Frequency generation within the forbidden band gap: All optical Rabi-like splitting in photonic crystals and microcavities

Based on three-dimensional time domain numerical simulations of the nonlinear dispersive Maxwell equations, we find evidence of all optical splitting of defect states in a photonic band gap structure. The result is analogous to the well known Rabi splitting and optical nutation in atomic two-level systems, and can be used for controlled in-gap generation of optical frequencies. Photon-echo-like behavior and third harmonic generation are also investigated.