ABSTRACT
Quantum and nonlinear optical processes involving atoms or excitons in certain photonic crystals (PCs) undergo basic modifications as compared to the corresponding processes in open space or in bulk media. This entry surveys the main results on these modifications, which can be attributed to three fundamental properties of PCs: 1) The density of modes (DOM) is characterized in PCs by strong suppression of the background DOM within PBGs, by sharp band-edge cutoffs, and intragap narrow lines associated with narrow-linewidth (high-Q) defect modes. The results are given for spontaneous and stimulated emission in PCs stem from the failure of perturbation theory and the onset of strong field–atom (–exciton) coupling near sharp photonic band gap (PBG) edges or narrow defect-mode lines in PCs. 2) Photon effective masses are associated with band-dispersion effects in PCs. These effects allow bound, spatially correlated two-photon propagation as a result of either near-resonant or Kerr nonlinear field–atom interaction in a PC doped with atoms. 3) Band edge and Bragg reflections cause spatial interference effects in optical field propagation through a PC. Consequently, pulsed propagation in optically nonlinear PCs exhibits a variety of fundamentally unique and technologically interesting regimes: nonlinear filtering, switching, and distributed-feedback amplification. Among these regimes, we concentrate on the intriguing solitary waves, known as gap solitons (GS), which can move or stand inside or near PBGs, due to near-resonant field–atom interactions in PCs. Of particular interest are stable, transversely localized GS solutions in two-dimensional PCs, which are related to light bullets in uniform near-resonant atomic media.
