I have a background in physics and I'm trying to get into antenna theory for a personal project. I had some questioning about standing waves, and reading Standing waves in Dipole antennas and the enlighting answers of @Vinzent, I would try to summarize and to point out some yet not-so-clear points:
The antenna is a continuation of the feed line coupled with vacuum by mean of an altered geometry. This alteration bring in impedence and reactances that can be modeled by an RLC circuit. Such circuit are know to resonate and store energy exchanging it between the C and the L component, the role of which in the antenna is played by E and H components of the induction field and by current and voltage standing waves. The resistive losses and radiative losses are restored by the feed-in voltage and current which are in phase and thus actually carry power.
What I still don't understand well is why the waves reflected from antenna tips do not propagate back across feed line. Maybe an impedance missmatch, as seen from antenna towards line, prevents this to happen? If so, such mismatch would not simmetrically affect line signal and reflect it back to source? Also, the statements: Resonance however is not to be confused with standing waves. I would advise you to read up on resonant circuits, I think it can help you understand what happens to the wave inside the antenna (it is roughly equivalent to a parallel RLC circuit) are highly confusing. A standing wave is a physical phenomena that occurs everywhere there is a oscillations susceptible closed system, bounded by some boundary conditions. Resonance is the response of an oscillating system to some forcing term. Eg: A guitar string oscillates by mean of standing waves and can be in resonance with a sound source. Both these aspects are present in an antenna. The equivalence with an RLC circuit can be invoked because of some real analogy, but the antenna is a physical system and thus each statement, Eg. "standing waves do not propagare back to line" must have a physical explanation, which, at the moment, I was not able to find even in literature.
Thanks for any comment.
As pointed out by @user287001 the wave equations must be solved simultaneously around the whole rods to get any idea what happens. this is clear. Also, you are affirming that the standing wave is a consequence of the solution of this equation (precisely the induction field part) not of the reflection by antenna tips. This make sense. However, I would like to note that if the standing wave assumption works good in describing the current, voltage and the field also outside the antenna (e. g. there is a derivation of the radiation lobe for the short dipole based on this) probabily it is because there is really a standing wave in the antenna, so there must be a reason why this oscillation does not propagate back to line, and the only possibility seems to me an impedance mismatch towards the line. This is not asking a miracle, is simply asking physical consistency to a model.