X-ray free-electron lasers (FEL) deliver high-power, ultra-short polarized X-ray pulses, where the polarization state is determined by the electron beam trajectory in the FEL undulator. In this way, the polarization state depends on the kind of a magnetic structure used, and is fixed along the entire pulse. However, it would be beneficial to control the dependence of the polarization shape on time over the scale of one single pulse duration (about tens of femtoseconds). Such radiation may enable study of ultrafast molecular dynamics and magnetism.
In this contribution, we discuss a new method to control the polarization state of a single FEL pulse longitudinally (in time) and/or transversely (spatially) on the scales of 100 femtoseconds and several micrometers respectively.
We propose to use a crossed-undulators setup consisting of a pair of two co-axial Apple-X undulators. These undulators are scheduled for installation downstream the nominal SASE3 undulator line of European XFEL and they may be tuned to emit radiation pulses with two orthogonal polarization states, e.g. linear (vertical and horizontal) or circular (right and left). Both pulses upon reaching the sample are overlapped both spatially and temporally with some phase difference. Their interference yields polarization states, circular or linear respectively, with orientation that depends on that phase difference. If the frequency of one of the pulses is detuned, polarization of the resulting radiation will be shaped temporally. If the distance between the undulator cells is considerable, a difference between the wavefront curvatures allows shaping the resulting polarization spatially. We investigate possibilities to maximize or minimize both effects with a focusing system and demonstrate it with numerical simulations.