Abstract
We have found the steady-state solutions in a homogeneously broadened two-level amplifying medium embedded in a dispersive and nonlinear Kerr host medium. The solution is of an unchirped hyperbolic-secant form. There are two kinds of solutions, π-pulse and 2π-pulse. The π-pulse propagates with the same velocity as that in the host, but the 2π-pulse propagates faster than that in the host. Each of the π-pulse and 2π-pulse solutions has a unique amplitude and pulse width which are determined by the parameters of the medium. The solutions exist only when the dipole moment of the laser medium and the parameters of the host medium satisfy a specific relationship, which can be realized by choosing a proper dispersion of the host medium in the negative region.
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