Amplification of fluorescence from the 3a P-1(0) doubly excited state in helium

We present a theoretical study of self-amplification of extreme ultraviolet light in a helium gas target. Resonant excitation to the 3a P-1(0) doubly excited state below the N = 2 threshold by 100 fs free-electron laser pulses is followed by fluorescence at 40.7 eV photon energy. The process is modeled by a three-level atomic system coupled to the continuum and described by the Maxwell-Bloch equations. The evolution of state populations and radiation fields is studied over a wide range of pump intensities and target pressures, clearly showing the regions of spontaneous emission, amplification, and saturation of light emitted in the forward direction. The treatment includes both coherent and SASE pump pulses. In both cases the amplified pulses are temporally coherent and exhibit a duration similar to that of the pump pulses.