| In this thesis, a theory for dispersive polaritonic bandgap (DPBG) and photonic bandgap (PBG) materials is developed. An ensemble of multi-level nanoparticles, such as non-interacting two-, three- and four-level atoms doped in DPBG and PBG materials is considered. The optical properties of these materials such as spontaneous emission, line broadening, fluorescence and narrowing of the natural linewidth have been studied using the density matrix method. Numerical simulations for these properties have been performed for the DPBG materials SiC and InAs, and for a PBG material with a 20 percent gap-to-midgap ratio.; When a three-level nanoparticle is doped into a DPBG material, it is predicted that one or two bound states exist when one or both resonance energies, respectively, lie in the bandgap. It is shown when a resonance energy lies below the bandgap, its spectral density peak weakens and broadens as the resonance energy increases to the lower band edge. For the first time it is predicted that when a nanoparticle's resonance energy lies above the bandgap, its spectral density peak weakens and broadens as the resonance energy increases. A relation is also found between spectral structure and gap-to-midgap ratios.; The dressed states of a two-level atom doped into a DPBG material under the influence of an intense monochromatic laser field are examined. The splitting of the dressed state energies is calculated, and it is predicted that the splitting depends on the polariton density of states and the Rabi frequency of laser field. The fluoresence is also examined, and for the first time two distinct control processes are found for the transition from one peak to three peaks. It was previously known that the Rabi frequency controlled the Stark effect, but this thesis predicts that the local of the peak with respect to the optical bandgap can cause a transition from one to three peaks even with a weak Rabi frequency.; The transient linewidth narrowing of PBG crystal emission peaks doped with four-level atoms is studied. It is found that linewidth narrowing is only dependent upon time delay when the resonance energy is not near a band edge. This is a new discovery. The density matrix method is employed to find the critical magnetic field at which spin flopping occurs in antiferromagnetic high temperature superconductors. It is found that this magnetic field depends upon the temperature, the anisotropy parameter and the doping concentration. Results are calculated for 1-2-3 HTSCs.; Keywords. Quantum Optics, Density Matrix, Photonic Bandgap Materials, Dispersive Polaritonic Bandgap Materials, Antiferromagnets. |
