Having spent all day using VHF PMR hand helds in my
alter ego as a fence judge at an equestrian cross-country,
I began to muse as to how the EM field transitions from the
near field around the helicoidal antenna to become the
radiating wave.

This is the point at which you realise that Maxwell's Equations
are only an elementary starting point despite the advanced level
of mathematical education at which you encounter them, and that
multi-parameter 3D numerical evaluations must follow.

The degree to which you'd need to manage mental arithmetic
suggests that there is an easier way to blow your mind,
and that is to smoke dynamite :-)