The Coupling of Poynting Vectors

Atthe first stage of analysis, the successive expressions of the Poynting vee-tor can be written ciunulating the relations (5.176) in a global siunmation  

The expression above can be simplified if its average over the unit cell is considered, a case in which r - / , i.e., meaning the neglecting of the variation of the first exponentials inside the cell and their replacement with a constant when h = h so that the averaged contribution of the last exponential to be canceled  

In the last expression, the vectorial product can be rewritten such as  

by assuming the fact that the differences in the modules for the eigen-wave vectors of the reciprocal lattice are negligible, the expression (5.180) will be rewritten such as  

If a single active node of the reciprocal lattice, respectively the diffraction on a single set of crystallographic planes (a single couple of diflfracted-transmitted H-0 waves) is considered, while a pair of coupling points corresponding to the same incidence is placed on the alpha and beta branches of DS, we will further obtain from (5.182)  

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