Propagation of an attosecond pulse in a dense two-level medium

We investigate the propagation of attosecond pulse in a dense two-level medium by using an iterative predictor-corrector finite-difference time-domain method. We find when attosecond pulse is considered, that the standard area theorem will break down even for small area pulses: ideal self-induced transparency cannot occur even for a 2π pulse, while the pulses whose areas are not integer multiples of 2π, such as 1.8π and 2.2π pulses, cannot evolve to 2π pulses as predicted by the standard area theorem. Significantly higher spectra components can occur on all these small area propagating pulses due to strong carrier reshaping. Furthermore, these higher spectral components dependent sensitively on the pulse area: the larger the pulse area is, the more evident are these higher spectral components