Abstract
The differential absorption and the differential change in the polarization state of an X-ray beam propagating inside a gyrotropic crystal are described using a 4 X 4 Muller matrix, the 16 elements of which are related to the anisotropic components of the multipolar polarizability tensors at the absorbing site. Analytical expressions are given up to third order for X-ray linear and circular dichroism, X-ray optical rotation and X-ray circular polarimetry in transmission. The same formalism is extended to discuss Fluorescence detected dichroism spectra with or without polarization analysis of the fluorescence. Fluorescence detected dichroism is strictly proportional to dichroism measured in the transmission geometry only for uniaxial crystals. In biaxial crystals, the tiny effects of X-ray gyrotropy are swamped by large linear dichroism signals due to the imperfect polarization transfer function of Bragg monochromators. Second order effects should also be taken into consideration. Our general formulation of linear and circular dichroism includes terms of odd parity with respect to the action of the time reversal operator: such terms cannot contribute to natural dichroism but can be activated by a magnetic field. The terms responsible for X-ray magnetic circular dichroism are well known but non-reciprocal X-ray gyrotropy effects are also predicted in magnetic crystals of appropriate symmetry.
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