Free Electron Laser Generation of X-Ray Poincar\'e Beams

An optics-free method is proposed to generate X-ray radiation with spatially variant states of polarization via an afterburner extension to a Free Electron Laser (FEL). Control of the polarization in the transverse plane is obtained through the overlap of different coherent transverse light distributions radiated from a bunched electron beam in two consecutive orthogonally polarised undulators. Different transverse profiles are obtained by emitting at a higher harmonic in one or both of the undulators. This method enables the generation of beams structured in their intensity, phase, and polarization - so-called Poincar\'e beams - at high powers with tunable wavelengths. Simulations are used to demonstrate the generation of two different classes of light with spatially inhomogeneous polarization - cylindrical vector beams and full Poincar\'e beams.