Effects of a general X-ray polarization in multiple-beam Bragg diffraction

The formalism of the N-beam dynamical theory of X-ray diffraction is extended to include all possible incident and diffracted polarizations. With this new formalism it is shown that the intensity of a simultaneously excited Bragg reflection can be described through a polarization density matrix that involves the Stokes-Poincaré parameters. In particular, the multibeam diffracted intensity is sensitive to the circularly polarized component in the incident beam and the structure-factor phases of the diffracting crystal. Experimental results on the GaAs 442 and Ge 333 reflections confirm the theoretical calculations. This kind of measurement can provide useful acentric phase information and can also be used for circular X-ray polarimetry. Another feature of N-beam diffraction is its ability to turn a linear polarization into an elliptical polarization, which means it can be used as an X-ray phase plate.