Propagation of a strong x-ray pulse: Pulse compression, stimulated Raman scattering, amplified spontaneous emission, lasing without inversion, and four-wave mixing

We study the compression of strong x-ray pulses from x-ray free-electron lasers (XFELs) propagating through the resonant medium of atomic argon. The simulations are based on the three-level model with the frequency of the incident x-ray pulse tuned in the 2p(3/2)-4s resonance. The pulse propagation is accompanied by the self-seeded stimulated resonant Raman scattering (SRRS). The SRRS starts from two channels of amplified spontaneous emission (ASE), 4s-2p(3/2) and 3s-2p(3/2), which form the extensive ringing pattern and widen the power spectrum. The produced seed field triggers the Stokes ASE channel 3s-2p(3/2). The population inversion is quenched for longer propagation distances where the ASE is followed by the lasing without inversion (LWI), which amplifies the Stokes component. Both ASE and LWI reshape the input pulse: The compressed front part of the pulse (up to 100 as) is followed by the long tail of the ringing and beating between the pump and Stokes frequencies. The pump pulse also generates weaker Stokes and anti-Stokes fields caused by four-wave mixing. These four spectral bands have fine structures caused by the dynamical Stark effect. A slowdown of the XFEL pulse up to 78% of the speed of light in vacuum is found because of a large nonlinear refractive index.