Studies of the generation and propagation of light fields in the extreme ultraviolet (XUV) can provide insights into the fundamental interaction of atoms in highly excited levels and ionized atoms. In this paper, we present experimental results of nonlinear four-wave mixing (FWM) processes using a combination of XUV radiation and optical pulses in argon gas. The XUV pulses are produced by phase-matched high-order harmonic generation (HHG). Optimized phase-matching of collinear multiple-cycle laser pulses with incommensurate frequencies (800 nm, 1400 nm, and 560 nm) is used to indicate the different pathways of the third-order and fifth-order nonlinear responses in the mixing process in a single gas cell configuration. A perturbative nonlinear optics approach can be used to explain our cascaded wave-mixing patterns. Our results reveal that the time-dependent spectral features of the mixing fields are associated with auto-ionization processes. Overall, the intensity and frequency modulation of the wave-mixing fields provides a new technique to investigate the dynamical evolution of electron wave-packets in atomic and molecular gases.
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