Généralisation de la notion de champs d'ondes en théorie dynamique

Using Takagi's theory of X-ray diffraction by a perfect crystal and the general theory of differential equations, a solution of Takagi's equations is given in the form of a linear combination of two unit vectors of the vectorial space formed by the solutions of these equations. The amplitude distribution inside the crystal is then the sum of two terms, each term being the convolution of a function depending on the amplitude distribution on the incident surface and one of the two principal solutions of Takagi's equation which are Hankel functions of the first and second kind, H¹_o and H²_o. This gives an extension of the notion of wavefields since this calculation can be done for any kind of incident wave on the entrance surface. It is shown that these two `generalized wavefields' present anomalous absorption. In the case of an incident plane wave or an incident spherical wave, these `generalized wavefields' become identical with the usual wavefields of the dynamical theory.