Non-Markovian radiative phenomena in photonic band-gap materials

We present theoretical analyses of coherent and incoherent radiative phenomena from active materials embedded within photonic crystals (PCs). Fluorescence in PCs is described in terms of the local density of electromagnetic modes (LDOS) at the position of the active elements. We derive expressions for experimentally measurable quantities and test our formalism using various models of the LDOS. The radiative emission of a classical dipole oscillator in a PC is then described by coupling the system oscillator to a large but finite set of discrete oscillators describing the reservoir density of modes within a PC. This classical analysis motivates the study of radiative emission from microwave PCs.; We next discuss the collective emission of light from N two-level atoms with a resonant frequency near the edge of a photonic band-gap (PBG). Mean-field theory shows a macroscopic atomic polarization in the atomic steady state. This suggests the existence of an associated coherent radiation field localized about the atoms, in the absence of an external cavity mode. The effects of quantum fluctuations on collective emission dynamics are shown to differ strongly from those in free space, due to the non-Markovian atom-field interaction near a photonic band-edge. A classical noise ansatz is introduced that simulates the effect of the temporally correlated quantum fluctuations of the electromagnetic reservoir. The laser-like properties of superradiant emission near a photonic band-edge lead us to hypothesize that a band-edge laser system may exhibit a reduced laser threshold and a laser field that will exhibit phase diffusion significantly different from that in a conventional cavity laser.; Finally, we propose as a unit of quantum information (qubit) the single photon occupation of a localized field mode within an engineered network of defects in a PBG material. Qubit operations are mediated by optically excited atoms interacting with these localized states of light as the atoms traverse the connected void network of the PBG structure. We describe conditions under which this system can have independent qubits with controllable interactions and very low decoherence, as required for quantum information processing.