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We study the Compton scattering of x-rays off electrons that are driven by arelativistically intense short optical laser pulse. The frequency spectrum ofthe laser-assisted Compton radiation shows a broad plateau in the vicinity ofthe laser-free Compton line due to a nonlinear mixing between x-ray and laserphotons. Special emphasis is placed on how the shape of the short assistinglaser pulse affects the spectrum of the scattered x-rays. In particular, weobserve sharp peak structures in the plateau region, whose number and locationsare highly sensitive to the laser pulse shape. These structures are interpretedas spectral caustics by using a semiclassical analysis of the laser-assistedQED matrix element.

Caustic structures in the spectrum of x-ray Compton scattering off electrons driven by a short intense laser pulse