A rate model approach for FEL pulse induced transmissions changes, saturable absorption, X ray transparency and stimulated emission

As the use of free electron laser FEL sources increases, so do the findings mentioning non linear phenomena occurring at these experiments, such as saturable absorption, induced transparency and scattering breakdowns. These are well known among the laser community, but are still rarely understood and expected among the X ray community and to date lack tools and theories to accurately predict the respective experimental parameters and results. We present a simple theoretical framework to access short X ray pulse induced light matter interactions which occur at intense short X ray pulses as available at FEL sources. Our approach allows to investigate effects such as saturable absorption, induced transparency and scattering suppression, stimulated emission, and transmission spectra, while including the density of state influence relevant to soft X ray spectroscopy in, for example, transition metal complexes or functional materials. This computationally efficient rate model based approach is intuitively adaptable to most solid state sample systems in the soft X ray spectrum with the potential to be extended for liquid and gas sample systems as well. The feasibility of the model to estimate the named effects and the influence of the density of state is demonstrated using the example of CoPd transition metal systems at the Co edge. We believe this work is an important contribution for the preparation, performance, and understanding of FEL based high intensity and short pulse experiments, especially on functional materials in the soft X ray spectru