  The radiation dynamics of a dipole antenna embedded in a Photonic Crystal are
modeled by an initially excited harmonic oscillator coupled to a non--Markovian
bath of harmonic oscillators representing the colored electromagnetic vacuum
within the crystal. Realistic coupling constants based on the natural modes of
the Photonic Crystal, i.e., Bloch waves and their associated dispersion
relation, are derived. For simple model systems, well-known results such as
decay times and emission spectra are reproduced. This approach enables direct
incorporation of realistic band structure computations into studies of
radiative emission from atoms and molecules within photonic crystals. We
therefore provide a predictive and interpretative tool for experiments in both
the microwave and optical regimes.
