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Optics Communications

Non-chirped distortionless pulse trains in inhomogeneously broadened resonant media

Václav Němec, Ljubomir Matulic

Published Apr 1, 1975• 3 citations
Publisher
DOI
10.1016/0030-4018(75)90127-3

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This paper presents the analytic solutions of self-induced transparency with transverse variations in resonant media by a self-consistent power series approximation method. We solve the Maxwell-Bloch equations by retaining all integral terms from the inhomogeneous broadening and the second-derivative terms with respect to distance and time. The lowest-order approximation is presented in detail. We discuss the characteristics of the distortionless pulses that propagate in an inhomogeneously broadening medium. It is shown that the group velocity and peak power of the self-induced transparency solitons could be represented in terms of the pulse width, the angle between phase velocity and group velocity, and the basic material parameters of the resonant medium. The chirping of the soliton is also discussed.
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.