Far field radiation and spherical waves

Question

I have a basic doubt about electromagnetic waves emitted by a certain source.

Depending on the shape and on the physical properties of the antenna, its electromagnetic waves may have different wavefronts. But it is known that in the so called far field region, the emitted wave is like a spherical wave (since its electric and magnetic will be like \$\frac{e^{-jkr}}{r}\$) which may be locally approximated with a plane wave.

Now my question is: how can this behaviour be true for any antenna? Let's consider for instance the following examples:

1) Dipole antenna:

It is not an isotropic (spherical radiator), as we may easily see from its radiation pattern: if I take a sphere in the space and I move along its lateral surface, I see different powers.

2) Parabolic antenna: it is an high directivity antenna, so it is a lot different from an antenna which generates a spherical wavefront

3) All kinds of antenna with pencil beam pattern

How can we say that the far field wave is spherical for those types of antennas? It seems an absurd to me.

Answer 1

A plane wave means that the vectors of the electrical and the magnetic field as well as the poynting vector will be perpendicular to each other. This will be the case at any point in the far field. At each observation point it looks as if a plane wave (or a spherical wave with a very large radius) would arrive there from a great distance.

However, it does not mean that the intensity of the electromagnetic field will be the same at any point. With the exception of an isotropic antenna, the intensity of the wave will depend on the direction from antenna to the observation point. This is what is expressed by the beam pattern.