Nonlinear phenomena in X-ray fluorescence from single nanoparticles under extreme conditions

Materials exposed to intense femtosecond X-ray pulses with energies above their K-shell absorption edge can enter an extremely ionized state, which could give rise to nonlinear phenomena, such as saturable absorption and reverse saturable absorption. In this work, we investigate these effects on single copper nanoparticles irradiated by an X-ray free-electron laser pulse. We study the properties of the K$\alpha$ fluorescence for two different short pulse durations and three X-ray incident energies below and above the K-shell absorption edge, and correlate these with incident fluence estimates based on coherent diffraction. We observe that the incident fluence of the pulse and not its duration, is the main factor that modulates the nonlinear response, which leads to an effective shortening of the fluorescence emission. Our findings have implications for fluorescence-based methods for imaging single particles using transiently coherent fluorescence, or diffractive imaging through transient resonances.