condition and field distribution in line-defect photonic crystal cavities

By applying a recently proposed coupled-Bloch-mode approach, we have derived the resonance condition for the longitudinal modes of passive photonic crystal (PhC) line-defect cavities. We have derived simple expressions for the electric field depending on the size of the cavity and the order of the resonant mode. We have shown that, as the cavity becomes longer, the fundamental mode turns from FP-like to DFB-like and the fraction of its wavevector components within the light cone is gradually suppressed. Importantly, we have clarified the physical origin for this behaviour.