in my antennas book (I do not put its reference because it is not in english) it is written that, at high distance from the source, the electromagnetic field radiated by it is a spherical wave.
This can be shown by analyzing the expression of the EM field at high distance generated by some specific antennas. For instance, for a half-wave dipole (which is not the short herzian dipole) we get (Reference here, page 17):
It is a spherical wave because its dependence on r is given by the term:
\$\frac{e^{-jkr}}{r}\$
I do not understand how can be this physically possible. A spherical wave is ideally generated only from a point source. I easily understand how even the wave generated by a small source (for example a short Herzian dipole) can be, at high distance, approximated as spherical. But in this case, in which the linear current source is not short, I don't understand why the wave cannot be, more plausibly (from a physical point of view), cylindrical. Furthermore, if it is true that at a great distance any wave is spherical, in which situations do cylindrical waves exist? I can't imagine how a cylinder becomes a sphere at a great distance.