Three-dimensional Maxwell-Bloch calculation of the temporal profile of a seeded soft x-ray laser pulse

We present three-dimensional modeling of amplification of a high-order harmonic seed by a soft x-ray laser plasma. The time-dependent evolution of the x-ray signal is determined from a fully dynamic Maxwell-Bloch calculation. At high seed intensities, a simplified one-dimensional calculation leads to strong Rabi-like temporal oscillations of the output signal. However, such oscillations have not been observed experimentally. Our calculations demonstrate that this is due to spatial non-uniformities in the plasma gain that cause the Rabi oscillations to dampen dramatically. Large amplitude Rabi-like oscillations are expected to appear only in long and uniform plasma. Such targets require optimized guiding techniques.