Abstract

Here we numerically investigate the propagation of unipolar half-cycle attosecond pulses with a duration much shorter than the period of the proper oscillations ${T_0}$ of the medium and its relaxation times ${T_1}$ and ${T_2}$ in a two-level resonant absorbing and amplifying medium. We find that despite breaking down of the famous McCall and Hahn area theorem, some phenomena described by this theorem are still qualitatively preserved. In particular, it is shown that pulses with small initial electric pulse area become sign-alternating upon the propagation, similar to the traditional $0\pi$ pulses; pulses with $4\pi$, $5\pi$, and $6\pi$ area are unstable and split into lower-order pulses, exactly as in the long-pulse case. The electric pulse area conservation rule and limitations of unipolar pulse amplification in two-level gain media, which follows from this rule, are discussed.

© 2021 Optical Society of America

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