Sub-cycle pulses in a two-level medium: The solitary wave propagation

The expressions of hyperbolic secant sub-cycle pulse are derived from the oscillating dipole model through the complex source point method. Using the expressions of sub-cycle pulse, the intrinsic properties of the sub-cycle pulse as the intrinsic chirp and self-induced blueshift of the center frequency are found to have an important effect on the propagation of sub-cycle pulse in a two-level medium. The sub-cycle solitary waves are obtained in a two-level absorbing medium. The complete population inversion cannot be obtained by an odd multiple π sub-cycle pulse. As the intrinsic properties of sub-cycle pulse, the complete population return is obtained for both cases that the carrier frequency is resonant and non-resonant with atom. Accordingly, the solitary wave regime and the self-induced transparency of sub-cycle pulse are obtained in both the resonant and non-resonant cases.