Even advanced (3rd year degree level) textbooks, such as Ramo, Whinnery and
Van Duzer's
"Fields and Waves in Communications Electronics" (Which was a 3rd-year
textbook me in 1972)
discuss the wavefron as it might appear some distance away from antennae in
the (very) far field.

What, though, is the shape of the emitted wave close-in to antennae? For
example, at opposite
ends of a half-wave dipole, the electric filds are equal and opposite, so
cannot be producing the
same part of the expanding wave.

Might such an analysis reveal the reason why short antennae are poor
radiatiors of RF?