Spectral caustics in laser-assisted x-ray Compton scattering

We study the process of laser-assisted Compton scattering: The Compton scattering of x-rays from an XFEL off electrons that are driven by a relativistically intense short optical laser pulse. The frequency spectrum of the laser-assisted Compton radiation shows a broad plateau in the vicinity of the laser-free Compton line due to a nonlinear mixing between x-ray and laser photons [1]. We observe sharp peak structures in the plateau region. These structures are interpreted as spectral caustics by using a semiclassical analysis of the laser-assisted QED matrix element, relating the caustic peak positions to the laser-driven electron motion [2].