Propagation of subcycle pulses in a two-level medium: Area-theorem breakdown and pulse shape

We solve the problem of ultrashort pulse propagation in a two-level medium beyond the rotating-wave (RWA) and slowly varying-envelope approximations. The method of solution is based on the Maxwell-Bloch equations represented in the form that allows one to switch between RWA and general (non-RWA) cases in the framework of a single numerical algorithm. Using this method, the effect of a subcycle pulse (containing less than a single period of field oscillations) on the two-level medium was analyzed. It is shown that for such short pulses, the clear breakdown of the area theorem occurs for the pulses of large enough area. Moreover, deviations from the area theorem appear to be strongly dependent on the pulse shape that cannot be observed for longer few-cycle pulses.

Figure 1

(a) The profile of the Gaussian 50-cycle $3\pi$ pulse transmitted through the two-level medium of length $L=100\lambda$. Calculations were carried out for the general case ($s=1$). (b) The difference between the intensity profiles obtained for $s=1$ and $s=0$. (c) The difference between the intensity profiles calculated by two different RWA schemes: the scheme of Eqs. (4) to (6) at $s=0$ and that of Ref. [16]. Intensities are normalized by $I_0={\Omega }_0^2$.

Figure 2

(a) Dynamics of the inversion at the entrance of the two-level medium excited by the Gaussian two-cycle $2\pi$ pulse. Calculations were carried out both for the general case ($s=1$) and for the RWA ($s=0$). (b) The difference between the inversion profiles obtained for $s=1$ and $s=0$. (c) The difference between the inversion profiles calculated by two different RWA schemes: the scheme of Eqs. (4) to (6) at $s=0$ and that of Ref. [16].

Figure 3

(a) Dynamics of the inversion at the entrance of the two-level medium excited by the Gaussian and hyperbolic secant $3\pi$ pulses of different numbers of cycles $N$. (b) The corresponding dependence of the FSI $w_f$ on the number of cycles. FSI was determined at the time point $t=50t_p$. The inset shows the field profiles of the half-cycle $3\pi$ pulses of the Gaussian and $\text{sech}$ shapes.

Figure 4

The dependence of the FSI $w_f$ on the area of the half-cycle pulses of the Gaussian and hyperbolic secant shapes. The results for the RWA case are given for comparison. FSI was determined at the time point $t=50t_p$.