The concept of “Standing Waves” (SW) that arise in the crystal dynamically “attacked” by the frequency fields X is analytically analyzed towards expressing, in almost all the cases, the total intensity of the fields on dispersion branches in the perfect crystal and for the embedded layer on the imperfect crystal using various extensions of the semi-classical dynamic theory, adapted or reparameterized, depending on the specific conditions of analysis performed.
Top13.2. Anomalous Absorption Vs. Fluorescence
Due to the condition of continuity and to the existence in the crystal subjected to the action of an external field with a frequency X, of two directions of propagation, transmitted-diffracted, the initial electric field dynamically splits into two internal fields, coherent, one on each direction, with different amplitudes and with the same temporal phase (Batterman &Cole 1964; Batterman 1959, 1962, 1964, 1969):
(13.1)Thus, by the dynamical internal splitting, of the same incident external field, we obtain a vector sum of coherent fields inside the crystal, resulting in the appearance of some standing fields, the interference effect:
(13.2) with
the polarization factor defined in Chapter 11; the sign on top corresponding to the alpha branch (1), and the bottom one to the beta branch (2).
The standing waves occur for a constant intensity of the local resultant of the waves along the propagation planes:
(13.3) which shows that the planes of constant intensity have to match with the atomic planes, i.e. satisfy the condition
, the standing waves (SW) forming between the atomic planes.
With this condition will be distinguished cases of interference as shown in Box 1 with the intuitive representation of Figure 1.