Do evanescent waves really exist in free space?

It is shown that in 2D-case any solution of the homogeneous Helmholtz equation in free space is spatially band limited and contains only spatial frequencies smaller than the wave number. It means that evanescent waves in the representation of a wavefield in the form of an angular spectrum of plane waves are absent. If for specified wave field the part of its Fourier spectrum for spatial frequencies greater than the wave number is not equal to zero then the field distribution is not exactly a solution of the homogeneous free space wave equation. In this case, the angular spectrum representation and diffraction integrals may be used only with analysis of approximation errors.