Distortionless pulse-train propagation in a nonlinear photonic bandgap structure doped uniformly with inhomogeneously broadening two-level atoms

The pulse propagation in a one-dimensional nonlinear photonic bandgap (PBG) structure doped uniformly with inhomogeneously broadening two-level atoms is investigated. The Maxwell-Bloch equations describing pulse propagation in such a uniformly doped PBG structure are derived first and further reduced to effective nonlinear coupled-mode equations. An exact analytic pulse-train solution to these effective coupled-mode equations is obtained. Such a distortionless; pulse-train solution is given by sinusoidal functions with a DC background and a modulated phase. Numerical examples of the distortionless pulse train in a silica-based PBG structure doped uniformly with Lorentzian lineshape two-level atoms are shown.