Chirality, birefringence, and polarization effects inα-quartzstudied by resonant elastic x-ray scattering

We show that enantiomers are extremely sensitive to the quality of the light polarization in resonant elastic x-ray scattering experiments. In $\ensuremath{\alpha}\text{-quartz}$, the (001) reflection shows a very strong sensitivity to a small fraction of linear component included in nominally circularly polarized light. This fraction induces an important phase difference between the angular dependence of the recorded intensity from each enantiomer. We are thus able to model all aspects of the resonant scattering and determine the dominant physics, extract the crystal chirality, and obtain very precise values for the Stokes polarization parameters. Effects of birefringence and of higher-order electric transitions are also quantified and it is shown that in comparison they are negligible.