Abstract
We present a numerical method for solving the Maxwell-Bloch equations describing pulse propagation for a two-level medium. The method is accurate, efficient, stable, and well suited for this type of simultaneous equations. By applying the numerical scheme we investigate the evolutions of pulse area, pulse propagation, pulse velocity, and spectral shapes under both homogeneous and inhomogeneous broadening conditions. The results show that the area evolution and pulse-reshaping procedure are significantly influenced by detuning and inhomogeneous line shape, which also impact the oscillation tail and pulse peak. In addition, the pulse-peak traces indicated the pulse velocity always increases with greater deviation in pulse-area value from the value 2\ensuremath{\pi}. We also demonstrate the pulse velocity increased for a larger detuning or a wider inhomogeneous line shape. Furthermore, the spectral feature shows that pulse spectra evolve into an oscillating shape.
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