Figure 1:
(Top) A small deformation of the lattice planes in a perfect crystal has a wave-guiding effect on an x-ray wave packet, effectively translating it by several mm through the crystal (G is a reciprocal lattice vector). (Bottom) A more detailed picture of how the curved lattice planes translate the x-ray “α mode” that propagates through the crystal. The purple lines indicate the lattice planes (u denotes the displacement as a function of space) and the blue lines denote the phase of the propagating α mode. As the α mode curves, the amplitudes of its constituent A_{0} and A_{G} waves changes [6], with the amplitude of A_{0} increasing with respect to A_{G}. Since the Poynting vector is parallel to |A_{0}|^{2} k_{0}+|A_{G}|^{2}(k_{0}+G), the exiting wave is mainly along k_{0}.