  Steady-state fluorescence spectra of a two-level atom embedded in a
three-dimensional photonic bandgap crystal and driven by a monochromatic
classical electrical field is calculated theoretically for the first time as we
know. The non-Markovian noises caused by the non-uniform distribution of photon
density of states near the photonic bandgap are handled by a new approach in
which the Liouville operator expansion is utilized to linearize the generalized
optical Bloch equations. The fluorescence spectra are then directly solved by
the linearized Bloch equations in the frequency domain. We find that if the
atomic energy level is far from the bandgap, fluorescence spectra with Mollow's
triplets are observed. However, 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.
