On the propagation of evanescent waves

The Fourier spectrum of the boundary value in propagation integrals is considered in general. It is shown that this spectrum is by the most part singular and thus the known theorems of Fourier transform cannot be applied. It follows that evanescent waves contribute into the total power passed through the initial plane. Evanescent waves contribute into the field everywhere but this contribution only compensates a part of the contribution from propagating modes. Thus, evanescent and propagating modes cannot be considered as physical objects: they are just mathematical oddities.