Dynamical X-ray propagation: a theoretical approach to the creation of new wave fields

Although it is commonly invoked, the phenomenon of 'creation of new wave fields', which is responsible for some of the features visible on topographic images, has never been really explained in theoretical terms. This is done here in the case of a crystal deformed by a uniform strain gradient. The appropriate Green function is expanded in reciprocal space as a wave packet of non-plane waves, each component corresponding to a single value of the deviation parameter at the entrance surface. It is then shown that each component of this wave packet is made up of four parts, two of which can be identified as 'normal' wave fields (i.e. those predicted by the Eikonal theory); the two others are the so-called 'created wave fields'; it is shown that they correspond to interbranch scattering from one branch of the dispersion surface to the other and give rise to two extra beams. These created wave fields extract a fraction e^-2π|v| out of the normal energy flow (|v| being inversely proportional to the strain gradient), in full agreement with previous computer experiments.