# Far field radiation and spherical waves

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.

• I don't know if you ever got your answer, but what is meant by a wavefront is a slice in space such that the radiation field is all at the same phase. Intensity does not matter. A spherical wave implies that if you take a spherical cut in the air centered around the radiation source, the radiation at every point on that sphere is at the same phase. Jul 7, 2020 at 0:26