FURION: modeling of FEL pulses propagation in dispersive soft X-ray beamline systems

Modern X-ray free-electron lasers (XFELs) can generate pulses with durations ranging from femtoseconds to attoseconds. The numerical evaluation of ultra-short XFEL pulses through beamline systems is a critical process of beamline system design. However, the bandwidth of such ultra-short XFEL pulses is often non-negligible, and the propagation cannot be simply approximated using the central wavelength, especially in dispersive beamline systems. We developed a numerical model which is called Fourier optics based Ultrashort x-Ray pulse propagatION tool (FURION). This model can not only be used to simulate dispersive beamline systems but also to evaluate non-dispersive beamline systems. The FURION model utilizes Fresnel integral and angular spectrum integral to perform ultra-short XFEL pulse propagation in free space. We also present the method for XFEL pulse propagation through different types of dispersive gratings, which are commonly used in soft X-ray beamline systems. By using FURION, a start-to-end simulation of the FEL-1 beamline system at Shenzhen superconducting soft X-ray free electron laser (S³FEL) is carried out. This model can also be used to evaluate gratings-based spectrometers, beam splitters, pulse compressors, and pulse stretchers. This work provides valuable insights into the start-to-end simulation of X-ray beamline systems.