Modifications to 8x8 dynamical theory: Polarizations redefined according to x-ray diffraction convention

Dynamical x-ray diffraction theory can be cast in matrix form. In recent years, an 8x8 matrix theory was developed that treated asymmetric reflections from strained crystals. The polarization of the incident, specularly reflected, reflected diffracted, transmitted diffracted, and transmitted electromagnetic wave fields were all defined as s or p. That is, polarizations were defined with respect to the plane containing the incident beam direction and the surface normal. The authors present modifications of the theory to treat {sigma} and {pi} polarizations for Bragg diffraction from asymmetric planes, that is, for polarizations defined with respect to the plane containing the incident beam direction and the reciprocal lattice vector for Bragg diffraction. They present results of this theory for unstrained crystals in the inclined geometry. In this geometry the incident beam wavevector, the reciprocal lattice vector, and the surface normal are not coplanar. The inclined crystal geometry appears promising for use in a high-heat-load monochromator for undulator radiation at the Advanced Photon Source. As expected, they find a weak {pi}-polarization component in the diffracted beam when the polarization of the incident beam is pure {sigma}.