Theory of fluorescence in photonic crystals

We present a formalism for the description of fluorescence from optically active materials embedded in a photonic crystal structure possessing a photonic band gap or pseudogap. An electromagnetic field expansion in terms of Bloch modes of the crystal is used to develop the equations for fluorescence in terms of the local density of photon modes available to the emitting atoms in either the high or low dielectric regions of the crystal. We then obtain expressions for fluorescence spectra and emission dynamics for luminescent materials in photonic crystals. The validity of our formalism is demonstrated through the calculation of relevant quantities for model photon densities of states. The connection of our calculations to the description of realistic systems is discussed. We also describe the consequences of these analyses on the accurate description of the interaction between radiative systems and the electromagnetic reservoir within photonic crystals.