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Resonance fluorescence spectrum near photonic bandgap

We theoretically calculate the resonance fluorescence spectrum from a two-level atom which is embedded in a photonic bandgap crystal and is resonantly driven by a classical pump light. 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. These linearized equations can be solved directly in the Fourier domain to obtain the correlation functions of the atomic operators and then the fluorescence spectrum from the atom. We find that if the atomic energy level is far from the bandgap, fluorescence spectra with Mollow triplets are observed. When the atomic energy level is near the bandgap, the relative magnitude and the number of the fluorescence peaks are found to be varied according to the wavelength offset.