Abstract
Steady state resonance fluorescence spectra from a two-level atom embedded in a photonic bandgap crystal and resonantly driven by a classical pump light are calculated. The photonic crystal is considered to be with a small bandgap which is in the order of magnitude of the Rabi frequency and is modeled by the anisotropic two-band dispersion relation. Non-Markovian noises caused by the non-uniform distribution of photon density states near the photonic bandgap are taken into account by a new approach which linearizes the optical Bloch equations by using the Liouville operator expansion. Fluorescence spectra that only exhibit sidebands of the Mollow triplet are found, indicating that there is no coherent Rayleigh scattering process.