Solitary propagation effect of a well-defined chirped femtosecond laser pulse in a resonance-absorbing medium

We investigate the solitary propagation effect of a well-defined chirped femtosecond laser pulse in a resonance-absorbing medium which is modeled by a two-level quantum dot ensemble. Employing full time-dependent and space-dependent Maxwell-Bloch equations, the evolution of the pulse and the population inversion as well as the spectrum are obtained. The results reveal that the special chirped pulse can retain its shape and resist breakup while propagating through the absorbing medium. Besides, the spectrum does not exhibit obvious broadening but the central and near-central frequency components tend to vanish. Moreover, the stable soliton formed by the special chirped-pulse design based on stimulated Raman adiabatic passage does not obey the area theorem.

Figure 1

The snap of the electric field with $4\pi$ area propagating in an absorbing medium with ${\varepsilon }_r=9.5$ at $t$ $=$ 0.15, 0.3, and 0.45 ps. The population inversion at 0.3 ps. (a) Standard field; (b) special chirped field.

Figure 2

(a) The snap of the special chirped pulse with $4\pi$ area propagating in an inhomogeneously broadened absorbing medium with ${\varepsilon }_r=9.5$ at $t$ $=$ 0.15, 0.3, and 0.45 ps. (b) The population inversion of the three detunings at 0.49 ps.

Figure 3

(a) The propagation of the standard pulse with $4\pi$ area propagating in an absorbing medium with ${\varepsilon }_r=1$, $t_p=2.4\mathrm{fs}$ at five different times. (b) The population inversion at $t$ $=$ 0.15, 0.3, and 0.45 ps. (c) The frequency spectrum of the pulse at $Z$ $=$ 24, 144, and 264 μm.

Figure 4

(a) The propagation of the special chirped pulse with $4\pi$ area propagating in an absorbing medium with ${\varepsilon }_r=1$, $t_p=2.4\mathrm{fs}$ at five different times. (b) The population inversion at $t$ $=$ 0.15, 0.3, and 0.45 ps. (c) The frequency spectrum of the pulse at $Z$ $=$ 24, 144, and 264 μm.

Figure 5

(a) The propagation of the special chirped pulse with $7\pi$ area propagating in an absorbing medium with ${\varepsilon }_r=9.5$ at $t$ $=$ 0.15, 0.3, and 0.45 ps. (b) The population inversion at 0.15, 0.3, and 0.45 ps.