I have a question about waves with cylindrical wavefront. Precisely, I have read that they may be generated by a linear source, while for instance plane and spherical waves are respectively generated by an infinite distant source and a point source, respectively. It is easy to see for instance in this picture:
The usual example I find for the generation of cylindrical waves is diffraction across around slit:
But I have not found other specific informations about how to generate cylindrical waves.
My question is: does any linear source of electromagnetic waves generate a cylindrical wave? Or simply, we can generate it through some of all possible linear sources?
For instance, if you consider the electric field generated by a half-wave dipole antenna (which is linear), you see that (reference):
$$E_{\theta}=\frac{-i\zeta _0 I_0 }{2\pi r} \frac{\cos(\frac{\pi}{2}\cos \theta)}{\sin \theta} e^{i(\omega t -kr)} $$
This is the structure of a dipole antenna:
You may see that this source is linear, but it generates a spherical waveform (which is in general generated by a point source) and not a cylindrical waveform (which would have had the square root of the radius at the denominator, as you can see here).