Abstract
The undamped Bloch equations are shown to have a more general analytic solution which includes the famous self-induced-transparency solution of McCall and Hahn, and the nonadiabatic excitation solution of Allen and Eberly as special cases. A generalized area characteristic for a laser pulse of modulated amplitude and frequency of the forms of hyperbolic secant and tangent is given. It resolves the difficulty of the previous area concept in the presence of frequency modulation. The solution provides an exact analytic result for the amplitude- and frequency-modulated pulse of any area.
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