Coherent effects in Bragg reflectors: light localization and oscillating solitary waves near absorption resonances

Summary form only given. In recent years, there has been considerable interest in nonlinear and quantum optics of photonic bandgap structures. Some of this attention has centered on the properties of gap solitary waves, which are light pulses tuned at a Bragg frequency within a forbidden bandgap of the periodic structure. These solitary waves may occur in a periodically modulated medium with a Kerr-like nonlinearity, and in the resonance grating as a two-wave soliton of self-induced transparency. In the later case, the coupled-mode Maxwell-Bloch equations which describe the on-resonance coherent interaction of the intense field with a periodic structure of thin layers of two-level atoms in the ground state, lead to an integrable sine-Gordon equation. In our study, we concentrate on the nonintegrable case, that is, amplification in a resonant Bragg structure by means of a comprehensive analysis that includes and numerical modelling of Dicke superradiance and coherent amplification.